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Statistics By Jim

Making statistics intuitive

One-Tailed and Two-Tailed Hypothesis Tests Explained

By Jim Frost 60 Comments

Choosing whether to perform a one-tailed or a two-tailed hypothesis test is one of the methodology decisions you might need to make for your statistical analysis. This choice can have critical implications for the types of effects it can detect, the statistical power of the test, and potential errors.

In this post, you’ll learn about the differences between one-tailed and two-tailed hypothesis tests and their advantages and disadvantages. I include examples of both types of statistical tests. In my next post, I cover the decision between one and two-tailed tests in more detail.

What Are Tails in a Hypothesis Test?

First, we need to cover some background material to understand the tails in a test. Typically, hypothesis tests take all of the sample data and convert it to a single value, which is known as a test statistic. You’re probably already familiar with some test statistics. For example, t-tests calculate t-values . F-tests, such as ANOVA, generate F-values . The chi-square test of independence and some distribution tests produce chi-square values. All of these values are test statistics. For more information, read my post about Test Statistics .

These test statistics follow a sampling distribution. Probability distribution plots display the probabilities of obtaining test statistic values when the null hypothesis is correct. On a probability distribution plot, the portion of the shaded area under the curve represents the probability that a value will fall within that range.

The graph below displays a sampling distribution for t-values. The two shaded regions cover the two-tails of the distribution.

Keep in mind that this t-distribution assumes that the null hypothesis is correct for the population. Consequently, the peak (most likely value) of the distribution occurs at t=0, which represents the null hypothesis in a t-test. Typically, the null hypothesis states that there is no effect. As t-values move further away from zero, it represents larger effect sizes. When the null hypothesis is true for the population, obtaining samples that exhibit a large apparent effect becomes less likely, which is why the probabilities taper off for t-values further from zero.

Related posts : How t-Tests Work and Understanding Probability Distributions

Critical Regions in a Hypothesis Test

In hypothesis tests, critical regions are ranges of the distributions where the values represent statistically significant results. Analysts define the size and location of the critical regions by specifying both the significance level (alpha) and whether the test is one-tailed or two-tailed.

Consider the following two facts:

• The significance level is the probability of rejecting a null hypothesis that is correct.
• The sampling distribution for a test statistic assumes that the null hypothesis is correct.

Consequently, to represent the critical regions on the distribution for a test statistic, you merely shade the appropriate percentage of the distribution. For the common significance level of 0.05, you shade 5% of the distribution.

Related posts : Significance Levels and P-values and T-Distribution Table of Critical Values

Two-Tailed Hypothesis Tests

Two-tailed hypothesis tests are also known as nondirectional and two-sided tests because you can test for effects in both directions. When you perform a two-tailed test, you split the significance level percentage between both tails of the distribution. In the example below, I use an alpha of 5% and the distribution has two shaded regions of 2.5% (2 * 2.5% = 5%).

When a test statistic falls in either critical region, your sample data are sufficiently incompatible with the null hypothesis that you can reject it for the population.

In a two-tailed test, the generic null and alternative hypotheses are the following:

• Null : The effect equals zero.
• Alternative :  The effect does not equal zero.

The specifics of the hypotheses depend on the type of test you perform because you might be assessing means, proportions, or rates.

Example of a two-tailed 1-sample t-test

Suppose we perform a two-sided 1-sample t-test where we compare the mean strength (4.1) of parts from a supplier to a target value (5). We use a two-tailed test because we care whether the mean is greater than or less than the target value.

To interpret the results, simply compare the p-value to your significance level. If the p-value is less than the significance level, you know that the test statistic fell into one of the critical regions, but which one? Just look at the estimated effect. In the output below, the t-value is negative, so we know that the test statistic fell in the critical region in the left tail of the distribution, indicating the mean is less than the target value. Now we know this difference is statistically significant.

We can conclude that the population mean for part strength is less than the target value. However, the test had the capacity to detect a positive difference as well. You can also assess the confidence interval. With a two-tailed hypothesis test, you’ll obtain a two-sided confidence interval. The confidence interval tells us that the population mean is likely to fall between 3.372 and 4.828. This range excludes the target value (5), which is another indicator of significance.

Advantages of two-tailed hypothesis tests

You can detect both positive and negative effects. Two-tailed tests are standard in scientific research where discovering any type of effect is usually of interest to researchers.

One-Tailed Hypothesis Tests

One-tailed hypothesis tests are also known as directional and one-sided tests because you can test for effects in only one direction. When you perform a one-tailed test, the entire significance level percentage goes into the extreme end of one tail of the distribution.

In the examples below, I use an alpha of 5%. Each distribution has one shaded region of 5%. When you perform a one-tailed test, you must determine whether the critical region is in the left tail or the right tail. The test can detect an effect only in the direction that has the critical region. It has absolutely no capacity to detect an effect in the other direction.

In a one-tailed test, you have two options for the null and alternative hypotheses, which corresponds to where you place the critical region.

You can choose either of the following sets of generic hypotheses:

• Null : The effect is less than or equal to zero.
• Alternative : The effect is greater than zero.

• Null : The effect is greater than or equal to zero.
• Alternative : The effect is less than zero.

Again, the specifics of the hypotheses depend on the type of test you perform.

Notice how for both possible null hypotheses the tests can’t distinguish between zero and an effect in a particular direction. For example, in the example directly above, the null combines “the effect is greater than or equal to zero” into a single category. That test can’t differentiate between zero and greater than zero.

Example of a one-tailed 1-sample t-test

Suppose we perform a one-tailed 1-sample t-test. We’ll use a similar scenario as before where we compare the mean strength of parts from a supplier (102) to a target value (100). Imagine that we are considering a new parts supplier. We will use them only if the mean strength of their parts is greater than our target value. There is no need for us to differentiate between whether their parts are equally strong or less strong than the target value—either way we’d just stick with our current supplier.

Consequently, we’ll choose the alternative hypothesis that states the mean difference is greater than zero (Population mean – Target value > 0). The null hypothesis states that the difference between the population mean and target value is less than or equal to zero.

To interpret the results, compare the p-value to your significance level. If the p-value is less than the significance level, you know that the test statistic fell into the critical region. For this study, the statistically significant result supports the notion that the population mean is greater than the target value of 100.

Confidence intervals for a one-tailed test are similarly one-sided. You’ll obtain either an upper bound or a lower bound. In this case, we get a lower bound, which indicates that the population mean is likely to be greater than or equal to 100.631. There is no upper limit to this range.

A lower-bound matches our goal of determining whether the new parts are stronger than our target value. The fact that the lower bound (100.631) is higher than the target value (100) indicates that these results are statistically significant.

This test is unable to detect a negative difference even when the sample mean represents a very negative effect.

Advantages and disadvantages of one-tailed hypothesis tests

One-tailed tests have more statistical power to detect an effect in one direction than a two-tailed test with the same design and significance level. One-tailed tests occur most frequently for studies where one of the following is true:

• Effects can exist in only one direction.
• Effects can exist in both directions but the researchers only care about an effect in one direction. There is no drawback to failing to detect an effect in the other direction. (Not recommended.)

The disadvantage of one-tailed tests is that they have no statistical power to detect an effect in the other direction.

As part of your pre-study planning process, determine whether you’ll use the one- or two-tailed version of a hypothesis test. To learn more about this planning process, read 5 Steps for Conducting Scientific Studies with Statistical Analyses .

This post explains the differences between one-tailed and two-tailed statistical hypothesis tests. How these forms of hypothesis tests function is clear and based on mathematics. However, there is some debate about when you can use one-tailed tests. My next post explores this decision in much more depth and explains the different schools of thought and my opinion on the matter— When Can I Use One-Tailed Hypothesis Tests .

If you’re learning about hypothesis testing and like the approach I use in my blog, check out my Hypothesis Testing book! You can find it at Amazon and other retailers.

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Reader Interactions

June 26, 2022 at 12:14 pm

Hi, Can help me with figuring out the null and alternative hypothesis of the following statement? Some claimed that the real average expenditure on beverage by general people is at least $10.

February 19, 2022 at 6:02 am

thank you for the thoroughly explanation, I’m still strugling to wrap my mind around the t-table and the relation between the alpha values for one or two tail probability and the confidence levels on the bottom (I’m understanding it so wrongly that for me it should be the oposite, like one tail 0,05 should correspond 95% CI and two tailed 0,025 should correspond to 95% because then you got the 2,5% on each side). In my mind if I picture the one tail diagram with an alpha of 0,05 I see the rest 95% inside the diagram, but for a one tail I only see 90% CI paired with a 5% alpha… where did the other 5% go? I tried to understand when you said we should just double the alpha for a one tail probability in order to find the CI but I still cant picture it. I have been trying to understand this. Like if you only have one tail and there is 0,05, shouldn’t the rest be on the other side? why is it then 90%… I know I’m missing a point and I can’t figure it out and it’s so frustrating…

February 23, 2022 at 10:01 pm

The alpha is the total shaded area. So, if the alpha = 0.05, you know that 5% of the distribution is shaded. The number of tails tells you how to divide the shaded areas. Is it all in one region (1-tailed) or do you split the shaded regions in two (2-tailed)?

So, for a one-tailed test with an alpha of 0.05, the 5% shading is all in one tail. If alpha = 0.10, then it’s 10% on one side. If it’s two-tailed, then you need to split that 10% into two–5% in both tails. Hence, the 5% in a one-tailed test is the same as a two-tailed test with an alpha of 0.10 because that test has the same 5% on one side (but there’s another 5% in the other tail).

It’s similar for CIs. However, for CIs, you shade the middle rather than the extremities. I write about that in one my articles about hypothesis testing and confidence intervals .

I’m not sure if I’m answering your question or not.

February 17, 2022 at 1:46 pm

I ran a post hoc Dunnett’s test alpha=0.05 after a significant Anova test in Proc Mixed using SAS. I want to determine if the means for treatment (t1, t2, t3) is significantly less than the means for control (p=pathogen). The code for the dunnett’s test is – LSmeans trt / diff=controll (‘P’) adjust=dunnett CL plot=control; I think the lower bound one tailed test is the correct test to run but I’m not 100% sure. I’m finding conflicting information online. In the output table for the dunnett’s test the mean difference between the control and the treatments is t1=9.8, t2=64.2, and t3=56.5. The control mean estimate is 90.5. The adjusted p-value by treatment is t1(p=0.5734), t2 (p=.0154) and t3(p=.0245). The adjusted lower bound confidence limit in order from t1-t3 is -38.8, 13.4, and 7.9. The adjusted upper bound for all test is infinity. The graphical output for the dunnett’s test in SAS is difficult to understand for those of us who are beginner SAS users. All treatments appear as a vertical line below the the horizontal line for control at 90.5 with t2 and t3 in the shaded area. For treatment 1 the shaded area is above the line for control. Looking at just the output table I would say that t2 and t3 are significantly lower than the control. I guess I would like to know if my interpretation of the outputs is correct that treatments 2 and 3 are statistically significantly lower than the control? Should I have used an upper bound one tailed test instead?

November 10, 2021 at 1:00 am

Thanks Jim. Please help me understand how a two tailed testing can be used to minimize errors in research

July 1, 2021 at 9:19 am

Hi Jim, Thanks for posting such a thorough and well-written explanation. It was extremely useful to clear up some doubts.

May 7, 2021 at 4:27 pm

Hi Jim, I followed your instructions for the Excel add-in. Thank you. I am very new to statistics and sort of enjoy it as I enter week number two in my class. I am to select if three scenarios call for a one or two-tailed test is required and why. The problem is stated:

30% of mole biopsies are unnecessary. Last month at his clinic, 210 out of 634 had benign biopsy results. Is there enough evidence to reject the dermatologist’s claim?

Part two, the wording changes to “more than of 30% of biopsies,” and part three, the wording changes to “less than 30% of biopsies…”

I am not asking for the problem to be solved for me, but I cannot seem to find direction needed. I know the elements i am dealing with are =30%, greater than 30%, and less than 30%. 210 and 634. I just don’t know what to with the information. I can’t seem to find an example of a similar problem to work with.

May 9, 2021 at 9:22 pm

As I detail in this post, a two-tailed test tells you whether an effect exists in either direction. Or, is it different from the null value in either direction. For the first example, the wording suggests you’d need a two-tailed test to determine whether the population proportion is ≠ 30%. Whenever you just need to know ≠, it suggests a two-tailed test because you’re covering both directions.

For part two, because it’s in one direction (greater than), you need a one-tailed test. Same for part three but it’s less than. Look in this blog post to see how you’d construct the null and alternative hypotheses for these cases. Note that you’re working with a proportion rather than the mean, but the principles are the same! Just plug your scenario and the concept of proportion into the wording I use for the hypotheses.

I hope that helps!

April 11, 2021 at 9:30 am

Hello Jim, great website! I am using a statistics program (SPSS) that does NOT compute one-tailed t-tests. I am trying to compare two independent groups and have justifiable reasons why I only care about one direction. Can I do the following? Use SPSS for two-tailed tests to calculate the t & p values. Then report the p-value as p/2 when it is in the predicted direction (e.g , SPSS says p = .04, so I report p = .02), and report the p-value as 1 – (p/2) when it is in the opposite direction (e.g., SPSS says p = .04, so I report p = .98)? If that is incorrect, what do you suggest (hopefully besides changing statistics programs)? Also, if I want to report confidence intervals, I realize that I would only have an upper or lower bound, but can I use the CI’s from SPSS to compute that? Thank you very much!

April 11, 2021 at 5:42 pm

Yes, for p-values, that’s absolutely correct for both cases.

For confidence intervals, if you take one endpoint of a two-side CI, it becomes a one-side bound with half the confidence level.

Consequently, to obtain a one-sided bound with your desired confidence level, you need to take your desired significance level (e.g., 0.05) and double it. Then subtract it from 1. So, if you’re using a significance level of 0.05, double that to 0.10 and then subtract from 1 (1 – 0.10 = 0.90). 90% is the confidence level you want to use for a two-sided test. After obtaining the two-sided CI, use one of the endpoints depending on the direction of your hypothesis (i.e., upper or lower bound). That’s produces the one-sided the bound with the confidence level that you want. For our example, we calculated a 95% one-sided bound.

