how to present results in quantitative research

How To Write The Results/Findings Chapter

For quantitative studies (dissertations & theses).

By: Derek Jansen (MBA). Expert Reviewed By: Kerryn Warren (PhD) | July 2021

So, you’ve completed your quantitative data analysis and it’s time to report on your findings. But where do you start? In this post, we’ll walk you through the results chapter (also called the findings or analysis chapter), step by step, so that you can craft this section of your dissertation or thesis with confidence. If you’re looking for information regarding the results chapter for qualitative studies, you can find that here .

Overview: Quantitative Results Chapter

• What exactly the results/findings/analysis chapter is
• What you need to include in your results chapter
• How to structure your results chapter
• A few tips and tricks for writing top-notch chapter

What exactly is the results chapter?

The results chapter (also referred to as the findings or analysis chapter) is one of the most important chapters of your dissertation or thesis because it shows the reader what you’ve found in terms of the quantitative data you’ve collected. It presents the data using a clear text narrative, supported by tables, graphs and charts. In doing so, it also highlights any potential issues (such as outliers or unusual findings) you’ve come across.

But how’s that different from the discussion chapter?

Well, in the results chapter, you only present your statistical findings. Only the numbers, so to speak – no more, no less. Contrasted to this, in the discussion chapter , you interpret your findings and link them to prior research (i.e. your literature review), as well as your research objectives and research questions . In other words, the results chapter presents and describes the data, while the discussion chapter interprets the data.

Let’s look at an example.

In your results chapter, you may have a plot that shows how respondents to a survey  responded: the numbers of respondents per category, for instance. You may also state whether this supports a hypothesis by using a p-value from a statistical test. But it is only in the discussion chapter where you will say why this is relevant or how it compares with the literature or the broader picture. So, in your results chapter, make sure that you don’t present anything other than the hard facts – this is not the place for subjectivity.

It’s worth mentioning that some universities prefer you to combine the results and discussion chapters. Even so, it is good practice to separate the results and discussion elements within the chapter, as this ensures your findings are fully described. Typically, though, the results and discussion chapters are split up in quantitative studies. If you’re unsure, chat with your research supervisor or chair to find out what their preference is.

What should you include in the results chapter?

Following your analysis, it’s likely you’ll have far more data than are necessary to include in your chapter. In all likelihood, you’ll have a mountain of SPSS or R output data, and it’s your job to decide what’s most relevant. You’ll need to cut through the noise and focus on the data that matters.

This doesn’t mean that those analyses were a waste of time – on the contrary, those analyses ensure that you have a good understanding of your dataset and how to interpret it. However, that doesn’t mean your reader or examiner needs to see the 165 histograms you created! Relevance is key.

How do I decide what’s relevant?

At this point, it can be difficult to strike a balance between what is and isn’t important. But the most important thing is to ensure your results reflect and align with the purpose of your study .  So, you need to revisit your research aims, objectives and research questions and use these as a litmus test for relevance. Make sure that you refer back to these constantly when writing up your chapter so that you stay on track.

As a general guide, your results chapter will typically include the following:

• Some demographic data about your sample
• Reliability tests (if you used measurement scales)
• Descriptive statistics
• Inferential statistics (if your research objectives and questions require these)
• Hypothesis tests (again, if your research objectives and questions require these)

We’ll discuss each of these points in more detail in the next section.

Importantly, your results chapter needs to lay the foundation for your discussion chapter . This means that, in your results chapter, you need to include all the data that you will use as the basis for your interpretation in the discussion chapter.

For example, if you plan to highlight the strong relationship between Variable X and Variable Y in your discussion chapter, you need to present the respective analysis in your results chapter – perhaps a correlation or regression analysis.

Need a helping hand?

How do I write the results chapter?

There are multiple steps involved in writing up the results chapter for your quantitative research. The exact number of steps applicable to you will vary from study to study and will depend on the nature of the research aims, objectives and research questions . However, we’ll outline the generic steps below.

Step 1 – Revisit your research questions

The first step in writing your results chapter is to revisit your research objectives and research questions . These will be (or at least, should be!) the driving force behind your results and discussion chapters, so you need to review them and then ask yourself which statistical analyses and tests (from your mountain of data) would specifically help you address these . For each research objective and research question, list the specific piece (or pieces) of analysis that address it.

At this stage, it’s also useful to think about the key points that you want to raise in your discussion chapter and note these down so that you have a clear reminder of which data points and analyses you want to highlight in the results chapter. Again, list your points and then list the specific piece of analysis that addresses each point. 

Next, you should draw up a rough outline of how you plan to structure your chapter . Which analyses and statistical tests will you present and in what order? We’ll discuss the “standard structure” in more detail later, but it’s worth mentioning now that it’s always useful to draw up a rough outline before you start writing (this advice applies to any chapter).

Step 2 – Craft an overview introduction

As with all chapters in your dissertation or thesis, you should start your quantitative results chapter by providing a brief overview of what you’ll do in the chapter and why . For example, you’d explain that you will start by presenting demographic data to understand the representativeness of the sample, before moving onto X, Y and Z.

This section shouldn’t be lengthy – a paragraph or two maximum. Also, it’s a good idea to weave the research questions into this section so that there’s a golden thread that runs through the document.

Step 3 – Present the sample demographic data

The first set of data that you’ll present is an overview of the sample demographics – in other words, the demographics of your respondents.

For example:

• What age range are they?
• How is gender distributed?
• How is ethnicity distributed?
• What areas do the participants live in?

The purpose of this is to assess how representative the sample is of the broader population. This is important for the sake of the generalisability of the results. If your sample is not representative of the population, you will not be able to generalise your findings. This is not necessarily the end of the world, but it is a limitation you’ll need to acknowledge.

Of course, to make this representativeness assessment, you’ll need to have a clear view of the demographics of the population. So, make sure that you design your survey to capture the correct demographic information that you will compare your sample to.

But what if I’m not interested in generalisability?

Well, even if your purpose is not necessarily to extrapolate your findings to the broader population, understanding your sample will allow you to interpret your findings appropriately, considering who responded. In other words, it will help you contextualise your findings . For example, if 80% of your sample was aged over 65, this may be a significant contextual factor to consider when interpreting the data. Therefore, it’s important to understand and present the demographic data.

 Step 4 – Review composite measures and the data “shape”.

Before you undertake any statistical analysis, you’ll need to do some checks to ensure that your data are suitable for the analysis methods and techniques you plan to use. If you try to analyse data that doesn’t meet the assumptions of a specific statistical technique, your results will be largely meaningless. Therefore, you may need to show that the methods and techniques you’ll use are “allowed”.

Most commonly, there are two areas you need to pay attention to:

#1: Composite measures

The first is when you have multiple scale-based measures that combine to capture one construct – this is called a composite measure .  For example, you may have four Likert scale-based measures that (should) all measure the same thing, but in different ways. In other words, in a survey, these four scales should all receive similar ratings. This is called “ internal consistency ”.

Internal consistency is not guaranteed though (especially if you developed the measures yourself), so you need to assess the reliability of each composite measure using a test. Typically, Cronbach’s Alpha is a common test used to assess internal consistency – i.e., to show that the items you’re combining are more or less saying the same thing. A high alpha score means that your measure is internally consistent. A low alpha score means you may need to consider scrapping one or more of the measures.

#2: Data shape

The second matter that you should address early on in your results chapter is data shape. In other words, you need to assess whether the data in your set are symmetrical (i.e. normally distributed) or not, as this will directly impact what type of analyses you can use. For many common inferential tests such as T-tests or ANOVAs (we’ll discuss these a bit later), your data needs to be normally distributed. If it’s not, you’ll need to adjust your strategy and use alternative tests.

To assess the shape of the data, you’ll usually assess a variety of descriptive statistics (such as the mean, median and skewness), which is what we’ll look at next.

Step 5 – Present the descriptive statistics

Now that you’ve laid the foundation by discussing the representativeness of your sample, as well as the reliability of your measures and the shape of your data, you can get started with the actual statistical analysis. The first step is to present the descriptive statistics for your variables.

For scaled data, this usually includes statistics such as:

• The mean – this is simply the mathematical average of a range of numbers.
• The median – this is the midpoint in a range of numbers when the numbers are arranged in order.
• The mode – this is the most commonly repeated number in the data set.
• Standard deviation – this metric indicates how dispersed a range of numbers is. In other words, how close all the numbers are to the mean (the average).
• Skewness – this indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph (this is called a normal or parametric distribution), or do they lean to the left or right (this is called a non-normal or non-parametric distribution).
• Kurtosis – this metric indicates whether the data are heavily or lightly-tailed, relative to the normal distribution. In other words, how peaked or flat the distribution is.

A large table that indicates all the above for multiple variables can be a very effective way to present your data economically. You can also use colour coding to help make the data more easily digestible.