March 3, 2021 at 8:27 am

Hi Jim. I used the one-tailed(right) statistical test to determine an anomaly in the below problem statement: On a daily basis, I calculate the (mapped_%) in a common field between two tables.

The way I used the t-test is: On any particular day, I calculate the sample_mean, S.D and sample_count (n=30) for the last 30 days including the current day. My null hypothesis, H0 (pop. mean)=95 and H1>95 (alternate hypothesis). So, I calculate the t-stat based on the sample_mean, pop.mean, sample S.D and n. I then choose the t-crit value for 0.05 from my t-ditribution table for dof(n-1). On the current day if my abs.(t-stat)>t-crit, then I reject the null hypothesis and I say the mapped_pct on that day has passed the t-test.

I get some weird results here, where if my mapped_pct is as low as 6%-8% in all the past 30 days, the t-test still gets a “pass” result. Could you help on this? If my hypothesis needs to be changed.

I would basically look for the mapped_pct >95, if it worked on a static trigger. How can I use the t-test effectively in this problem statement?

December 18, 2020 at 8:23 pm

Hello Dr. Jim, I am wondering if there is evidence in one of your books or other source you could provide, which supports that it is OK not to divide alpha level by 2 in one-tailed hypotheses. I need the source for supporting evidence in a Portfolio exercise and couldn’t find one.

I am grateful for your reply and for your statistics knowledge sharing!

November 27, 2020 at 10:31 pm

If I did a one directional F test ANOVA(one tail ) and wanted to calculate a confidence interval for each individual groups (3) mean . Would I use a one tailed or two tailed t , within my confidence interval .

November 29, 2020 at 2:36 am

Hi Bashiru,

F-tests for ANOVA will always be one-tailed for the reasons I discuss in this post. To learn more about, read my post about F-tests in ANOVA .

For the differences between my groups, I would not use t-tests because the family-wise error rate quickly grows out of hand. To learn more about how to compare group means while controlling the familywise error rate, read my post about using post hoc tests with ANOVA . Typically, these are two-side intervals but you’d be able to use one-sided.

November 26, 2020 at 10:51 am

Hi Jim, I had a question about the formulation of the hypotheses. When you want to test if a beta = 1 or a beta = 0. What will be the null hypotheses? I’m having trouble with finding out. Because in most cases beta = 0 is the null hypotheses but in this case you want to test if beta = 0. so i’m having my doubts can it in this case be the alternative hypotheses or is it still the null hypotheses?

Kind regards, Noa

November 27, 2020 at 1:21 am

Typically, the null hypothesis represents no effect or no relationship. As an analyst, you’re hoping that your data have enough evidence to reject the null and favor the alternative.

Assuming you’re referring to beta as in regression coefficients, zero represents no relationship. Consequently, beta = 0 is the null hypothesis.

You might hope that beta = 1, but you don’t usually include that in your alternative hypotheses. The alternative hypothesis usually states that it does not equal no effect. In other words, there is an effect but it doesn’t state what it is.

There are some exceptions to the above but I’m writing about the standard case.

November 22, 2020 at 8:46 am

Your articles are a help to intro to econometrics students. Keep up the good work! More power to you!

November 6, 2020 at 11:25 pm

Hello Jim. Can you help me with these please?

Write the null and alternative hypothesis using a 1-tailed and 2-tailed test for each problem. (In paragraph and symbols)

A teacher wants to know if there is a significant difference in the performance in MAT C313 between her morning and afternoon classes.

It is known that in our university canteen, the average waiting time for a customer to receive and pay for his/her order is 20 minutes. Additional personnel has been added and now the management wants to know if the average waiting time had been reduced.

November 8, 2020 at 12:29 am

I cover how to write the hypotheses for the different types of tests in this post. So, you just need to figure which type of test you need to use. In your case, you want to determine whether the mean waiting time is less than the target value of 20 minutes. That’s a 1-sample t-test because you’re comparing a mean to a target value (20 minutes). You specifically want to determine whether the mean is less than the target value. So, that’s a one-tailed test. And, you’re looking for a mean that is “less than” the target.

So, go to the one-tailed section in the post and look for the hypotheses for the effect being less than. That’s the one with the critical region on the left side of the curve.

Now, you need include your own information. In your case, you’re comparing the sample estimate to a population mean of 20. The 20 minutes is your null hypothesis value. Use the symbol mu μ to represent the population mean.

You put all that together and you get the following:

Null: μ ≥ 20 Alternative: μ 0 to denote the null hypothesis and H 1 or H A to denote the alternative hypothesis if that’s what you been using in class.

October 17, 2020 at 12:11 pm

I was just wondering if you could please help with clarifying what the hypothesises would be for say income for gamblers and, age of gamblers. I am struggling to find which means would be compared.

October 17, 2020 at 7:05 pm

Those are both continuous variables, so you’d use either correlation or regression for them. For both of those analyses, the hypotheses are the following:

Null : The correlation or regression coefficient equals zero (i.e., there is no relationship between the variables) Alternative : The coefficient does not equal zero (i.e., there is a relationship between the variables.)

When the p-value is less than your significance level, you reject the null and conclude that a relationship exists.

October 17, 2020 at 3:05 am

I was ask to choose and justify the reason between a one tailed and two tailed test for dummy variables, how do I do that and what does it mean?

October 17, 2020 at 7:11 pm

I don’t have enough information to answer your question. A dummy variable is also known as an indicator variable, which is a binary variable that indicates the presence or absence of a condition or characteristic. If you’re using this variable in a hypothesis test, I’d presume that you’re using a proportions test, which is based on the binomial distribution for binary data.

Choosing between a one-tailed or two-tailed test depends on subject area issues and, possibly, your research objectives. Typically, use a two-tailed test unless you have a very good reason to use a one-tailed test. To understand when you might use a one-tailed test, read my post about when to use a one-tailed hypothesis test .

October 16, 2020 at 2:07 pm

In your one-tailed example, Minitab describes the hypotheses as “Test of mu = 100 vs > 100”. Any idea why Minitab says the null is “=” rather than “= or less than”? No ASCII character for it?

October 16, 2020 at 4:20 pm

I’m not entirely sure even though I used to work there! I know we had some discussions about how to represent that hypothesis but I don’t recall the exact reasoning. I suspect that it has to do with the conclusions that you can draw. Let’s focus on the failing to reject the null hypothesis. If the test statistic falls in that region (i.e., it is not significant), you fail to reject the null. In this case, all you know is that you have insufficient evidence to say it is different than 100. I’m pretty sure that’s why they use the equal sign because it might as well be one.

Mathematically, I think using ≤ is more accurate, which you can really see when you look at the distribution plots. That’s why I phrase the hypotheses using ≤ or ≥ as needed. However, in terms of the interpretation, the “less than” portion doesn’t really add anything of importance. You can conclude that its equal to 100 or greater than 100, but not less than 100.

October 15, 2020 at 5:46 am

Thank you so much for your timely feedback. It helps a lot

October 14, 2020 at 10:47 am

How can i use one tailed test at 5% alpha on this problem?

A manufacturer of cellular phone batteries claims that when fully charged, the mean life of his product lasts for 26 hours with a standard deviation of 5 hours. Mr X, a regular distributor, randomly picked and tested 35 of the batteries. His test showed that the average life of his sample is 25.5 hours. Is there a significant difference between the average life of all the manufacturer’s batteries and the average battery life of his sample?

October 14, 2020 at 8:22 pm

I don’t think you’d want to use a one-tailed test. The goal is to determine whether the sample is significantly different than the manufacturer’s population average. You’re not saying significantly greater than or less than, which would be a one-tailed test. As phrased, you want a two-tailed test because it can detect a difference in either direct.

It sounds like you need to use a 1-sample t-test to test the mean. During this test, enter 26 as the test mean. The procedure will tell you if the sample mean of 25.5 hours is a significantly different from that test mean. Similarly, you’d need a one variance test to determine whether the sample standard deviation is significantly different from the test value of 5 hours.

For both of these tests, compare the p-value to your alpha of 0.05. If the p-value is less than this value, your results are statistically significant.

September 22, 2020 at 4:16 am

Hi Jim, I didn’t get an idea that when to use two tail test and one tail test. Will you please explain?

September 22, 2020 at 10:05 pm

I have a complete article dedicated to that: When Can I Use One-Tailed Tests .

Basically, start with the assumption that you’ll use a two-tailed test but then consider scenarios where a one-tailed test can be appropriate. I talk about all of that in the article.

If you have questions after reading that, please don’t hesitate to ask!

July 31, 2020 at 12:33 pm

Thank you so so much for this webpage.

I have two scenarios that I need some clarification. I will really appreciate it if you can take a look:

So I have several of materials that I know when they are tested after production. My hypothesis is that the earlier they are tested after production, the higher the mean value I should expect. At the same time, the later they are tested after production, the lower the mean value. Since this is more like a “greater or lesser” situation, I should use one tail. Is that the correct approach?

On the other hand, I have several mix of materials that I don’t know when they are tested after production. I only know the mean values of the test. And I only want to know whether one mean value is truly higher or lower than the other, I guess I want to know if they are only significantly different. Should I use two tail for this? If they are not significantly different, I can judge based on the mean values of test alone. And if they are significantly different, then I will need to do other type of analysis. Also, when I get my P-value for two tail, should I compare it to 0.025 or 0.05 if my confidence level is 0.05?

Thank you so much again.

July 31, 2020 at 11:19 pm

For your first, if you absolutely know that the mean must be lower the later the material is tested, that it cannot be higher, that would be a situation where you can use a one-tailed test. However, if that’s not a certainty, you’re just guessing, use a two-tail test. If you’re measuring different items at the different times, use the independent 2-sample t-test. However, if you’re measuring the same items at two time points, use the paired t-test. If it’s appropriate, using the paired t-test will give you more statistical power because it accounts for the variability between items. For more information, see my post about when it’s ok to use a one-tailed test .

For the mix of materials, use a two-tailed test because the effect truly can go either direction.

Always compare the p-value to your full significance level regardless of whether it’s a one or two-tailed test. Don’t divide the significance level in half.

June 17, 2020 at 2:56 pm

Is it possible that we reach to opposite conclusions if we use a critical value method and p value method Secondly if we perform one tail test and use p vale method to conclude our Ho, then do we need to convert sig value of 2 tail into sig value of one tail. That can be done just by dividing it with 2

June 18, 2020 at 5:17 pm

The p-value method and critical value method will always agree as long as you’re not changing anything about how the methodology.

If you’re using statistical software, you don’t need to make any adjustments. The software will do that for you.

However, if you calculating it by hand, you’ll need to take your significance level and then look in the table for your test statistic for a one-tailed test. For example, you’ll want to look up 5% for a one-tailed test rather than a two-tailed test. That’s not as simple as dividing by two. In this article, I show examples of one-tailed and two-tailed tests for the same degrees of freedom. The t critical value for the two-tailed test is +/- 2.086 while for the one-sided test it is 1.725. It is true that probability associated with those critical values doubles for the one-tailed test (2.5% -> 5%), but the critical value itself is not half (2.086 -> 1.725). Study the first several graphs in this article to see why that is true.

For the p-value, you can take a two-tailed p-value and divide by 2 to determine the one-sided p-value. However, if you’re using statistical software, it does that for you.

June 11, 2020 at 3:46 pm

Hello Jim, if you have the time I’d be grateful if you could shed some clarity on this scenario:

“A researcher believes that aromatherapy can relieve stress but wants to determine whether it can also enhance focus. To test this, the researcher selected a random sample of students to take an exam in which the average score in the general population is 77. Prior to the exam, these students studied individually in a small library room where a lavender scent was present. If students in this group scored significantly above the average score in general population [is this one-tailed or two-tailed hypothesis?], then this was taken as evidence that the lavender scent enhanced focus.”

Thank you for your time if you do decide to respond.

June 11, 2020 at 4:00 pm

It’s unclear from the information provided whether the researchers used a one-tailed or two-tailed test. It could be either. A two-tailed test can detect effects in both directions, so it could definitely detect an average group score above the population score. However, you could also detect that effect using a one-tailed test if it was set up correctly. So, there’s not enough information in what you provided to know for sure. It could be either.

However, that’s irrelevant to answering the question. The tricky part, as I see it, is that you’re not entirely sure about why the scores are higher. Are they higher because the lavender scent increased concentration or are they higher because the subjects have lower stress from the lavender? Or, maybe it’s not even related to the scent but some other characteristic of the room or testing conditions in which they took the test. You just know the scores are higher but not necessarily why they’re higher.

I’d say that, no, it’s not necessarily evidence that the lavender scent enhanced focus. There are competing explanations for why the scores are higher. Also, it would be best do this as an experiment with a control and treatment group where subjects are randomly assigned to either group. That process helps establish causality rather than just correlation and helps rules out competing explanations for why the scores are higher.

By the way, I spend a lot of time on these issues in my Introduction to Statistics ebook .

June 9, 2020 at 1:47 pm

If a left tail test has an alpha value of 0.05 how will you find the value in the table

April 19, 2020 at 10:35 am

Hi Jim, My question is in regards to the results in the table in your example of the one-sample T (Two-Tailed) test. above. What about the P-value? The P-value listed is .018. I assuming that is compared to and alpha of 0.025, correct?

In regression analysis, when I get a test statistic for the predictive variable of -2.099 and a p-value of 0.039. Am I comparing the p-value to an alpha of 0.025 or 0.05? Now if I run a Bootstrap for coefficients analysis, the results say the sig (2-tail) is 0.098. What are the critical values and alpha in this case? I’m trying to reconcile what I am seeing in both tables.

Thanks for your help.

April 20, 2020 at 3:24 am

Hi Marvalisa,

For one-tailed tests, you don’t need to divide alpha in half. If you can tell your software to perform a one-tailed test, it’ll do all the calculations necessary so you don’t need to adjust anything. So, if you’re using an alpha of 0.05 for a one-tailed test and your p-value is 0.04, it is significant. The procedures adjust the p-values automatically and it all works out. So, whether you’re using a one-tailed or two-tailed test, you always compare the p-value to the alpha with no need to adjust anything. The procedure does that for you!

The exception would be if for some reason your software doesn’t allow you to specify that you want to use a one-tailed test instead of a two-tailed test. Then, you divide the p-value from a two-tailed test in half to get the p-value for a one tailed test. You’d still compare it to your original alpha.