For categorical data, where you show the percentage of people who chose or fit into a category, for instance, you can either just plain describe the percentages or numbers of people who responded to something or use graphs and charts (such as bar graphs and pie charts) to present your data in this section of the chapter.

When using figures, make sure that you label them simply and clearly , so that your reader can easily understand them. There’s nothing more frustrating than a graph that’s missing axis labels! Keep in mind that although you’ll be presenting charts and graphs, your text content needs to present a clear narrative that can stand on its own. In other words, don’t rely purely on your figures and tables to convey your key points: highlight the crucial trends and values in the text. Figures and tables should complement the writing, not carry it .

Depending on your research aims, objectives and research questions, you may stop your analysis at this point (i.e. descriptive statistics). However, if your study requires inferential statistics, then it’s time to deep dive into those .

Step 6 – Present the inferential statistics

Inferential statistics are used to make generalisations about a population , whereas descriptive statistics focus purely on the sample . Inferential statistical techniques, broadly speaking, can be broken down into two groups .

First, there are those that compare measurements between groups , such as t-tests (which measure differences between two groups) and ANOVAs (which measure differences between multiple groups). Second, there are techniques that assess the relationships between variables , such as correlation analysis and regression analysis. Within each of these, some tests can be used for normally distributed (parametric) data and some tests are designed specifically for use on non-parametric data.

There are a seemingly endless number of tests that you can use to crunch your data, so it’s easy to run down a rabbit hole and end up with piles of test data. Ultimately, the most important thing is to make sure that you adopt the tests and techniques that allow you to achieve your research objectives and answer your research questions .

In this section of the results chapter, you should try to make use of figures and visual components as effectively as possible. For example, if you present a correlation table, use colour coding to highlight the significance of the correlation values, or scatterplots to visually demonstrate what the trend is. The easier you make it for your reader to digest your findings, the more effectively you’ll be able to make your arguments in the next chapter.

Step 7 – Test your hypotheses

If your study requires it, the next stage is hypothesis testing. A hypothesis is a statement , often indicating a difference between groups or relationship between variables, that can be supported or rejected by a statistical test. However, not all studies will involve hypotheses (again, it depends on the research objectives), so don’t feel like you “must” present and test hypotheses just because you’re undertaking quantitative research.

The basic process for hypothesis testing is as follows:

• Specify your null hypothesis (for example, “The chemical psilocybin has no effect on time perception).
• Specify your alternative hypothesis (e.g., “The chemical psilocybin has an effect on time perception)
• Set your significance level (this is usually 0.05)
• Calculate your statistics and find your p-value (e.g., p=0.01)
• Draw your conclusions (e.g., “The chemical psilocybin does have an effect on time perception”)

Finally, if the aim of your study is to develop and test a conceptual framework , this is the time to present it, following the testing of your hypotheses. While you don’t need to develop or discuss these findings further in the results chapter, indicating whether the tests (and their p-values) support or reject the hypotheses is crucial.

Step 8 – Provide a chapter summary

To wrap up your results chapter and transition to the discussion chapter, you should provide a brief summary of the key findings . “Brief” is the keyword here – much like the chapter introduction, this shouldn’t be lengthy – a paragraph or two maximum. Highlight the findings most relevant to your research objectives and research questions, and wrap it up.

Some final thoughts, tips and tricks

Now that you’ve got the essentials down, here are a few tips and tricks to make your quantitative results chapter shine:

• When writing your results chapter, report your findings in the past tense . You’re talking about what you’ve found in your data, not what you are currently looking for or trying to find.
• Structure your results chapter systematically and sequentially . If you had two experiments where findings from the one generated inputs into the other, report on them in order.
• Make your own tables and graphs rather than copying and pasting them from statistical analysis programmes like SPSS. Check out the DataIsBeautiful reddit for some inspiration.
• Once you’re done writing, review your work to make sure that you have provided enough information to answer your research questions , but also that you didn’t include superfluous information.

If you’ve got any questions about writing up the quantitative results chapter, please leave a comment below. If you’d like 1-on-1 assistance with your quantitative analysis and discussion, check out our hands-on coaching service , or book a free consultation with a friendly coach.

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Quantitative Data Analysis

9 Presenting the Results of Quantitative Analysis

Mikaila Mariel Lemonik Arthur

This chapter provides an overview of how to present the results of quantitative analysis, in particular how to create effective tables for displaying quantitative results and how to write quantitative research papers that effectively communicate the methods used and findings of quantitative analysis.

Writing the Quantitative Paper

Standard quantitative social science papers follow a specific format. They begin with a title page that includes a descriptive title, the author(s)’ name(s), and a 100 to 200 word abstract that summarizes the paper. Next is an introduction that makes clear the paper’s research question, details why this question is important, and previews what the paper will do. After that comes a literature review, which ends with a summary of the research question(s) and/or hypotheses. A methods section, which explains the source of data, sample, and variables and quantitative techniques used, follows. Many analysts will include a short discussion of their descriptive statistics in the methods section. A findings section details the findings of the analysis, supported by a variety of tables, and in some cases graphs, all of which are explained in the text. Some quantitative papers, especially those using more complex techniques, will include equations. Many papers follow the findings section with a discussion section, which provides an interpretation of the results in light of both the prior literature and theory presented in the literature review and the research questions/hypotheses. A conclusion ends the body of the paper. This conclusion should summarize the findings, answering the research questions and stating whether any hypotheses were supported, partially supported, or not supported. Limitations of the research are detailed. Papers typically include suggestions for future research, and where relevant, some papers include policy implications. After the body of the paper comes the works cited; some papers also have an Appendix that includes additional tables and figures that did not fit into the body of the paper or additional methodological details. While this basic format is similar for papers regardless of the type of data they utilize, there are specific concerns relating to quantitative research in terms of the methods and findings that will be discussed here.

In the methods section, researchers clearly describe the methods they used to obtain and analyze the data for their research. When relying on data collected specifically for a given paper, researchers will need to discuss the sample and data collection; in most cases, though, quantitative research relies on pre-existing datasets. In these cases, researchers need to provide information about the dataset, including the source of the data, the time it was collected, the population, and the sample size. Regardless of the source of the data, researchers need to be clear about which variables they are using in their research and any transformations or manipulations of those variables. They also need to explain the specific quantitative techniques that they are using in their analysis; if different techniques are used to test different hypotheses, this should be made clear. In some cases, publications will require that papers be submitted along with any code that was used to produce the analysis (in SPSS terms, the syntax files), which more advanced researchers will usually have on hand. In many cases, basic descriptive statistics are presented in tabular form and explained within the methods section.

The findings sections of quantitative papers are organized around explaining the results as shown in tables and figures. Not all results are depicted in tables and figures—some minor or null findings will simply be referenced—but tables and figures should be produced for all findings to be discussed at any length. If there are too many tables and figures, some can be moved to an appendix after the body of the text and referred to in the text (e.g. “See Table 12 in Appendix A”).

Discussions of the findings should not simply restate the contents of the table. Rather, they should explain and interpret it for readers, and they should do so in light of the hypothesis or hypotheses that are being tested. Conclusions—discussions of whether the hypothesis or hypotheses are supported or not supported—should wait for the conclusion of the paper.

Creating Effective Tables

When creating tables to display the results of quantitative analysis, the most important goals are to create tables that are clear and concise but that also meet standard conventions in the field. This means, first of all, paring down the volume of information produced in the statistical output to just include the information most necessary for interpreting the results, but doing so in keeping with standard table conventions. It also means making tables that are well-formatted and designed, so that readers can understand what the tables are saying without struggling to find information. For example, tables (as well as figures such as graphs) need clear captions; they are typically numbered and referred to by number in the text. Columns and rows should have clear headings. Depending on the content of the table, formatting tools may need to be used to set off header rows/columns and/or total rows/columns; cell-merging tools may be necessary; and shading may be important in tables with many rows or columns.

Here, you will find some instructions for creating tables of results from descriptive, crosstabulation, correlation, and regression analysis that are clear, concise, and meet normal standards for data display in social science. In addition, after the instructions for creating tables, you will find an example of how a paper incorporating each table might describe that table in the text.

Descriptive Statistics

When presenting the results of descriptive statistics, we create one table with columns for each type of descriptive statistic and rows for each variable. Note, of course, that depending on level of measurement only certain descriptive statistics are appropriate for a given variable, so there may be many cells in the table marked with an — to show that this statistic is not calculated for this variable. So, consider the set of descriptive statistics below, for occupational prestige, age, highest degree earned, and whether the respondent was born in this country.

To display these descriptive statistics in a paper, one might create a table like Table 2. Note that for discrete variables, we use the value label in the table, not the value.