For regression, the same thing applies. If you want to use a one-tailed test for a cofficient, just divide the p-value in half if you can’t tell the software that you want a one-tailed test. The default is two-tailed. If your software has the option for one-tailed tests for any procedure, including regression, it’ll adjust the p-value for you. So, in the normal course of things, you won’t need to adjust anything.

March 26, 2020 at 12:00 pm

Hey Jim, for a one-tailed hypothesis test with a .05 confidence level, should I use a 95% confidence interval or a 90% confidence interval? Thanks

March 26, 2020 at 5:05 pm

You should use a one-sided 95% confidence interval. One-sided CIs have either an upper OR lower bound but remains unbounded on the other side.

March 16, 2020 at 4:30 pm

This is not applicable to the subject but… When performing tests of equivalence, we look at the confidence interval of the difference between two groups, and we perform two one-sided t-tests for equivalence..

March 15, 2020 at 7:51 am

Thanks for this illustrative blogpost. I had a question on one of your points though.

By definition of H1 and H0, a two-sided alternate hypothesis is that there is a difference in means between the test and control. Not that anything is ‘better’ or ‘worse’.

Just because we observed a negative result in your example, does not mean we can conclude it’s necessarily worse, but instead just ‘different’.

Therefore while it enables us to spot the fact that there may be differences between test and control, we cannot make claims about directional effects. So I struggle to see why they actually need to be used instead of one-sided tests.

What’s your take on this?

March 16, 2020 at 3:02 am

Hi Dominic,

If you’ll notice, I carefully avoid stating better or worse because in a general sense you’re right. However, given the context of a specific experiment, you can conclude whether a negative value is better or worse. As always in statistics, you have to use your subject-area knowledge to help interpret the results. In some cases, a negative value is a bad result. In other cases, it’s not. Use your subject-area knowledge!

I’m not sure why you think that you can’t make claims about directional effects? Of course you can!

As for why you shouldn’t use one-tailed tests for most cases, read my post When Can I Use One-Tailed Tests . That should answer your questions.

May 10, 2019 at 12:36 pm

Your website is absolutely amazing Jim, you seem like the nicest guy for doing this and I like how there’s no ulterior motive, (I wasn’t automatically signed up for emails or anything when leaving this comment). I study economics and found econometrics really difficult at first, but your website explains it so clearly its been a big asset to my studies, keep up the good work!

May 10, 2019 at 2:12 pm

Thank you so much, Jack. Your kind words mean a lot!

April 26, 2019 at 5:05 am

Hy Jim I really need your help now pls

One-tailed and two- tailed hypothesis, is it the same or twice, half or unrelated pls

April 26, 2019 at 11:41 am

Hi Anthony,

I describe how the hypotheses are different in this post. You’ll find your answers.

February 8, 2019 at 8:00 am

Thank you for your blog Jim, I have a Statistics exam soon and your articles let me understand a lot!

February 8, 2019 at 10:52 am

You’re very welcome! I’m happy to hear that it’s been helpful. Best of luck on your exam!

January 12, 2019 at 7:06 am

Hi Jim, When you say target value is 5. Do you mean to say the population mean is 5 and we are trying to validate it with the help of sample mean 4.1 using Hypo tests ?.. If it is so.. How can we measure a population parameter as 5 when it is almost impossible o measure a population parameter. Please clarify

January 12, 2019 at 6:57 pm

When you set a target for a one-sample test, it’s based on a value that is important to you. It’s not a population parameter or anything like that. The example in this post uses a case where we need parts that are stronger on average than a value of 5. We derive the value of 5 by using our subject area knowledge about what is required for a situation. Given our product knowledge for the hypothetical example, we know it should be 5 or higher. So, we use that in the hypothesis test and determine whether the population mean is greater than that target value.

When you perform a one-sample test, a target value is optional. If you don’t supply a target value, you simply obtain a confidence interval for the range of values that the parameter is likely to fall within. But, sometimes there is meaningful number that you want to test for specifically.

I hope that clarifies the rational behind the target value!

November 15, 2018 at 8:08 am

I understand that in Psychology a one tailed hypothesis is preferred. Is that so

November 15, 2018 at 11:30 am

No, there’s no overall preference for one-tailed hypothesis tests in statistics. That would be a study-by-study decision based on the types of possible effects. For more information about this decision, read my post: When Can I Use One-Tailed Tests?

November 6, 2018 at 1:14 am

I’m grateful to you for the explanations on One tail and Two tail hypothesis test. This opens my knowledge horizon beyond what an average statistics textbook can offer. Please include more examples in future posts. Thanks

November 5, 2018 at 10:20 am

Thank you. I will search it as well.

Stan Alekman

November 4, 2018 at 8:48 pm

Jim, what is the difference between the central and non-central t-distributions w/respect to hypothesis testing?

November 5, 2018 at 10:12 am

Hi Stan, this is something I will need to look into. I know central t-distribution is the common Student t-distribution, but I don’t have experience using non-central t-distributions. There might well be a blog post in that–after I learn more!

November 4, 2018 at 7:42 pm

this is awesome.

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5.2 - writing hypotheses.

The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_a\)).

When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

• At this point we can write hypotheses for a single mean (\(\mu\)), paired means(\(\mu_d\)), a single proportion (\(p\)), the difference between two independent means (\(\mu_1-\mu_2\)), the difference between two proportions (\(p_1-p_2\)), a simple linear regression slope (\(\beta\)), and a correlation (\(\rho\)). 
• The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
• The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., \(\mu_0\) and \(p_0\)). For the difference between two groups, regression, and correlation, this value is typically 0.

Hypotheses are always written in terms of population parameters (e.g., \(p\) and \(\mu\)).  The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).

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What Is a Two-Tailed Test?

Understanding a two-tailed test, special considerations, two-tailed vs. one-tailed test.

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What Is a Two-Tailed Test? Definition and Example

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A two-tailed test, in statistics, is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. It is used in null-hypothesis testing and testing for statistical significance . If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.

Key Takeaways

• In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values.
• It is used in null-hypothesis testing and testing for statistical significance.
• If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.
• By convention two-tailed tests are used to determine significance at the 5% level, meaning each side of the distribution is cut at 2.5%.

A basic concept of inferential statistics is hypothesis testing , which determines whether a claim is true or not given a population parameter. A hypothesis test that is designed to show whether the mean of a sample is significantly greater than and significantly less than the mean of a population is referred to as a two-tailed test. The two-tailed test gets its name from testing the area under both tails of a normal distribution , although the test can be used in other non-normal distributions.

A two-tailed test is designed to examine both sides of a specified data range as designated by the probability distribution involved. The probability distribution should represent the likelihood of a specified outcome based on predetermined standards. This requires the setting of a limit designating the highest (or upper) and lowest (or lower) accepted variable values included within the range. Any data point that exists above the upper limit or below the lower limit is considered out of the acceptance range and in an area referred to as the rejection range.

There is no inherent standard about the number of data points that must exist within the acceptance range. In instances where precision is required, such as in the creation of pharmaceutical drugs, a rejection rate of 0.001% or less may be instituted. In instances where precision is less critical, such as the number of food items in a product bag, a rejection rate of 5% may be appropriate.

A two-tailed test can also be used practically during certain production activities in a firm, such as with the production and packaging of candy at a particular facility. If the production facility designates 50 candies per bag as its goal, with an acceptable distribution of 45 to 55 candies, any bag found with an amount below 45 or above 55 is considered within the rejection range.

To confirm the packaging mechanisms are properly calibrated to meet the expected output, random sampling may be taken to confirm accuracy. A simple random sample takes a small, random portion of the entire population to represent the entire data set, where each member has an equal probability of being chosen.

For the packaging mechanisms to be considered accurate, an average of 50 candies per bag with an appropriate distribution is desired. Additionally, the number of bags that fall within the rejection range needs to fall within the probability distribution limit considered acceptable as an error rate. Here, the null hypothesis would be that the mean is 50 while the alternate hypothesis would be that it is not 50.

If, after conducting the two-tailed test, the z-score falls in the rejection region, meaning that the deviation is too far from the desired mean, then adjustments to the facility or associated equipment may be required to correct the error. Regular use of two-tailed testing methods can help ensure production stays within limits over the long term.

Be careful to note if a statistical test is one- or two-tailed as this will greatly influence a model's interpretation.

When a hypothesis test is set up to show that the sample mean would be only higher than the population mean, this is referred to as a  one-tailed test . A formulation of this hypothesis would be, for example, that "the returns on an investment fund would be  at least  x%." One-tailed tests could also be set up to show that the sample mean could be only less than the population mean. The key difference from a two-tailed test is that in a two-tailed test, the sample mean could be different from the population mean by being  either  higher or lower than it.

If the sample being tested falls into the one-sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis. A one-tailed test is also known as a directional hypothesis or directional test.

A two-tailed test, on the other hand, is designed to examine both sides of a specified data range to test whether a sample is greater than or less than the range of values.

Example of a Two-Tailed Test

As a hypothetical example, imagine that a new  stockbroker , named XYZ, claims that their brokerage fees are lower than that of your current stockbroker, ABC) Data available from an independent research firm indicates that the mean and standard deviation of all ABC broker clients are $18 and $6, respectively.

A sample of 100 clients of ABC is taken, and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and the sample standard deviation is $6, can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?

• H 0 : Null Hypothesis: mean = 18
• H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)
• Rejection region: Z <= - Z 2.5  and Z>=Z 2.5  (assuming 5% significance level, split 2.5 each on either side).
• Z = (sample mean – mean) / (std-dev / sqrt (no. of samples)) = (18.75 – 18) / (6/(sqrt(100)) = 1.25

This calculated Z value falls between the two limits defined by: - Z 2.5  = -1.96 and Z 2.5  = 1.96.

This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker. Therefore, the null hypothesis cannot be rejected. Alternatively, the p-value = P(Z< -1.25)+P(Z >1.25) = 2 * 0.1056 = 0.2112 = 21.12%, which is greater than 0.05 or 5%, leads to the same conclusion.

How Is a Two-Tailed Test Designed?

A two-tailed test is designed to determine whether a claim is true or not given a population parameter. It examines both sides of a specified data range as designated by the probability distribution involved. As such, the probability distribution should represent the likelihood of a specified outcome based on predetermined standards.

What Is the Difference Between a Two-Tailed and One-Tailed Test?

A two-tailed hypothesis test is designed to show whether the sample mean is significantly greater than  or  significantly less than the mean of a population. The two-tailed test gets its name from testing the area under both tails (sides) of a normal distribution. A one-tailed hypothesis test, on the other hand, is set up to show only one test; that the sample mean would be higher than the population mean, or, in a separate test, that the sample mean would be lower than the population mean.

What Is a Z-score?

A Z-score numerically describes a value's relationship to the mean of a group of values and is measured in terms of the number of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score whereas Z-scores of 1.0 and -1.0 would indicate values one standard deviation above or below the mean. In most large data sets, 99% of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above and below the mean.

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Research Hypothesis In Psychology: Types, & Examples

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A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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Two Tailed Hypothesis

Ai generator.

In the vast realm of scientific inquiry, the two-tailed hypothesis holds a special place, serving as a compass for researchers exploring possibilities in two opposing directions. Instead of predicting a specific direction of the relationship between variables, it remains open to outcomes on both ends of the spectrum. Understanding how to craft such a hypothesis, enriched with insights and nuances, can elevate the robustness of one’s research. Delve into its world, discover thesis statement examples, learn the art of its formulation, and grasp tips to master its intricacies.

What is Two Tailed Hypothesis? – Definition

A two-tailed hypothesis, also known as a non-directional hypothesis , is a type of hypothesis used in statistical testing that predicts a relationship between variables without specifying the direction of the relationship. In other words, it tests for the possibility of the relationship in both directions. This approach is used when a researcher believes there might be a difference due to the experiment but doesn’t have enough preliminary evidence or basis to predict a specific direction of that difference.

What is an example of a Two Tailed hypothesis statement?

Let’s consider a study on the impact of a new teaching method on student performance:

Hypothesis Statement : The new teaching method will have an effect on student performance.

Notice that the hypothesis doesn’t specify whether the effect will be positive or negative (i.e., whether student performance will improve or decline). It’s open to both possibilities, making it a two-tailed hypothesis.

Two Tailed Hypothesis Statement Examples

The two-tailed hypothesis, an essential tool in research, doesn’t predict a specific directional outcome between variables. Instead, it posits that an effect exists, without specifying its nature. This approach offers flexibility, as it remains open to both positive and negative outcomes. Below are various examples from diverse fields to shed light on this versatile research method. You may also be interested to browse through our other  one-tailed hypothesis .