If we were then to discuss our descriptive statistics in a quantitative paper, we might write something like this (note that we do not need to repeat every single detail from the table, as readers can peruse the table themselves):

This analysis relies on four variables from the 2021 General Social Survey: occupational prestige score, age, highest degree earned, and whether the respondent was born in the United States. Descriptive statistics for all four variables are shown in Table 2. The median occupational prestige score is 47, with a range from 16 to 80. 50% of respondents had occupational prestige scores scores between 35 and 59. The median age of respondents is 53, with a range from 18 to 89. 50% of respondents are between ages 37 and 66. Both variables have little skew. Highest degree earned ranges from less than high school to a graduate degree; the median respondent has earned an associate’s degree, while the modal response (given by 39.8% of the respondents) is a high school degree. 88.8% of respondents were born in the United States.

Crosstabulation

When presenting the results of a crosstabulation, we simplify the table so that it highlights the most important information—the column percentages—and include the significance and association below the table. Consider the SPSS output below.

Table 4 shows how a table suitable for include in a paper might look if created from the SPSS output in Table 3. Note that we use asterisks to indicate the significance level of the results: * means p < 0.05; ** means p < 0.01; *** means p < 0.001; and no stars mean p > 0.05 (and thus that the result is not significant). Also note than N is the abbreviation for the number of respondents.

If we were going to discuss the results of this crosstabulation in a quantitative research paper, the discussion might look like this:

A crosstabulation of respondent’s class identification and their highest degree earned, with class identification as the independent variable, is significant, with a Spearman correlation of 0.419, as shown in Table 4. Among lower class and working class respondents, more than 50% had earned a high school degree. Less than 20% of poor respondents and less than 40% of working-class respondents had earned more than a high school degree. In contrast, the majority of middle class and upper class respondents had earned at least a bachelor’s degree. In fact, 50% of upper class respondents had earned a graduate degree.

Correlation

When presenting a correlating matrix, one of the most important things to note is that we only present half the table so as not to include duplicated results. Think of the line through the table where empty cells exist to represent the correlation between a variable and itself, and include only the triangle of data either above or below that line of cells. Consider the output in Table 5.

Table 6 shows what the contents of Table 5 might look like when a table is constructed in a fashion suitable for publication.

If we were to discuss the results of this bivariate correlation analysis in a quantitative paper, the discussion might look like this:

Bivariate correlations were run among variables measuring age, occupational prestige, the highest year of school respondents completed, and family income in constant 1986 dollars, as shown in Table 6. Correlations between age and highest year of school completed and between age and family income are not significant. All other correlations are positive and significant at the p<0.001 level. The correlation between age and occupational prestige is weak; the correlations between income and occupational prestige and between income and educational attainment are moderate, and the correlation between education and occupational prestige is strong.

To present the results of a regression, we create one table that includes all of the key information from the multiple tables of SPSS output. This includes the R 2 and significance of the regression, either the B or the beta values (different analysts have different preferences here) for each variable, and the standard error and significance of each variable. Consider the SPSS output in Table 7.

The regression output in shown in Table 7 contains a lot of information. We do not include all of this information when making tables suitable for publication. As can be seen in Table 8, we include the Beta (or the B), the standard error, and the significance asterisk for each variable; the R 2 and significance for the overall regression; the degrees of freedom (which tells readers the sample size or N); and the constant; along with the key to p/significance values.

If we were to discuss the results of this regression in a quantitative paper, the results might look like this:

Table 8 shows the results of a regression in which age, occupational prestige, and highest year of school completed are the independent variables and family income is the dependent variable. The regression results are significant, and all of the independent variables taken together explain 15.6% of the variance in family income. Age is not a significant predictor of income, while occupational prestige and educational attainment are. Educational attainment has a larger effect on family income than does occupational prestige. For every year of additional education attained, family income goes up on average by $3,988.545; for every one-unit increase in occupational prestige score, family income goes up on average by $522.887. [1]

• Choose two discrete variables and three continuous variables from a dataset of your choice. Produce appropriate descriptive statistics on all five of the variables and create a table of the results suitable for inclusion in a paper.
• Using the two discrete variables you have chosen, produce an appropriate crosstabulation, with significance and measure of association. Create a table of the results suitable for inclusion in a paper.
• Using the three continuous variables you have chosen, produce a correlation matrix. Create a table of the results suitable for inclusion in a paper.
• Using the three continuous variables you have chosen, produce a multivariate linear regression. Create a table of the results suitable for inclusion in a paper.
• Write a methods section describing the dataset, analytical methods, and variables you utilized in questions 1, 2, 3, and 4 and explaining the results of your descriptive analysis.
• Write a findings section explaining the results of the analyses you performed in questions 2, 3, and 4.
• Note that the actual numberical increase comes from the B values, which are shown in the SPSS output in Table 7 but not in the reformatted Table 8. ↵

Social Data Analysis Copyright © 2021 by Mikaila Mariel Lemonik Arthur is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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20 16. Reporting quantitative results

Chapter outline.

• Reporting quantitative results (8 minute read time)

Content warning: Brief discussion of violence against women.

16.1 Reporting quantitative results

Learning objectives.

Learners will be able to…

• Execute a quantitative research report using key elements for accuracy and openness

So you’ve completed your quantitative analyses and are ready to report your results. We’re going to spend some time talking about what matters in quantitative research reports, but the very first thing to understand is this: openness with your data and analyses is key. You should never hide what you did to get to a particular conclusion and, if someone wanted to and could ethically access your data, they should be able to replicate more or less exactly what you did. While your quantitative report won’t have every single step you took to get to your conclusion, it should have plenty of detail so someone can get the picture.

Below, I’m going to take you through the key elements of a quantitative research report. This overview is pretty general and conceptual, and it will be helpful for you to look at existing scholarly articles that deal with quantitative research (like ones in your literature review) to see the structure applied. Also keep in mind that your instructor may want the sections broken out slightly differently; nonetheless, the content I outline below should be in your research report.

Introduction and literature review

These are what you’re working on building with your research proposal this semester. They should be included as part of your research report so that readers have enough information to evaluate your research for themselves. What’s here should be very similar to the introduction and literature review from your research proposal, where you described the literature relevant to the study you wanted to do. With your results in hand, though, you may find that you have to add information to the literature you wrote previously to help orient the reader of the report to important topics needed to understand the results of your study.

In this section, you should explicitly lay out your study design – for instance, if it was experimental, be specific about the type of experimental design. Discuss the type of sampling that you used, if that’s applicable to your project. You should also go into a general description of your data, including the time period, any exclusions you made from the original data set and the source – i.e., did you collect it yourself or was it secondary data?  Next, talk about the specific statistical methods you used, like t- tests, Chi-square tests, or regression analyses. For descriptive statistics, you can be relatively general – you don’t need to say “I looked at means and medians,” for instance. You need to provide enough information here that someone could replicate what you did.

In this section, you should also discuss how you operationalized your variables. What did you mean when you asked about educational attainment – did you ask for a grade number, or did you ask them to pick a range that you turned into a category? This is key information for readers to understand your research. Remember when you were looking for ways to operationalize your variables? Be the kind of author who provides enough information on operationalization so people can actually understand what they did.

You’re going to run lots of different analyses to settle on what finally makes sense to get a result – positive or negative – for your study. For this section, you’re going to provide tables with descriptions of your sample, including, but not limited to, sample size, frequencies of sample characteristics like race and gender, levels of measurement, appropriate measures of central tendency, standard deviations and variances. Here you will also want to focus on the analyses you used to actually draw whatever conclusion you settled on, both descriptive and inferential (i.e., bivariate or multivariate).

The actual statistics you report depend entirely on the kind of statistical analysis you do. For instance, if you’re reporting on a logistic regression, it’s going to look a little different than reporting on an ANOVA. In the previous chapter, we provided links to open textbooks that detail how to conduct quantitative data analysis. You should look at these resources and consult with your research professor to help you determine what is expected in a report about the particular statistical method you used.

The important thing to remember here – as we mentioned above – is that you need to be totally transparent about your results, even and especially if they don’t support your hypothesis. There is value in a disproved hypothesis, too – you now know something about how the state of the world is not .

In this section, you’re going to connect your statistical results back to your hypothesis and discuss whether your results support your hypothesis or not. You are also going to talk about what the results mean for the larger field of study of which your research is a part, the implications of your findings if you’re evaluating some kind of intervention, and how your research relates to what is already out there in this field. When your research doesn’t pan out the way you expect, if you’re able to make some educated guesses as to why this might be (supported by literature if possible, but practice wisdom works too), share those as well.

Let’s take a minute to talk about what happens when your findings disprove your hypothesis or actually indicate something negative about the group you are studying. The discussion section is where you can contextualize “negative” findings. For example, say you conducted a study that indicated that a certain group is more likely to commit violent crime. Here, you have an opportunity to talk about why this might be the case outside of their membership in that group, and how membership in that group does not automatically mean someone will commit a violent crime. You can present mitigating factors, like a history of personal and community trauma. It’s extremely important to provide this relevant context so that your results are more difficult to use against a group you are studying in a way that doesn’t reflect your actual findings.