• Sleep and Cognitive Ability : Sleep duration affects cognitive performance in adults.
• Dietary Fiber and Digestion : Consumption of dietary fiber influences digestion rates.
• Exercise and Stress Levels : Engaging in physical activity impacts stress levels.
• Vitamin C and Immunity : Intake of Vitamin C has an effect on immunity strength.
• Noise Levels and Concentration : Ambient noise levels influence individual concentration ability.
• Artificial Sweeteners and Appetite : Consumption of artificial sweeteners affects appetite.
• UV Light and Skin Health : Exposure to UV light influences skin health.
• Coffee Intake and Sleep Quality : Consuming coffee has an effect on sleep quality.
• Air Pollution and Respiratory Issues : Levels of air pollution impact respiratory health.
• Meditation and Blood Pressure : Practicing meditation affects blood pressure readings.
• Pet Ownership and Loneliness : Having a pet influences feelings of loneliness.
• Green Spaces and Mental Wellbeing : Exposure to green spaces impacts mental health.
• Music Tempo and Heart Rate : Listening to music of varying tempos affects heart rate.
• Chocolate Consumption and Mood : Eating chocolate has an effect on mood.
• Social Media Usage and Self-Esteem : The frequency of social media usage influences self-esteem.
• E-reading and Eye Strain : Using e-readers affects eye strain levels.
• Vegan Diets and Energy Levels : Following a vegan diet influences daily energy levels.
• Carbonated Drinks and Tooth Decay : Consumption of carbonated drinks has an effect on tooth decay rates.
• Distance Learning and Student Engagement : Engaging in distance learning impacts student involvement.
• Organic Foods and Health Perceptions : Consuming organic foods influences perceptions of health.
• Urban Living and Stress Levels : Living in urban environments affects stress levels.
• Plant-Based Diets and Cholesterol : Adopting a plant-based diet impacts cholesterol levels.
• Virtual Reality Training and Skill Acquisition : Using virtual reality for training influences the rate of skill acquisition.
• Video Game Play and Hand-Eye Coordination : Playing video games has an effect on hand-eye coordination.
• Aromatherapy and Sleep Quality : Using aromatherapy impacts the quality of sleep.
• Bilingualism and Cognitive Flexibility : Being bilingual affects cognitive flexibility.
• Microplastics and Marine Health : The presence of microplastics in oceans influences marine organism health.
• Yoga Practice and Joint Health : Engaging in yoga has an effect on joint health.
• Processed Foods and Metabolism : Consuming processed foods impacts metabolic rates.
• Home Schooling and Social Skills : Being homeschooled influences the development of social skills.
• Smartphone Usage and Attention Span : Regular smartphone use affects attention spans.
• E-commerce and Consumer Trust : Engaging with e-commerce platforms influences levels of consumer trust.
• Work-from-Home and Productivity : The practice of working from home has an effect on productivity levels.
• Classical Music and Plant Growth : Exposing plants to classical music impacts their growth rate.
• Public Transport and Community Engagement : Using public transport influences community engagement levels.
• Digital Note-taking and Memory Retention : Taking notes digitally affects memory retention.
• Acoustic Music and Relaxation : Listening to acoustic music impacts feelings of relaxation.
• GMO Foods and Public Perception : Consuming GMO foods influences public perception of food safety.
• LED Lights and Eye Comfort : Using LED lights affects visual comfort.
• Fast Fashion and Consumer Satisfaction : Engaging with fast fashion brands influences consumer satisfaction levels.
• Diverse Teams and Innovation : Working in diverse teams impacts the level of innovation.
• Local Produce and Nutritional Value : Consuming local produce affects its nutritional value.
• Podcasts and Language Acquisition : Listening to podcasts influences the speed of language acquisition.
• Augmented Reality and Learning Efficiency : Using augmented reality in education has an effect on learning efficiency.
• Museums and Historical Interest : Visiting museums impacts interest in history.
• E-books vs. Physical Books and Reading Retention : The type of book, whether e-book or physical, affects memory retention from reading.
• Biophilic Design and Worker Well-being : Implementing biophilic designs in office spaces influences worker well-being.
• Recycled Products and Consumer Preference : Using recycled materials in products impacts consumer preferences.
• Interactive Learning and Critical Thinking : Engaging in interactive learning environments affects the development of critical thinking skills.
• High-Intensity Training and Muscle Growth : Participating in high-intensity training has an effect on muscle growth rate.
• Pet Therapy and Anxiety Levels : Engaging with therapy animals influences anxiety levels.
• 3D Printing and Manufacturing Efficiency : Implementing 3D printing in manufacturing affects production efficiency.
• Electric Cars and Public Adoption Rates : Introducing more electric cars impacts the rate of public adoption.
• Ancient Architectural Study and Modern Design Inspiration : Studying ancient architecture influences modern design inspirations.
• Natural Lighting and Productivity : The amount of natural lighting in a workspace affects worker productivity.
• Streaming Platforms and Traditional TV Viewing : The rise of streaming platforms has an effect on traditional TV viewing habits.
• Handwritten Notes and Conceptual Understanding : Taking notes by hand influences the depth of conceptual understanding.
• Urban Farming and Community Engagement : Implementing urban farming practices impacts levels of community engagement.
• Influencer Marketing and Brand Loyalty : Collaborating with influencers affects brand loyalty among consumers.
• Online Workshops and Skill Enhancement : Participating in online workshops influences skill enhancement.
• Virtual Reality and Empathy Development : Using virtual reality experiences influences the development of empathy.
• Gardening and Mental Well-being : Engaging in gardening activities affects overall mental well-being.
• Drones and Wildlife Observation : The use of drones impacts the accuracy of wildlife observations.
• Artificial Intelligence and Job Markets : The introduction of artificial intelligence in industries has an effect on job availability.
• Online Reviews and Purchase Decisions : Reading online reviews influences purchase decisions for consumers.
• Blockchain Technology and Financial Security : Implementing blockchain technology affects financial transaction security.
• Minimalism and Life Satisfaction : Adopting a minimalist lifestyle influences levels of life satisfaction.
• Microlearning and Long-term Retention : Engaging in microlearning practices impacts long-term information retention.
• Virtual Teams and Communication Efficiency : Operating in virtual teams has an effect on the efficiency of communication.
• Plant Music and Growth Rates : Exposing plants to specific music frequencies influences their growth rates.
• Green Building Practices and Energy Consumption : Implementing green building designs affects overall energy consumption.
• Fermented Foods and Gut Health : Consuming fermented foods impacts gut health.
• Digital Art Platforms and Creative Expression : Using digital art platforms influences levels of creative expression.
• Aquatic Therapy and Physical Rehabilitation : Engaging in aquatic therapy has an effect on the rate of physical rehabilitation.
• Solar Energy and Utility Bills : Adopting solar energy solutions influences monthly utility bills.
• Immersive Theatre and Audience Engagement : Experiencing immersive theatre performances affects audience engagement levels.
• Podcast Popularity and Radio Listening Habits : The rise in podcast popularity impacts traditional radio listening habits.
• Vertical Farming and Crop Yield : Implementing vertical farming techniques has an effect on crop yields.
• DIY Culture and Craftsmanship Appreciation : The rise of DIY culture influences public appreciation for craftsmanship.
• Crowdsourcing and Solution Innovation : Utilizing crowdsourcing methods affects the innovativeness of solutions derived.
• Urban Beekeeping and Local Biodiversity : Introducing urban beekeeping practices impacts local biodiversity levels.
• Digital Nomad Lifestyle and Work-Life Balance : Adopting a digital nomad lifestyle affects perceptions of work-life balance.
• Virtual Tours and Tourism Interest : Offering virtual tours of destinations influences interest in real-life visits.
• Neurofeedback Training and Cognitive Abilities : Engaging in neurofeedback training has an effect on various cognitive abilities.
• Sensory Gardens and Stress Reduction : Visiting sensory gardens impacts levels of stress reduction.
• Subscription Box Services and Consumer Spending : The popularity of subscription box services influences overall consumer spending patterns.
• Makerspaces and Community Collaboration : Introducing makerspaces in communities affects collaboration levels among members.
• Remote Work and Company Loyalty : Adopting long-term remote work policies impacts employee loyalty towards the company.
• Upcycling and Environmental Awareness : Engaging in upcycling activities influences levels of environmental awareness.
• Mixed Reality in Education and Engagement : Implementing mixed reality tools in education affects student engagement.
• Microtransactions in Gaming and Player Commitment : The presence of microtransactions in video games impacts player commitment and longevity.
• Floating Architecture and Sustainable Living : Adopting floating architectural solutions influences perceptions of sustainable living.
• Edible Packaging and Waste Reduction : Introducing edible packaging in markets has an effect on overall waste reduction.
• Space Tourism and Interest in Astronomy : The advent of space tourism influences the general public’s interest in astronomy.
• Urban Green Roofs and Air Quality : Implementing green roofs in urban settings impacts the local air quality.
• Smart Mirrors and Fitness Consistency : Using smart mirrors for workouts affects consistency in fitness routines.
• Open Source Software and Technological Innovation : Promoting open-source software has an effect on the rate of technological innovation.
• Microgreens and Nutrient Intake : Consuming microgreens influences nutrient intake.
• Aquaponics and Sustainable Farming : Implementing aquaponic systems impacts perceptions of sustainable farming.
• Esports Popularity and Physical Sport Engagement : The rise of esports affects engagement in traditional physical sports.

Two Tailed Hypothesis Statement Examples in Research

In academic research, a two-tailed hypothesis is versatile, not pointing to a specific direction of effect but remaining open to outcomes on both ends of the spectrum. Such hypothesis aim to determine if a particular variable affects another, without specifying how. Here are examples tailored to research scenarios.

• Interdisciplinary Collaboration and Innovation : Engaging in interdisciplinary collaborations impacts the degree of innovation in research findings.
• Open Access Journals and Citation Rates : Publishing in open-access journals influences the citation rates of the papers.
• Research Grants and Publication Quality : Receiving larger research grants affects the quality of resulting publications.
• Laboratory Environment and Data Accuracy : The physical conditions of a research laboratory impact the accuracy of experimental data.
• Peer Review Process and Research Integrity : The stringency of the peer review process influences the overall integrity of published research.
• Researcher Mobility and Knowledge Transfer : The mobility of researchers between institutions affects the rate of knowledge transfer.
• Interdisciplinary Conferences and Networking Opportunities : Attending interdisciplinary conferences impacts the depth and breadth of networking opportunities.
• Qualitative Methods and Research Depth : Incorporating qualitative methods in research affects the depth of findings.
• Data Visualization Tools and Research Comprehension : Utilizing advanced data visualization tools influences the comprehension of complex research data.
• Collaborative Tools and Research Efficiency : The adoption of modern collaborative tools impacts research efficiency and productivity.

Two Tailed Testing Hypothesis Statement Examples

In hypothesis testing , a two-tailed test examines the possibility of a relationship in both directions. Unlike one-tailed tests, it doesn’t anticipate a specific direction of the relationship. The following are examples that encapsulate this approach within varied testing scenarios.

• Load Testing and Website Speed : Conducting load testing on a website influences its loading speed.
• A/B Testing and Conversion Rates : Implementing A/B testing affects the conversion rates of a webpage.
• Drug Efficacy Testing and Patient Recovery : Testing a new drug’s efficacy impacts patient recovery rates.
• Usability Testing and User Engagement : Conducting usability testing on an app influences user engagement metrics.
• Genetic Testing and Disease Prediction : Utilizing genetic testing affects the accuracy of disease prediction.
• Water Quality Testing and Contaminant Levels : Performing water quality tests influences our understanding of contaminant levels.
• Battery Life Testing and Device Longevity : Conducting battery life tests impacts claims about device longevity.
• Product Safety Testing and Recall Rates : Implementing rigorous product safety tests affects the rate of product recalls.
• Emissions Testing and Pollution Control : Undertaking emissions testing on vehicles influences pollution control measures.
• Material Strength Testing and Product Durability : Testing the strength of materials affects predictions about product durability.

How do you know if a hypothesis is two-tailed?

To determine if a hypothesis is two-tailed, you must look at the nature of the prediction. A two-tailed hypothesis is neutral concerning the direction of the predicted relationship or difference between groups. It simply predicts a difference or relationship without specifying whether it will be positive, negative, greater, or lesser. The hypothesis tests for effects in both directions.

What is one-tailed and two-tailed Hypothesis test with example?

In hypothesis testing, the choice between a one-tailed and a two-tailed test is determined by the nature of the research question.

One-tailed hypothesis: This tests for a specific direction of the effect. It predicts the direction of the relationship or difference between groups. For example, a one-tailed hypothesis might state: “The new drug will reduce symptoms more effectively than the standard treatment.”

Two-tailed hypothesis: This doesn’t specify the direction. It predicts that there will be a difference, but it doesn’t forecast whether the difference will be positive or negative. For example, a two-tailed hypothesis might state: “The new drug will have a different effect on symptoms compared to the standard treatment.”

What is a two-tailed hypothesis in psychology?

In psychology, a two-tailed hypothesis is frequently used when researchers are exploring new areas or relationships without a strong prior basis to predict the direction of findings. For instance, a psychologist might use a two-tailed hypothesis to explore whether a new therapeutic method has different outcomes than a traditional method, without predicting whether the outcomes will be better or worse.

What does a two-tailed alternative hypothesis look like?

A two-tailed alternative hypothesis is generally framed to show that a parameter is simply different from a certain value, without specifying the direction of the difference. Using mathematical notation, for a population mean (μ) and a proposed value (k), the two-tailed hypothesis would look like: H1: μ ≠ k.

How do you write a Two-Tailed hypothesis statement? – A Step by Step Guide

• Identify the Variables: Start by identifying the independent and dependent variables you want to study.
• Formulate a Relationship: Consider the potential relationship between these variables without setting a direction.
• Avoid Directional Language: Words like “increase”, “decrease”, “more than”, or “less than” should be avoided as they point to a one-tailed hypothesis.
• Keep it Simple: The statement should be clear, concise, and to the point.
• Use Neutral Language: For instance, words like “affects”, “influences”, or “has an impact on” can be used to indicate a relationship without specifying a direction.
• Finalize the Statement: Once the relationship is clear in your mind, form a coherent sentence that describes the relationship between your variables.

Tips for Writing Two Tailed Hypothesis

• Start Broad: Given that you’re not seeking a specific direction, it’s okay to start with a broad idea.
• Be Objective: Avoid letting any biases or expectations shape your hypothesis.
• Stay Informed: Familiarize yourself with existing research on the topic to ensure your hypothesis is novel and not inadvertently directional.
• Seek Feedback: Share your hypothesis with colleagues or mentors to ensure it’s indeed non-directional.
• Revisit and Refine: As with any research process, be open to revisiting and refining your hypothesis as you delve deeper into the literature or collect preliminary data.

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• Instructive
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10 Examples of Public speaking

20 Examples of Gas lighting

Hypothesis Testing for Means & Proportions

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Hypothesis Testing: Upper-, Lower, and Two Tailed Tests

Type i and type ii errors.

All Modules

Z score Table

t score Table

The procedure for hypothesis testing is based on the ideas described above. Specifically, we set up competing hypotheses, select a random sample from the population of interest and compute summary statistics. We then determine whether the sample data supports the null or alternative hypotheses. The procedure can be broken down into the following five steps.  

• Step 1. Set up hypotheses and select the level of significance α.

H 0 : Null hypothesis (no change, no difference);  

H 1 : Research hypothesis (investigator's belief); α =0.05

• Step 2. Select the appropriate test statistic.  

The test statistic is a single number that summarizes the sample information.   An example of a test statistic is the Z statistic computed as follows:

When the sample size is small, we will use t statistics (just as we did when constructing confidence intervals for small samples). As we present each scenario, alternative test statistics are provided along with conditions for their appropriate use.

• Step 3.  Set up decision rule.  

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H 0 if Z > 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

• The decision rule depends on whether an upper-tailed, lower-tailed, or two-tailed test is proposed. In an upper-tailed test the decision rule has investigators reject H 0 if the test statistic is larger than the critical value. In a lower-tailed test the decision rule has investigators reject H 0 if the test statistic is smaller than the critical value.  In a two-tailed test the decision rule has investigators reject H 0 if the test statistic is extreme, either larger than an upper critical value or smaller than a lower critical value.
• The exact form of the test statistic is also important in determining the decision rule. If the test statistic follows the standard normal distribution (Z), then the decision rule will be based on the standard normal distribution. If the test statistic follows the t distribution, then the decision rule will be based on the t distribution. The appropriate critical value will be selected from the t distribution again depending on the specific alternative hypothesis and the level of significance.  
• The third factor is the level of significance. The level of significance which is selected in Step 1 (e.g., α =0.05) dictates the critical value.   For example, in an upper tailed Z test, if α =0.05 then the critical value is Z=1.645.  

The following figures illustrate the rejection regions defined by the decision rule for upper-, lower- and two-tailed Z tests with α=0.05. Notice that the rejection regions are in the upper, lower and both tails of the curves, respectively. The decision rules are written below each figure.

Rejection Region for Upper-Tailed Z Test (H : μ > μ ) with α=0.05 The decision rule is: Reject H if Z 1.645.