Limitations

In this section, you’re going to critique your own study. What are the advantages, disadvantages, and trade-offs of what you did to define and analyze your variables? Some questions you might consider include:  What limits the study’s applicability to the population at large? Were there trade-offs you had to make between rigor and available data? Did the statistical analyses you used mean that you could only get certain types of results? What would have made the study more widely applicable or more useful for a certain group? You should be thinking about this throughout the analysis process so you can properly contextualize your results.

In this section, you may also consider discussing any threats to internal validity that you identified and whether you think you can generalize your research. Finally, if you used any measurement tools that haven’t been validated yet, discuss how this could have affected your results.

Significance and conclusions

Finally, you want to use the conclusions section to bring it full circle for your reader – why did this research matter? Talk about how it contributed to knowledge around the topic and how might it be used to further practice. Identify and discuss ethical implications of your findings for social workers and social work research. Finally, make sure to talk about the next steps for you, other researchers, or policy-makers based on your research findings.

Key Takeaways

• Your quantitative research report should provide the reader with transparent, replicable methods and put your research into the context of existing literature, real-world practice and social work ethics.
• Think about the research project you are building now. What could a negative finding be, and how might you provide your reader with context to ensure that you are not harming your study population?

The process of determining how to measure a construct that cannot be directly observed

Ability to say that one variable "causes" something to happen to another variable. Very important to assess when thinking about studies that examine causation such as experimental or quasi-experimental designs.

Graduate research methods in social work Copyright © 2020 by Matthew DeCarlo, Cory Cummings, Kate Agnelli is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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7.1 Reading results in quantitative research

Learning objectives.

Learners will be able to…

• Describe how statistical significance and confidence intervals demonstrate which results are most important

Pre-awareness check (Knowledge)

What do you know about previously conducted research on your topic (e.g., statistical analyses, qualitative and quantitative results)?

If you recall, empirical journal articles are those that report the results of quantitative or qualitative data analyzed by the author. They follow a set structure—introduction, methods, results, discussion/conclusions. This chapter is about reading what is often the most challenging section: results.

Quantitative results

Quantitative articles often contain tables, and scanning them is a good way to begin reading the results. A table usually provides a quick, condensed summary of the report’s key findings. Tables are a concise way to report large amounts of data. Some tables present descriptive information about a researcher’s sample (often the first table in a results section). These tables will likely contain frequencies ( n ) and percentages (%). For example, if gender happened to be an important variable for the researcher’s analysis, a descriptive table would show how many and what percent of all study participants are of a particular gender. Frequencies or “how many” will probably be listed as n , while the percent symbol (%) might be used to indicate percentages. The symbol N is used for the entire sample size, and  n is used for the size of a portion of the entire sample.

In a table presenting a causal relationship, two sets of variables are represented. The independent variable , or cause, and the dependent variable , the effect. We’ll go into more detail on variables in Chapter 8. Independent variable attributes are typically presented in the table’s columns, while dependent variable attributes are presented in rows. This allows the reader to scan a table’s rows to see how values on the dependent variable change as the independent variable values change. Tables displaying results of quantitative analysis will also likely include some information about which relationships are significant or not. We will discuss the details of significance and p -values later in this section.

Let’s look at a specific example: Table 7.1 below.

Table 7.1 presents the association between gender and experiencing harassing behaviors at work. In this example, gender is the independent variable (the predictor) and the harassing behaviors listed are the dependent variables (the outcome). [1] Therefore, we place gender in the table’s columns and harassing behaviors in the table’s rows.

Reading across the table’s top row, we see that 2.9% of women in the sample reported experiencing subtle or obvious threats to their safety at work, while 4.7% of men in the sample reported the same. We can read across each of the rows of the table in this way. Reading across the bottom row, we see that 9.4% of women in the sample reported experiencing staring or invasion of their personal space at work while just 2.3% of men in the sample reported having the same experience. We’ll discuss  p- values later in this section.

While you can certainly scan tables for key results, they are often difficult to understand without reading the text of the article. The article and table were meant to complement each other, and the text should provide information on how the authors interpret their findings. The table is not redundant with the text of the results section. Additionally, the first table in most results sections is a summary of the study’s sample, which provides more background information on the study than information about hypotheses and findings. It is also a good idea to look back at the methods section of the article as the data analysis plan the authors outline should walk you through the steps they took to analyze their data which will inform how they report them in the results section.

Statistical significance

The statistics reported in Table 7.1 represent what the researchers found in their sample. The purpose of statistical analysis is usually to generalize from a the small number of people in a study’s sample to a larger population of people. Thus, the researchers intend to make causal arguments about harassing behaviors at workplaces beyond those covered in the sample.