α Z 0.10 1.282 0.05 1.645 0.025 1.960 0.010 2.326 0.005 2.576 0.001 3.090 0.0001 3.719 Rejection Region for Lower-Tailed Z Test (H 1 : μ < μ 0 ) with α =0.05 The decision rule is: Reject H 0 if Z < 1.645. a Z 0.10 -1.282 0.05 -1.645 0.025 -1.960 0.010 -2.326 0.005 -2.576 0.001 -3.090 0.0001 -3.719 Rejection Region for Two-Tailed Z Test (H 1 : μ ≠ μ 0 ) with α =0.05 The decision rule is: Reject H 0 if Z < -1.960 or if Z > 1.960. 0.20 1.282 0.10 1.645 0.05 1.960 0.010 2.576 0.001 3.291 0.0001 3.819 The complete table of critical values of Z for upper, lower and two-tailed tests can be found in the table of Z values to the right in "Other Resources." Critical values of t for upper, lower and two-tailed tests can be found in the table of t values in "Other Resources." Step 4. Compute the test statistic.   Here we compute the test statistic by substituting the observed sample data into the test statistic identified in Step 2. Step 5. Conclusion.   The final conclusion is made by comparing the test statistic (which is a summary of the information observed in the sample) to the decision rule. The final conclusion will be either to reject the null hypothesis (because the sample data are very unlikely if the null hypothesis is true) or not to reject the null hypothesis (because the sample data are not very unlikely).   If the null hypothesis is rejected, then an exact significance level is computed to describe the likelihood of observing the sample data assuming that the null hypothesis is true. The exact level of significance is called the p-value and it will be less than the chosen level of significance if we reject H 0 . Statistical computing packages provide exact p-values as part of their standard output for hypothesis tests. In fact, when using a statistical computing package, the steps outlined about can be abbreviated. The hypotheses (step 1) should always be set up in advance of any analysis and the significance criterion should also be determined (e.g., α =0.05). Statistical computing packages will produce the test statistic (usually reporting the test statistic as t) and a p-value. The investigator can then determine statistical significance using the following: If p < α then reject H 0 .   Step 1. Set up hypotheses and determine level of significance H 0 : μ = 191 H 1 : μ > 191                 α =0.05 The research hypothesis is that weights have increased, and therefore an upper tailed test is used. Step 2. Select the appropriate test statistic. Because the sample size is large (n > 30) the appropriate test statistic is Step 3. Set up decision rule.   In this example, we are performing an upper tailed test (H 1 : μ> 191), with a Z test statistic and selected α =0.05.   Reject H 0 if Z > 1.645. We now substitute the sample data into the formula for the test statistic identified in Step 2.   We reject H 0 because 2.38 > 1.645. We have statistically significant evidence at a =0.05, to show that the mean weight in men in 2006 is more than 191 pounds. Because we rejected the null hypothesis, we now approximate the p-value which is the likelihood of observing the sample data if the null hypothesis is true. An alternative definition of the p-value is the smallest level of significance where we can still reject H 0 . In this example, we observed Z=2.38 and for α=0.05, the critical value was 1.645. Because 2.38 exceeded 1.645 we rejected H 0 . In our conclusion we reported a statistically significant increase in mean weight at a 5% level of significance. Using the table of critical values for upper tailed tests, we can approximate the p-value. If we select α=0.025, the critical value is 1.96, and we still reject H 0 because 2.38 > 1.960. If we select α=0.010 the critical value is 2.326, and we still reject H 0 because 2.38 > 2.326. However, if we select α=0.005, the critical value is 2.576, and we cannot reject H 0 because 2.38 < 2.576. Therefore, the smallest α where we still reject H 0 is 0.010. This is the p-value. A statistical computing package would produce a more precise p-value which would be in between 0.005 and 0.010. Here we are approximating the p-value and would report p < 0.010.                   In all tests of hypothesis, there are two types of errors that can be committed. The first is called a Type I error and refers to the situation where we incorrectly reject H 0 when in fact it is true. This is also called a false positive result (as we incorrectly conclude that the research hypothesis is true when in fact it is not). When we run a test of hypothesis and decide to reject H 0 (e.g., because the test statistic exceeds the critical value in an upper tailed test) then either we make a correct decision because the research hypothesis is true or we commit a Type I error. The different conclusions are summarized in the table below. Note that we will never know whether the null hypothesis is really true or false (i.e., we will never know which row of the following table reflects reality). Table - Conclusions in Test of Hypothesis   is True Correct Decision Type I Error is False Type II Error Correct Decision In the first step of the hypothesis test, we select a level of significance, α, and α= P(Type I error). Because we purposely select a small value for α, we control the probability of committing a Type I error. For example, if we select α=0.05, and our test tells us to reject H 0 , then there is a 5% probability that we commit a Type I error. Most investigators are very comfortable with this and are confident when rejecting H 0 that the research hypothesis is true (as it is the more likely scenario when we reject H 0 ). When we run a test of hypothesis and decide not to reject H 0 (e.g., because the test statistic is below the critical value in an upper tailed test) then either we make a correct decision because the null hypothesis is true or we commit a Type II error. Beta (β) represents the probability of a Type II error and is defined as follows: β=P(Type II error) = P(Do not Reject H 0 | H 0 is false). Unfortunately, we cannot choose β to be small (e.g., 0.05) to control the probability of committing a Type II error because β depends on several factors including the sample size, α, and the research hypothesis. When we do not reject H 0 , it may be very likely that we are committing a Type II error (i.e., failing to reject H 0 when in fact it is false). Therefore, when tests are run and the null hypothesis is not rejected we often make a weak concluding statement allowing for the possibility that we might be committing a Type II error. If we do not reject H 0 , we conclude that we do not have significant evidence to show that H 1 is true. We do not conclude that H 0 is true.  The most common reason for a Type II error is a small sample size. return to top | previous page | next page Content ©2017. All Rights Reserved. Date last modified: November 6, 2017. Wayne W. LaMorte, MD, PhD, MPH In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation. Hypothesis ( AQA A Level Psychology ) Revision note. Psychology Content Creator A hypothesis is a testable statement written as a prediction of what the researcher expects to find as a result of their experiment A hypothesis should be no more than one sentence long The hypothesis needs to include the independent variable (IV) and the dependent variable (DV) For example - stating that you will measure ‘aggression’ is not enough ('aggression' has not been operationalised) by exposing some children to an aggressive adult model whilst other children are not exposed to an aggressive adult model (operationalisation of the IV)  number of imitative and non-imitative acts of aggression performed by the child (operationalisation of the DV) The Experimental Hypothesis Children who are exposed to an aggressive adult model will perform more acts of imitative and non-imitative aggression than children who have not been exposed to an aggressive adult model The experimental hypothesis can be written as a  directional hypothesis or as a non-directional hypothesis The Experimental Hypothesis: Directional  A directional experimental hypothesis (also known as one-tailed)  predicts the direction of the change/difference (it anticipates more specifically what might happen) A directional hypothesis is usually used when there is previous research which support a particular theory or outcome i.e. what a researcher might expect to happen Participants who drink 200ml of an energy drink 5 minutes before running 100m will be faster (in seconds) than participants who drink 200ml of water 5 minutes before running 100m Participants who learn a poem in a room in which loud music is playing will recall less of the poem's content than participants who learn the same poem in a silent room  The Experimental Hypothesis: Non-Directional  A non-directional experimental hypothesis (also known as two -tailed) does not predict the direction of the change/difference (it is an 'open goal' i.e. anything could happen) A non-directional hypothesis is usually used when there is either no or little previous research which support a particular theory or outcome i.e. what the researcher cannot be confident as to what will happen There will be a difference in time taken (in seconds) to run 100m depending on whether participants have drunk 200ml of an energy drink or 200ml of water 5 minutes before running  There will be a difference in recall of a poem depending on whether participants learn the poem in a room in which loud music is playing or in a silent room The Null Hypothesis All published psychology research must include the null hypothesis There will be no difference in children's acts of imitative and non-imitative aggression depending on whether they have observed an aggressive adult model or a non-aggressive adult model The null hypothesis has to begin with the idea that the IV will have no effect on the DV  because until the experiment is run and the results are analysed it is impossible to state anything else!  To put this in 'laymen's terms: if you bought a lottery ticket you could not predict that you are going to win the jackpot: you have to wait for the results to find out (spoiler alert: the chances of this happening are soooo low that you might as well save your cash!) There will be no difference in time taken (in seconds) to run 100m depending on whether participants have drunk 200ml of an energy drink or 200ml of water 5 minutes before running  There will be no difference in recall of a poem depending on whether participants learn the poem in a room in which loud music is playing or in a silent room (NB this is not quite so slick and easy with a directional hypothesis as this sort of hypothesis will never begin with 'There will be a difference') this is why the null hypothesis is so important - it tells the researcher whether or not their experiment has shown a difference in conditions (which is generally what they want to see, otherwise it's back to the drawing board...) Worked example Jim wants to test the theory that chocolate helps your ability to solve word-search puzzles He believes that sugar helps memory as he has read some research on this in a text book He puts up a poster in his sixth-form common room asking for people to take part after school one day and explains that they will be required to play two memory games, where eating chocolate will be involved (a)  Should Jim use a directional hypothesis in this study? Explain your answer (2 marks) (b)  Write a suitable hypothesis for this study. (4 marks) a) Jim should use a directional hypothesis (1 mark)     because previous research exists that states what might happen (2 nd mark) b)  'Participants will remember more items from a shopping list in a memory game within the hour after eating 50g of chocolate, compared to when they have not consumed any chocolate' 1 st mark for directional 2 nd mark for IV- eating chocolate 3 rd mark for DV- number of items remembered 4 th mark for operationalising both IV & DV If you write a non-directional or null hypothesis the mark is 0 If you do not get the direction correct the mark is zero Remember to operationalise the IV & DV You've read 0 of your 0 free revision notes Get unlimited access. to absolutely everything: Downloadable PDFs Unlimited Revision Notes Topic Questions Past Papers Model Answers Videos (Maths and Science) Join the 100,000 + Students that ❤️ Save My Exams the (exam) results speak for themselves: Did this page help you? Author: Claire Neeson Claire has been teaching for 34 years, in the UK and overseas. She has taught GCSE, A-level and IB Psychology which has been a lot of fun and extremely exhausting! Claire is now a freelance Psychology teacher and content creator, producing textbooks, revision notes and (hopefully) exciting and interactive teaching materials for use in the classroom and for exam prep. Her passion (apart from Psychology of course) is roller skating and when she is not working (or watching 'Coronation Street') she can be found busting some impressive moves on her local roller rink. Statistics Tutorial Descriptive statistics, inferential statistics, stat reference, statistics - hypothesis testing a mean (two tailed). A population mean is an average of value a population. Hypothesis tests are used to check a claim about the size of that population mean. Hypothesis Testing a Mean The following steps are used for a hypothesis test: Check the conditions Define the claims Decide the significance level Calculate the test statistic For example: Population : Nobel Prize winners Category : Age when they received the prize. And we want to check the claim: "The average age of Nobel Prize winners when they received the prize is not 60" By taking a sample of 30 randomly selected Nobel Prize winners we could find that: The mean age in the sample (\(\bar{x}\)) is 62.1 The standard deviation of age in the sample (\(s\)) is 13.46 From this sample data we check the claim with the steps below. 1. Checking the Conditions The conditions for calculating a confidence interval for a proportion are: The sample is randomly selected The population data is normally distributed Sample size is large enough A moderately large sample size, like 30, is typically large enough. In the example, the sample size was 30 and it was randomly selected, so the conditions are fulfilled. Note: Checking if the data is normally distributed can be done with specialized statistical tests. 2. Defining the Claims We need to define a null hypothesis (\(H_{0}\)) and an alternative hypothesis (\(H_{1}\)) based on the claim we are checking. The claim was: In this case, the parameter is the mean age of Nobel Prize winners when they received the prize (\(\mu\)). The null and alternative hypothesis are then: Null hypothesis : The average age was 60. Alternative hypothesis : The average age is not 60. Which can be expressed with symbols as: \(H_{0}\): \(\mu = 60 \) \(H_{1}\): \(\mu \neq 60 \) This is a ' two-tailed ' test, because the alternative hypothesis claims that the proportion is different from the null hypothesis. If the data supports the alternative hypothesis, we reject the null hypothesis and accept the alternative hypothesis. Advertisement 3. Deciding the Significance Level The significance level (\(\alpha\)) is the uncertainty we accept when rejecting the null hypothesis in a hypothesis test. The significance level is a percentage probability of accidentally making the wrong conclusion. Typical significance levels are: \(\alpha = 0.1\) (10%) \(\alpha = 0.05\) (5%) \(\alpha = 0.01\) (1%) A lower significance level means that the evidence in the data needs to be stronger to reject the null hypothesis. There is no "correct" significance level - it only states the uncertainty of the conclusion. Note: A 5% significance level means that when we reject a null hypothesis: We expect to reject a true null hypothesis 5 out of 100 times. 4. Calculating the Test Statistic The test statistic is used to decide the outcome of the hypothesis test. The test statistic is a standardized value calculated from the sample. The formula for the test statistic (TS) of a population mean is: \(\displaystyle \frac{\bar{x} - \mu}{s} \cdot \sqrt{n} \) \(\bar{x}-\mu\) is the difference between the sample mean (\(\bar{x}\)) and the claimed population mean (\(\mu\)). \(s\) is the sample standard deviation . \(n\) is the sample size. In our example: The claimed (\(H_{0}\)) population mean (\(\mu\)) was \( 60 \) The sample mean (\(\bar{x}\)) was \(62.1\) The sample standard deviation (\(s\)) was \(13.46\) The sample size (\(n\)) was \(30\) So the test statistic (TS) is then: \(\displaystyle \frac{62.1-60}{13.46} \cdot \sqrt{30} = \frac{2.1}{13.46} \cdot \sqrt{30} \approx 0.156 \cdot 5.477 = \underline{0.855}\) You can also calculate the test statistic using programming language functions: With Python use the scipy and math libraries to calculate the test statistic. With R use built-in math and statistics functions to calculate the test statistic. 5. Concluding There are two main approaches for making the conclusion of a hypothesis test: The critical value approach compares the test statistic with the critical value of the significance level. The P-value approach compares the P-value of the test statistic and with the significance level. Note: The two approaches are only different in how they present the conclusion. The Critical Value Approach For the critical value approach we need to find the critical value (CV) of the significance level (\(\alpha\)). For a population mean test, the critical value (CV) is a T-value from a student's t-distribution . This critical T-value (CV) defines the rejection region for the test. The rejection region is an area of probability in the tails of the standard normal distribution. Because the claim is that the population proportion is different from 60, the rejection region is split into both the left and right tail: The student's t-distribution is adjusted for the uncertainty from smaller samples. This adjustment is called degrees of freedom (df), which is the sample size \((n) - 1\) In this case the degrees of freedom (df) is: \(30 - 1 = \underline{29} \) Choosing a significance level (\(\alpha\)) of 0.05, or 5%, we can find the critical T-value from a T-table , or with a programming language function: Note: Because this is a two-tailed test the tail area (\(\alpha\)) needs to be split in half (divided by 2). With Python use the Scipy Stats library t.ppf() function find the T-Value for an \(\alpha\)/2 = 0.025 at 29 degrees of freedom (df). With R use the built-in qt() function to find the t-value for an \(\alpha\)/ = 0.025 at 29 degrees of freedom (df). Using either method we can find that the critical T-Value is \(\approx \underline{-2.045}\) For a two-tailed test we need to check if the test statistic (TS) is smaller than the negative critical value (-CV), or bigger than the positive critical value (CV). If the test statistic is smaller than the negative critical value, the test statistic is in the rejection region . If the test statistic is bigger than the positive critical value, the test statistic is in the rejection region . When the test statistic is in the rejection region, we reject the null hypothesis (\(H_{0}\)). Here, the test statistic (TS) was \(\approx \underline{0.855}\) and the critical value was \(\approx \underline{-2.045}\) Here is an illustration of this test in a graph: Since the test statistic is between the critical values we keep the null hypothesis. This means that the sample data does not support the alternative hypothesis. And we can summarize the conclusion stating: The sample data does not support the claim that "The average age of Nobel Prize winners when they received the prize is not 60" at a 5% significance level . The P-Value Approach For the P-value approach we need to find the P-value of the test statistic (TS). If the P-value is smaller than the significance level (\(\alpha\)), we reject the null hypothesis (\(H_{0}\)). The test statistic was found to be \( \approx \underline{0.855} \) For a population proportion test, the test statistic is a T-Value from a student's t-distribution . Because this is a two-tailed test, we need to find the P-value of a T-value bigger than 0.855 and multiply it by 2 . The student's t-distribution is adjusted according to degrees of freedom (df), which is the sample size \((30) - 1 = \underline{29}\) We can find the P-value using a T-table , or with a programming language function: With Python use the Scipy Stats library t.cdf() function find the P-value of a T-value bigger than 0.855 for a two tailed test at 29 degrees of freedom (df): With R use the built-in pt() function find the P-value of a T-Value bigger than 0.855 for a two tailed test at 29 degrees of freedom (df): Using either method we can find that the P-value is \(\approx \underline{0.3996}\) This tells us that the significance level (\(\alpha\)) would need to be smaller 0.3996, or 39.96%, to reject the null hypothesis. This P-value is bigger than any of the common significance levels (10%, 5%, 1%). So the null hypothesis is kept at all of these significance levels. The sample data does not support the claim that "The average age of Nobel Prize winners when they received the prize is not 60" at a 10%, 5%, or 1% significance level . Calculating a P-Value for a Hypothesis Test with Programming Many programming languages can calculate the P-value to decide outcome of a hypothesis test. Using software and programming to calculate statistics is more common for bigger sets of data, as calculating manually becomes difficult. The P-value calculated here will tell us the lowest possible significance level where the null-hypothesis can be rejected. With Python use the scipy and math libraries to calculate the P-value for a two tailed hypothesis test for a mean. Here, the sample size is 30, the sample mean is 62.1, the sample standard deviation is 13.46, and the test is for a mean different from 60. With R use built-in math and statistics functions find the P-value for a two tailed hypothesis test for a mean. Left-Tailed and Two-Tailed Tests This was an example of a left tailed test, where the alternative hypothesis claimed that parameter is smaller than the null hypothesis claim. You can check out an equivalent step-by-step guide for other types here: Right-Tailed Test Two-Tailed Test COLOR PICKER Contact Sales If you want to use W3Schools services as an educational institution, team or enterprise, send us an e-mail: [email protected] Report Error If you want to report an error, or if you want to make a suggestion, send us an e-mail: [email protected] Top Tutorials Top references, top examples, get certified. Have a language expert improve your writing Run a free plagiarism check in 10 minutes, generate accurate citations for free. Knowledge Base Methodology How to Write a Strong Hypothesis | Steps & Examples How to Write a Strong Hypothesis | Steps & Examples Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023. A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection . Example: Hypothesis Daily apple consumption leads to fewer doctor’s visits. Table of contents What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses. A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question. A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data). Variables in hypotheses Hypotheses propose a relationship between two or more types of variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures. If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results. In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect . Receive feedback on language, structure, and formatting Professional editors proofread and edit your paper by focusing on: Academic style Vague sentences Style consistency See an example Step 1. Ask a question Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Step 2. Do some preliminary research Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find. At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs. Step 3. Formulate your hypothesis Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence. 4. Refine your hypothesis You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain: The relevant variables The specific group being studied The predicted outcome of the experiment or analysis 5. Phrase your hypothesis in three ways To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable. In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables. If you are comparing two groups, the hypothesis can state what difference you expect to find between them. 6. Write a null hypothesis If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a . H 0 : The number of lectures attended by first-year students has no effect on their final exam scores. H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores. Research question Hypothesis Null hypothesis What are the health benefits of eating an apple a day? Increasing apple consumption in over-60s will result in decreasing frequency of doctor’s visits. Increasing apple consumption in over-60s will have no effect on frequency of doctor’s visits. Which airlines have the most delays? Low-cost airlines are more likely to have delays than premium airlines. Low-cost and premium airlines are equally likely to have delays. Can flexible work arrangements improve job satisfaction? Employees who have flexible working hours will report greater job satisfaction than employees who work fixed hours. There is no relationship between working hour flexibility and job satisfaction. How effective is high school sex education at reducing teen pregnancies? Teenagers who received sex education lessons throughout high school will have lower rates of unplanned pregnancy teenagers who did not receive any sex education. High school sex education has no effect on teen pregnancy rates. What effect does daily use of social media have on the attention span of under-16s? There is a negative between time spent on social media and attention span in under-16s. There is no relationship between social media use and attention span in under-16s. If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples. Sampling methods Simple random sampling Stratified sampling Cluster sampling Likert scales Reproducibility  Statistics Null hypothesis Statistical power Probability distribution Effect size Poisson distribution Research bias Optimism bias Cognitive bias Implicit bias Hawthorne effect Anchoring bias Explicit bias Prevent plagiarism. Run a free check. A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data). Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship. Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance. Cite this Scribbr article If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator. McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved June 24, 2024, from https://www.scribbr.com/methodology/hypothesis/ Is this article helpful? Shona McCombes Other students also liked, construct validity | definition, types, & examples, what is a conceptual framework | tips & examples, operationalization | a guide with examples, pros & cons, what is your plagiarism score. school Campus Bookshelves menu_book Bookshelves perm_media Learning Objects login Login how_to_reg Request Instructor Account hub Instructor Commons Margin Size Download Page (PDF) Download Full Book (PDF) Periodic Table Physics Constants Scientific Calculator Reference & Cite Tools expand_more Readability selected template will load here This action is not available. 11.4: One- and Two-Tailed Tests Last updated Save as PDF Page ID 2148 Rice University \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \) \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\) \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\) \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\) \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vectorC}[1]{\textbf{#1}} \) \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \) \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \) \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \) Learning Objectives Define Type I and Type II errors Interpret significant and non-significant differences Explain why the null hypothesis should not be accepted when the effect is not significant In the James Bond case study, Mr. Bond was given \(16\) trials on which he judged whether a martini had been shaken or stirred. He was correct on \(13\) of the trials. From the binomial distribution, we know that the probability of being correct \(13\) or more times out of \(16\) if one is only guessing is \(0.0106\). Figure \(\PageIndex{1}\) shows a graph of the binomial distribution. The red bars show the values greater than or equal to \(13\). As you can see in the figure, the probabilities are calculated for the upper tail of the distribution. A probability calculated in only one tail of the distribution is called a "one-tailed probability." Binomial Calculator A slightly different question can be asked of the data: "What is the probability of getting a result as extreme or more extreme than the one observed?" Since the chance expectation is \(8/16\), a result of \(3/16\) is equally as extreme as \(13/16\). Thus, to calculate this probability, we would consider both tails of the distribution. Since the binomial distribution is symmetric when \(\pi =0.5\), this probability is exactly double the probability of \(0.0106\) computed previously. Therefore, \(p = 0.0212\). A probability calculated in both tails of a distribution is called a "two-tailed probability" (see Figure \(\PageIndex{2}\)). Should the one-tailed or the two-tailed probability be used to assess Mr. Bond's performance? That depends on the way the question is posed. If we are asking whether Mr. Bond can tell the difference between shaken or stirred martinis, then we would conclude he could if he performed either much better than chance or much worse than chance. If he performed much worse than chance, we would conclude that he can tell the difference, but he does not know which is which. Therefore, since we are going to reject the null hypothesis if Mr. Bond does either very well or very poorly, we will use a two-tailed probability. On the other hand, if our question is whether Mr. Bond is better than chance at determining whether a martini is shaken or stirred, we would use a one-tailed probability. What would the one-tailed probability be if Mr. Bond were correct on only \(3\) of the \(16\) trials? Since the one-tailed probability is the probability of the right-hand tail, it would be the probability of getting \(3\) or more correct out of \(16\). This is a very high probability and the null hypothesis would not be rejected. The null hypothesis for the two-tailed test is \(\pi =0.5\). By contrast, the null hypothesis for the one-tailed test is \(\pi \leq 0.5\). Accordingly, we reject the two-tailed hypothesis if the sample proportion deviates greatly from \(0.5\) in either direction. The one-tailed hypothesis is rejected only if the sample proportion is much greater than \(0.5\). The alternative hypothesis in the two-tailed test is \(\pi \neq 0.5\). In the one-tailed test it is \(\pi > 0.5\). You should always decide whether you are going to use a one-tailed or a two-tailed probability before looking at the data. Statistical tests that compute one-tailed probabilities are called one-tailed tests; those that compute two-tailed probabilities are called two-tailed tests. Two-tailed tests are much more common than one-tailed tests in scientific research because an outcome signifying that something other than chance is operating is usually worth noting. One-tailed tests are appropriate when it is not important to distinguish between no effect and an effect in the unexpected direction. For example, consider an experiment designed to test the efficacy of a treatment for the common cold. The researcher would only be interested in whether the treatment was better than a placebo control. It would not be worth distinguishing between the case in which the treatment was worse than a placebo and the case in which it was the same because in both cases the drug would be worthless. Some have argued that a one-tailed test is justified whenever the researcher predicts the direction of an effect. The problem with this argument is that if the effect comes out strongly in the non-predicted direction, the researcher is not justified in concluding that the effect is not zero. Since this is unrealistic, one-tailed tests are usually viewed skeptically if justified on this basis alone. One and Two Tailed Tests Suppose we have a null hypothesis H 0 and an alternative hypothesis H 1 . We consider the distribution given by the null hypothesis and perform a test to determine whether or not the null hypothesis should be rejected in favour of the alternative hypothesis. There are two different types of tests that can be performed. A one-tailed test looks for an increase or decrease in the parameter whereas a two-tailed test looks for any change in the parameter (which can be any change- increase or decrease). We can perform the test at any level (usually 1%, 5% or 10%). For example, performing the test at a 5% level means that there is a 5% chance of wrongly rejecting H 0 . If we perform the test at the 5% level and decide to reject the null hypothesis, we say "there is significant evidence at the 5% level to suggest the hypothesis is false". One-Tailed Test We choose a critical region. In a one-tailed test, the critical region will have just one part (the red area below). If our sample value lies in this region, we reject the null hypothesis in favour of the alternative. Suppose we are looking for a definite decrease. Then the critical region will be to the left. Note, however, that in the one-tailed test the value of the parameter can be as high as you like. Suppose we are given that X has a Poisson distribution and we want to carry out a hypothesis test on the mean, l, based upon a sample observation of 3. Suppose the hypotheses are: H 0 : l = 9 H 1 : l < 9 We want to test if it is "reasonable" for the observed value of 3 to have come from a Poisson distribution with parameter 9. So what is the probability that a value as low as 3 has come from a Po(9)? P(X < 3) = 0.0212 (this has come from a Poisson table) The probability is less than 0.05, so there is less than a 5% chance that the value has come from a Poisson(3) distribution. We therefore reject the null hypothesis in favour of the alternative at the 5% level. However, the probability is greater than 0.01, so we would not reject the null hypothesis in favour of the alternative at the 1% level. Two-Tailed Test In a two-tailed test, we are looking for either an increase or a decrease. So, for example, H 0 might be that the mean is equal to 9 (as before). This time, however, H 1 would be that the mean is not equal to 9. In this case, therefore, the critical region has two parts: Lets test the parameter p of a Binomial distribution at the 10% level. Suppose a coin is tossed 10 times and we get 7 heads. We want to test whether or not the coin is fair. If the coin is fair, p = 0.5 . Put this as the null hypothesis: H 0 : p = 0.5 H 1 : p =(doesn' equal) 0.5 Now, because the test is 2-tailed, the critical region has two parts. Half of the critical region is to the right and half is to the left. So the critical region contains both the top 5% of the distribution and the bottom 5% of the distribution (since we are testing at the 10% level). If H 0 is true, X ~ Bin(10, 0.5). If the null hypothesis is true, what is the probability that X is 7 or above? P(X > 7) = 1 - P(X < 7) = 1 - P(X < 6) = 1 - 0.8281 = 0.1719 Is this in the critical region? No- because the probability that X is at least 7 is not less than 0.05 (5%), which is what we need it to be. So there is not significant evidence at the 10% level to reject the null hypothesis. One Tailed Test or Two in Hypothesis Testing; One Tailed Distribution Area Contents (Click to slip to that section): Alpha levels When should you use either test? One tailed distribution (how to find the area) One tailed test or two in Hypothesis Testing: Overview In hypothesis testing , you are asked to decide if a claim is true or not. For example, if someone says “all Floridian’s have a 50% increased chance of melanoma”, it’s up to you to decide if this claim holds merit. One of the first steps is to look up a z-score , and in order to do that , you need to know if it’s a one tailed test or two . You can figure this out in just a couple of steps. Back to top One tailed test or two in Hypothesis Testing: Steps If you’re lucky enough to be given a picture, you’ll be able to tell if your test is one-tailed or two-tailed by comparing it to the image above. However, most of the time you’re given questions, not pictures. So it’s a matter of deciphering the problem and picking out the important piece of information. You’re basically looking for keywords like equals , more than , or less than . Example question #1: A government official claims that the dropout rate for local schools is 25% . Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official’s claim? Example question #2: A government official claims that the dropout rate for local schools is less than 25%. Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official’s claim? Example question #3: A government official claims that the dropout rate for local schools is greater than 25%. Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official’s claim? Step 1: Read the question. Step 2: Rephrase the claim in the question with an equation. In example question #1, Drop out rate = 25% In example question #2, Drop out rate < 25% In example question #3, Drop out rate > 25%. Step 3: If step 2 has an equals sign in it, this is a two-tailed test. If it has > or < it is a one-tailed test. Like the explanation? Check out the Statistics How To Handbook , which has hundreds of easy to understand definitions and examples, just like this one! Back to top One Tailed Test or Two: Onto some more technical stuff The above should have given you a brief overview of the differences between one-tailed tests and two-tailed tests. For the very beginning of your stats class, that’s probably all the information you need to get by. But once you hit ANOVA and regression analysis , things get a little more challenging. 1. Alpha levels Alpha levels (sometimes just called “significance levels”) are used in hypothesis tests ; it is the probability of making the wrong decision when the null hypothesis is true. A one-tailed test has the entire 5% of the alpha level in one tail (in either the left, or the right tail). A two-tailed test splits your alpha level in half (as in the image to the left). Let’s say you’re working with the standard alpha level of 0.5 (5%). A two tailed test will have half of this (2.5%) in each tail. Very simply, the hypothesis test might go like this: A null hypothesis might state that the mean = x . You’re testing if the mean is way above this or way below. You run a t-test , which churns out a t-statistic . If this test statistic falls in the top 2.5% or bottom 2.5% of its probability distribution (in this case, the t-distribution ), you would reject the null hypothesis . The “cut off” areas created by your alpha levels are called rejection regions . It’s where you would reject the null hypothesis, if your test statistic happens to fall into one of those rejection areas. The terms “one tailed” and “two tailed” can more precisely be defined as referring to where your rejection regions are located. Back to top A one-tailed test is where you are only interested in one direction. If a mean is x, you might want to know if a set of results is more than x or less than x. A one-tailed test is more powerful than a two-tailed test, as you aren’t considering an effect in the opposite direction. Next : Left tailed test or right tailed test? Back to top 3. When Should You Use a One-Tailed Test? In the above examples, you were given specific wording like “greater than” or “less than.” Sometimes you, the researcher, do not have this information and you have to choose the test. For example, you develop a drug which you think is just as effective as a drug already on the market (it also happens to be cheaper). You could run a two-tailed test (to test that it is more effective and to also check that it is less effective). But you don’t really care about it being more effective, just that it isn’t any less effective (after all, your drug is cheaper). You can run a one-tailed test to check that your drug is at least as effective as the existing drug. On the other hand, it would be inappropriate (and perhaps, unethical) to run a one-tailed test for this scenario in the opposite direction (i.e. to show the drug is more effective). This sounds reasonable until you consider there may be certain circumstances where the drug is less effective. If you fail to test for that, your research will be useless. Consider both directions when deciding if you should run a one tailed test or two. If you can skip one tail and it’s not irresponsible or unethical to do so, then you can run a one-tailed test. Back to top One tailed Test or Two: How to find the area of a one-tailed distribution: Steps There are a few ways to find the area under a one tailed distribution curve. The easiest, by far, is looking up the value in a table like the z-table . A z-table gives you percentages, which represent the area under a curve . For example, a table value of 0.5000 is 50% of the area and 0.2000 is 20% of the area. If you are looking for other area problems*, see the normal distribution curve index . The index lists seven possible types of area, including two tailed, one tailed, and areas to the left and right of z. *You can also calculate areas with integral calculus . See The Area Problem . Note : In order to use a z-table , you need to split your z-value up into decimal places (e.g. tenths and hundredths). For example, if you are asked to find the area in a one tailed distribution with a z-value of 0.21, split this into tenths (0.2) and hundredths (0.01). One tailed distribution: Steps for finding the area in a z-table Step 1: Look up your z-score in the z-table . Looking up the value means finding the intersection of your two decimals (see note above). For example, if you are asked to find the area in a one tailed distribution to the left of z = -0.46, look up 0.46 in the table (note: ignore negative values. If you have a negative value, use its absolute value ). The table below shows that the value in the intersection for 0.46 is .1772. This figure was obtained by looking up 0.4 in the left hand column and 0.06 in the top row. z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 Step 2: Take the area you just found in step 2 and add .500. That’s because the area in the right-hand z-table is the area between the mean and the z-score. You want the entire area up to that point, so: .5000 + .1772 = .6772. Step 3: Subtract from 1 to get the tail area: 1 – .6772 = 0.3228. That’s it! One Tailed Test or Two: References Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Heath, D. (2002). An Introduction to Experimental Design and Statistics for Biology. CRC Press. IDRE: FAQ: What are the differences between one-tailed and two-tailed tests? Retrieved May 27, 2018 from: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-the-differences-between-one-tailed-and-two-tailed-tests/ If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. AP®︎/College Statistics Course: ap®︎/college statistics   >   unit 11, hypotheses for a two-sample t test. Example of hypotheses for paired and two-sample t tests Writing hypotheses to test the difference of means Two-sample t test for difference of means Test statistic in a two-sample t test P-value in a two-sample t test Conclusion for a two-sample t test using a P-value Conclusion for a two-sample t test using a confidence interval Making conclusions about the difference of means Want to join the conversation? Upvote Button navigates to signup page Downvote Button navigates to signup page Flag Button navigates to signup page Video transcript Statistics Made Easy One-Tailed Hypothesis Tests: 3 Example Problems In statistics, we use hypothesis tests to determine whether some claim about a population parameter is true or not. Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H 0 (Null Hypothesis): Population parameter = ≤, ≥ some value H A (Alternative Hypothesis): Population parameter <, >, ≠ some value There are two types of hypothesis tests: Two-tailed test : Alternative hypothesis contains the ≠ sign One-tailed test : Alternative hypothesis contains either < or > sign In a one-tailed test , the alternative hypothesis contains the less than (“<“) or greater than (“>”) sign. This indicates that we’re testing whether or not there is a positive or negative effect. Check out the following example problems to gain a better understanding of one-tailed tests. Example 1: Factory Widgets Suppose it’s assumed that the average weight of a certain widget produced at a factory is 20 grams. However, one engineer believes that a new method produces widgets that weigh less than 20 grams. To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses: H 0 (Null Hypothesis): μ ≥ 20 grams H A (Alternative Hypothesis): μ < 20 grams Note : We can tell this is a one-tailed test because the alternative hypothesis contains the less than ( < ) sign. Specifically, we would call this a left-tailed test because we’re testing if some population parameter is less than a specific value. To test this, he uses the new method to produce 20 widgets and obtains the following information: n = 20 widgets x = 19.8 grams s = 3.1 grams Plugging these values into the One Sample t-test Calculator , we obtain the following results: t-test statistic: -0.288525 one-tailed p-value: 0.388 Since the p-value is not less than .05, the engineer fails to reject the null hypothesis. He does not have sufficient evidence to say that the true mean weight of widgets produced by the new method is less than 20 grams. Example 2: Plant Growth Suppose a standard fertilizer has been shown to cause a species of plants to grow by an average of 10 inches. However, one botanist believes a new fertilizer can cause this species of plants to grow by an average of greater than 10 inches. To test this, she can perform a one-tailed hypothesis test with the following null and alternative hypotheses: H 0 (Null Hypothesis): μ ≤ 10 inches H A (Alternative Hypothesis): μ > 10 inches Note : We can tell this is a one-tailed test because the alternative hypothesis contains the greater than ( > ) sign. Specifically, we would call this a right-tailed test because we’re testing if some population parameter is greater than a specific value. To test this claim, she applies the new fertilizer to a simple random sample of 15 plants and obtains the following information: n = 15 plants x = 11.4 inches s = 2.5 inches t-test statistic: 2.1689 one-tailed p-value: 0.0239 Since the p-value is less than .05, the botanist rejects the null hypothesis. She has sufficient evidence to conclude that the new fertilizer causes an average increase of greater than 10 inches. Example 3: Studying Method A professor currently teaches students to use a studying method that results in an average exam score of 82. However, he believes a new studying method can produce exam scores with an average value greater than 82. To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses: H 0 (Null Hypothesis): μ ≤ 82 H A (Alternative Hypothesis): μ > 82 To test this claim, the professor has 25 students use the new studying method and then take the exam. He collects the following data on the exam scores for this sample of students: t-test statistic: 3.6586 one-tailed p-value: 0.0006 Since the p-value is less than .05, the professor rejects the null hypothesis. He has sufficient evidence to conclude that the new studying method produces exam scores with an average score greater than 82. Additional Resources The following tutorials provide additional information about hypothesis testing: Introduction to Hypothesis Testing What is a Directional Hypothesis? When Do You Reject the Null Hypothesis? Featured Posts Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations. Leave a Reply Cancel reply Your email address will not be published. Required fields are marked * Join the Statology Community Sign up to receive Statology's exclusive study resource: 100 practice problems with step-by-step solutions. Plus, get our latest insights, tutorials, and data analysis tips straight to your inbox! By subscribing you accept Statology's Privacy Policy. One-Tailed T-Test: Hypothesis Testing Explained In the realm of statistics, hypothesis testing plays a crucial role in drawing inferences from data. One of the common statistical tests used is the t-test, which is particularly useful for comparing means of two groups. The t-test can be further categorized into one-tailed and two-tailed tests, each with its specific application and interpretation. Understanding the One-Tailed T-Test A one-tailed t-test is a type of hypothesis test that examines whether the mean of a population is significantly greater than or less than a specific value. This test is directional, meaning it focuses on a single direction of the difference. Imagine you are studying the effectiveness of a new medication for reducing blood pressure. You want to see if the medication leads to a significant decrease in blood pressure. In this scenario, you would use a one-tailed t-test to investigate whether the mean blood pressure of patients receiving the medication is significantly lower than the mean blood pressure of a control group. Key Concepts in Hypothesis Testing Null Hypothesis (H 0 ): This hypothesis assumes no difference or relationship between the variables being studied. In our example, the null hypothesis would be that there is no difference in mean blood pressure between the medication group and the control group. Alternative Hypothesis (H 1 ): This hypothesis proposes that there is a difference or relationship between the variables. In our example, the alternative hypothesis would be that the mean blood pressure of the medication group is significantly lower than the control group. Significance Level (α): This value represents the probability of rejecting the null hypothesis when it is actually true. It is typically set at 0.05, meaning there is a 5% chance of making a Type I error (rejecting a true null hypothesis). Test Statistic: This value is calculated from the data and represents the observed difference between the sample means. It is compared to the critical value to determine the outcome of the test. Critical Value: This value is determined based on the significance level and the degrees of freedom. It represents the threshold for rejecting the null hypothesis. Steps Involved in Performing a One-Tailed T-Test Here’s a step-by-step guide to conducting a one-tailed t-test: Define the Hypotheses: Formulate the null and alternative hypotheses based on the research question. Choose the Significance Level: Set the significance level (α) based on the desired level of confidence. Calculate the Test Statistic: Use the appropriate formula to calculate the t-statistic based on the sample data. Determine the Critical Value: Find the critical value corresponding to the chosen significance level and the degrees of freedom. Compare the Test Statistic and Critical Value: If the absolute value of the test statistic is greater than the critical value, reject the null hypothesis. Interpret the Results: Conclude whether there is sufficient evidence to support the alternative hypothesis. Example: One-Tailed T-Test for Blood Pressure Reduction Let’s assume we have data on blood pressure readings for 20 patients receiving the new medication and 20 patients in the control group. The mean blood pressure reduction for the medication group is 10 mmHg, while the mean reduction for the control group is 5 mmHg. We want to test if the medication leads to a significantly greater reduction in blood pressure. Hypotheses: H 0 : μ medication ≤ μ control (There is no difference in mean blood pressure reduction) H 1 : μ medication > μ control (The medication leads to a significantly greater reduction in blood pressure) Significance Level: α = 0.05 Test Statistic: Using the appropriate formula, we calculate the t-statistic to be 2.5. Critical Value: For a one-tailed test with 38 degrees of freedom and α = 0.05, the critical value is 1.684. Conclusion: Since the absolute value of the test statistic (2.5) is greater than the critical value (1.684), we reject the null hypothesis. This means there is sufficient evidence to support the alternative hypothesis that the medication leads to a significantly greater reduction in blood pressure. Advantages and Disadvantages of One-Tailed T-Test Increased Power: One-tailed tests have greater power to detect a difference in the desired direction, as they focus on a specific alternative hypothesis. Simplicity: The interpretation of results is straightforward, as it only considers one direction of the difference. Disadvantages Limited Scope: One-tailed tests cannot detect differences in the opposite direction. Risk of Type II Error: If the true difference is in the opposite direction, a one-tailed test may fail to detect it, leading to a Type II error (failing to reject a false null hypothesis). The one-tailed t-test is a valuable tool for hypothesis testing when the research question focuses on a specific direction of difference. It is important to carefully consider the advantages and disadvantages before choosing a one-tailed or two-tailed test. For further understanding and practice, explore online resources, statistical software, and textbooks that provide detailed explanations and examples of one-tailed t-tests. Data Analysis © 2024 by SchoolTube Username or Email Address Remember Me Forgot password? Enter your account data and we will send you a link to reset your password. Your password reset link appears to be invalid or expired. Privacy policy. To use social login you have to agree with the storage and handling of your data by this website. Privacy Policy Add to Collection Public collection title Private collection title No Collections Here you'll find all collections you've created before. More From Forbes Why the world’s rarest rattlesnake is a ‘scientific masterpiece’—according to this herpetologist. Share to Facebook Share to Twitter Share to Linkedin The Santa Catalina Island rattlesnake isn’t noteworthy just because it’s the rarest species of ... [+] rattlesnake. It’s also the only rattlesnake that has no rattle. The Santa Catalina Island rattlesnake ( Crotalus catalinensis ) is at the top of my list of “most exquisite snake species.” Sure, it may not be as colorful as the gorgeous green tree python, or as intimidating as the king cobra, or as gigantic as the anaconda or extinct titan boa , but it is every bit as scientifically interesting as any other snake species–perhaps moreso. The Santa Catalina Island rattlesnake is native to Santa Catalina Island, located off the east coast of Mexico’s Baja Peninsula in the Gulf of California. The island is relatively small, measuring approximately eight miles long and two miles wide. This rattlesnake is classified as critically endangered on the IUCN Red List due to its limited distribution, threats from invasive species and human persecution. The introduction of domestic cats to the island significantly pressured the rattlesnake population, as the cats preyed on the snakes and competed for the same food sources. Fortunately, invasive cats were eradicated from the island in 2004. Despite this success, local fishermen continue to kill the snakes out of fear of bites. Additionally, the rattlesnake faces pressure from illegal collecting for the pet trade. The Santa Catalina Island rattlesnake is a venomous species of pit viper. It is thought to be mostly nocturnal, hunting for mice and small reptiles at night. It is a small rattlesnake, measuring approximately two feet in length. While none of these descriptors make it sound particularly noteworthy, aside from its geographically limited population, here are two reasons why the snake is so scientifically interesting. Google Pixel Deadline—10 Days To Update Or Stop Using Your Phone Samsung makes surprise free offer for galaxy s24 ultra buyers, apple confirms iphone upgrade with 2 key new features is here in days, 1. evolution made its rattle go away. The Santa Catalina Island rattlesnake (Crotalus catalinensis), pictured here, is a "rattleless" ... [+] rattlesnake. The hallmark of a rattlesnake is its rattle–a warning sound delivered to would-be predators to retreat or else face a venomous bite. The only problem is that the Santa Catalina Island rattlesnake doesn’t have one. Theories abound as to why evolution made the rattle of the Santa Catalina Island rattlesnake go away. One hypothesis is that losing the rattle was a stealth adaptation that made the Santa Catalina Island rattlesnake quieter and more effective arboreal hunters of birds and mice in the island’s vegetation patches. However, research from a 2008 South American Journal of Herpetology study casts doubt on this theory. The researchers studied the snake’s movement and hunting patterns over a three-year period and found little evidence to suggest that the Santa Catalina Island rattlesnake spent much time at all climbing in the island’s vegetation patches. Although the Santa Catalina Island rattlesnake lacks a rattle, it still vibrates its tail when ... [+] threatened, similar to other rattlesnakes, but without producing any noise. “These results make the hypothesis of the loss of the rattle as a stealth adaptation for hunting on the vegetation very unlikely, since such a low frequency of use of vegetation may not function as a selective agent that could lead to an adaptive loss of the rattle,” state the researchers. Perhaps a more plausible theory is that the Santa Catalina Island rattlesnake lost its rattle over evolutionary time because there weren’t many predators on the island that prompted its use. The island doesn’t have nearly as many predator populations (including humans) as mainland Mexico. The absence of predators and the evolutionary force known as “genetic drift” (random changes the gene frequencies within a population) can strongly influence small island populations, leading to the rapid development of unique traits. Island snakes, in particular, are often noted for their distinctive characteristics . 2. Its Close Relatives Have Been Hard To Pinpoint Isolated island species can sometimes be difficult to place within their proper evolutionary lineage. This is true of the Santa Catalina Island rattlesnake. Originally, researchers suspected that the island snake was most closely related to the red diamond rattlesnake ( Crotalus ruber )–a common species of snake that looks similar to the Santa Catalina Island rattlesnake and is found throughout the Baja peninsula of Mexico, geographically close to Santa Catalina Island. Although as its name suggests, this species is reddish in coloration and much larger than the Santa Catalina Island rattlesnake. The red diamond rattlesnake (Crotalus ruber), pictured here, is hypothesized to be one of the ... [+] closest relatives of the Santa Catalina Island rattlesnake. However, it was later theorized that the Santa Catalina Island rattlesnake may in fact be more closely related to the Mojave rattlesnake ( Crotalus scutulatus ), based on similar morphological characteristics such as head scale type and count and coloration. It was also suggested that the snake might be a derivative of Crotalus atrox , the western diamondback rattlesnake. Early genetic research conducted by Robert Murphy and Ben Crabtree, though not definitive, suggested that the Santa Catalina Island rattlesnake is mostly closely related to the red diamond rattlesnake, as initially theorized–and that the observed similarity to the Mojave rattlesnake likely reflects either “convergent evolution” or the retention of primitive character states. This relationship was further supported by more recent genetic research . “This is another situation in Baja California reptiles where morphological similarity does not reflect phylogenetic relationships,” state the authors. All of this underscores the fact that island species are some of the most interesting species to study from an evolutionary standpoint. They are a true testing ground for nature’s evolutionary design trajectory–and comparisons to mainland relatives tend to yield significant scientific insights. The rare and rattleless Santa Catalina Island rattlesnake is a case in point. Editorial Standards Reprints & Permissions Join The Conversation One Community. Many Voices. Create a free account to share your thoughts.  Forbes Community Guidelines Our community is about connecting people through open and thoughtful conversations. We want our readers to share their views and exchange ideas and facts in a safe space. 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Please read the full list of posting rules found in our site's  Terms of Service. 187 IMAGES Edu Write 2 Tailed Hypothesis Two Tailed Hypothesis PPT Edu Write 2 Tailed Hypothesis Two-Tailed Hypothesis Test Hypothesis Testing: Upper, Lower, and Two Tailed Tests VIDEO Test of Hypothesis 1 tailed and 2 tailed Hypothesis One tailed hypothesis and two tailed hypothesis Two-Tailed Hypothesis Test for the Population Mean single tailed hypothesis test explained Hypothesis Testing & Two-tailed and One-tailed Test (tagalog and basic) COMMENTS One-Tailed and Two-Tailed Hypothesis Tests Explained Two-tailed hypothesis tests are also known as nondirectional and two-sided tests because you can test for effects in both directions. When you perform a two-tailed test, you split the significance level percentage between both tails of the distribution. ... Write the null and alternative hypothesis using a 1-tailed and 2-tailed test for each ... 5.2 5.2 - Writing Hypotheses. The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ( H 0) and an alternative hypothesis ( H a ). When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the ... Two-Tailed Hypothesis Tests: 3 Example Problems Two-Tailed Hypothesis Tests: 3 Example Problems. In statistics, we use hypothesis tests to determine whether some claim about a population parameter is true or not. Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter ... Hypothesis Testing So let's perform the step -1 of hypothesis testing which is: Specify the Null (H0) and Alternate (H1) hypothesis. Null hypothesis (H0): The null hypothesis here is what currently stated to be true about the population. In our case it will be the average height of students in the batch is 100. H0 : μ = 100. One-tailed and two-tailed tests (video) To decide if a one-tailed test can be used, one has to have some extra information about the experiment to know the direction from the mean (H1: drug lowers the response time). If the direction of the effect is unknown, a two tailed test has to be used, and the H1 must be stated in a way where the direction of the effect is left uncertain (H1 ... What Is a Two-Tailed Test? Definition and Example Two-Tailed Test: A two-tailed test is a statistical test in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values ... Research Hypothesis In Psychology: Types, & Examples If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis. Make it Testable: Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of ... Two Tailed Test: Definition, Examples A two tailed test tells you that you're finding the area in the middle of a distribution. In other words, your rejection region (the place where you would reject the null hypothesis) is in both tails. For example, let's say you were running a z test with an alpha level of 5% (0.05). In a one tailed test, the entire 5% would be in a single tail. Hypothesis testing: One-tailed and two-tailed tests At this point, you might use a statistical test, like unpaired or 2-sample t-test, to see if there's a significant difference between the two groups' means. Typically, an unpaired t-test starts with two hypotheses. The first hypothesis is called the null hypothesis, and it basically says there's no difference in the means of the two groups. Hypothesis Testing There are 5 main steps in hypothesis testing: State your research hypothesis as a null hypothesis and alternate hypothesis (H o) and (H a or H 1 ). Collect data in a way designed to test the hypothesis. Perform an appropriate statistical test. Decide whether to reject or fail to reject your null hypothesis. Present the findings in your results ... Two Tailed Hypothesis A two-tailed alternative hypothesis is generally framed to show that a parameter is simply different from a certain value, without specifying the direction of the difference. Using mathematical notation, for a population mean (μ) and a proposed value (k), the two-tailed hypothesis would look like: H1: μ ≠ k. Hypothesis Testing: Upper-, Lower, and Two Tailed Tests Step 1. Set up hypotheses and select the level of significance α. H 0: Null hypothesis (no change, no difference); H 1: Research hypothesis (investigator's belief); α =0.05. Upper-tailed, Lower-tailed, Two-tailed Tests. The research or alternative hypothesis can take one of three forms. Two-Tailed Test in Statistics Two-Tailed Test Example. A two-tailed hypothesis test example: A machine is used to fill bags with coffee, and each bag is 1 kg. A randomly selected sample of 30 bags has a mean weight of 1.01 kg ... 7.2.2 Hypothesis A non-directional experimental hypothesis (also known as two-tailed) does not predict the direction of the change/difference (it is an 'open goal' i.e. anything could happen) A non-directional hypothesis is usually used when there is either no or little previous research which support a particular theory or outcome i.e. what the researcher ... Statistics The test statistic is used to decide the outcome of the hypothesis test. The test statistic is a standardized value calculated from the sample. The formula for the test statistic (TS) of a population mean is: x ¯ − μ s ⋅ n. x ¯ − μ is the difference between the sample mean ( x ¯) and the claimed population mean ( μ ). How to Write a Strong Hypothesis Developing a hypothesis (with example) Step 1. Ask a question. Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Example: Research question. 11.4: One- and Two-Tailed Tests The one-tailed hypothesis is rejected only if the sample proportion is much greater than \(0.5\). The alternative hypothesis in the two-tailed test is \(\pi \neq 0.5\). In the one-tailed test it is \(\pi > 0.5\). You should always decide whether you are going to use a one-tailed or a two-tailed probability before looking at the data. One and Two Tailed Tests A one-tailed test looks for an increase or decrease in the parameter whereas a two-tailed test looks for any change in the parameter (which can be any change- increase or decrease). We can perform the test at any level (usually 1%, 5% or 10%). For example, performing the test at a 5% level means that there is a 5% chance of wrongly rejecting H 0. One Tailed Test or Two in Hypothesis Testing: How ... The two red tails are the alpha level, divided by two (i.e. α/2). Alpha levels (sometimes just called "significance levels") are used in hypothesis tests; it is the probability of making the wrong decision when the null hypothesis is true. A one-tailed test has the entire 5% of the alpha level in one tail (in either the left, or the right tail). Two Sample t-test: Definition, Formula, and Example A two-sample t-test always uses the following null hypothesis: H 0: μ 1 = μ 2 (the two population means are equal) The alternative hypothesis can be either two-tailed, left-tailed, or right-tailed: H 1 (two-tailed): μ 1 ≠ μ 2 (the two population means are not equal) H 1 (left-tailed): μ 1 < μ 2 (population 1 mean is less than population ... One Tailed and Two Tailed Tests, Critical Values ... This statistics video tutorial explains when you should use a one tailed test vs a two tailed test when solving problems associated with hypothesis testing. ... Hypotheses for a two-sample t test (video) On the other hand, a two-sample T test is where you're thinking about two different populations. For example, you could be thinking about a population of men, and you could be thinking about the population of women. And you wanna compare the means between these two, say, the mean salary. So, you have the mean salary for men and you have the ... One-Tailed Hypothesis Tests: 3 Example Problems In statistics, we use hypothesis tests to determine whether some claim about a population parameter is true or not. Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H 0 (Null Hypothesis): Population parameter = ≤, ≥ some value One-Tailed T-Test: Hypothesis Testing Explained The t-test can be further categorized into one-tailed and two-tailed tests, each with its specific application and interpretation. Understanding the One-Tailed T-Test. A one-tailed t-test is a type of hypothesis test that examines whether the mean of a population is significantly greater than or less than a specific value. Why The World's Rarest Rattlesnake Is A 'Scientific ... "These results make the hypothesis of the loss of the rattle as a stealth adaptation for hunting on the vegetation very unlikely, since such a low frequency of use of vegetation may not function ... assignment essay homework paper phd report resume review speech thesis