Generalizing is key to understanding statistical significance . According to Cassidy et al. (2019), [2] 89% of research methods textbooks in psychology define statistical significance incorrectly. This includes an early draft of this textbook which defined statistical significance as “the likelihood that the relationships we observe could be caused by something other than chance.” If you have previously had a research methods class, this might sound familiar to you. It certainly did to me!

But statistical significance is less about “random chance” than more about the null hypothesis . Basically, at the beginning of a study a researcher develops a hypothesis about what they expect to find, usually that there is a statistical relationship between two or more variables . The null hypothesis is the opposite. It is the hypothesis that there is no relationship between the variables in a research study. Researchers then can hopefully reject the null hypothesis because they find a relationship between the variables.

For example, in Table 7.1 researchers were examining whether gender impacts harassment. Of course, researchers assumed that women were more likely to experience harassment than men. The null hypothesis, then, would be that gender has no impact on harassment. Once we conduct the study, our results will hopefully lead us to reject the null hypothesis because we find that gender impacts harassment. We would then generalize from our study’s sample to the larger population of people in the workplace.

Statistical significance is calculated using a p -value which is obtained by comparing the statistical results with a hypothetical set of results if the researchers re-ran their study a large number of times. Keeping with our example, imagine we re-ran our study with different men and women from different workplaces hundreds and hundred of times and we assume that the null hypothesis is true that gender has no impact on harassment. If results like ours come up pretty often when the null hypothesis is true, our results probably don’t mean much. “The smaller the p -value, the greater the statistical incompatibility with the null hypothesis” (Wasserstein & Lazar, 2016, p. 131). [3] Generally, researchers in the social sciences have set alpha at .05 for the value at which a result is significant ( p is less than or equal to .05) or not significant ( p is greater than .05). The p -value .05 refers to if less than 5% of those hypothetical results from re-running our study show the same or more extreme relationships when the null hypothesis is true. Researchers, however, may choose a stricter standard such as .01 in which 1% or less of those hypothetical results are more extreme or a more lenient standard like .1 in which 10% or less of those hypothetical results are more extreme than what was found in the study.

Let’s look back at Table 7.1. Which one of the relationships between gender and harassing behaviors is statistically significant? It’s the last one in the table, “staring or invasion of personal space,” whose p -value is .039 (under the p<.05 standard to establish statistical significance). Again, this indicates that if we re-ran our study over and over again and gender did not  impact staring/invasion of space (i.e., the null hypothesis was true), only 3.9% of the time would we find similar or more extreme differences between men and women than what we observed in our study. Thus, we conclude that for staring or invasion of space only , there is a statistically significant relationship.

For contrast, let’s look at “being pushed, hit, or grabbed” and run through the same analysis to see if it is statistically significant. If we re-ran our study over and over again and the null hypothesis was true, 48% of the time ( p =.48) we would find similar or more extreme differences between men and women. That means these results are not statistically significant.

This discussion should also highlight a point we discussed previously: that it is important to read the full results section, rather than simply relying on the summary in the abstract. If the abstract stated that most tests revealed no statistically significant relationships between gender and harassment, you would have missed the detail on which behaviors were and were not associated with gender. Read the full results section! And don’t be afraid to ask for help from a professor in understanding what you are reading, as results sections are often not written to be easily understood.

Statistical significance and p -values have been critiqued recently for a number of reasons, including that they are misused and misinterpreted (Wasserstein & Lazar, 2016) [4] , that researchers deliberately manipulate their analyses to have significant results (Head et al., 2015) [5] , and factor into the difficulty scientists have today in reproducing many of the results of previous social science studies (Peng, 2015). [6] For this reason, we share these principles, adapted from those put forth by the American Statistical Association, [7]  for understanding and using p -values in social science:

• p -values provide evidence against a null hypothesis.
• p -values do not indicate whether the results were produced by random chance alone or if the researcher’s hypothesis is true, though both are common misconceptions.
• Statistical significance can be detected in minuscule differences that have very little effect on the real world.
• Nuance is needed to interpret scientific findings, as a conclusion does not become true or false when the p -value passes from p =.051 to p =.049.
• Real-world decision-making must use more than reported p -values. It’s easy to run analyses of large datasets and only report the significant findings.
• Greater confidence can be placed in studies that pre-register their hypotheses and share their data and methods openly with the public.
• “By itself, a p -value does not provide a good measure of evidence regarding a model or hypothesis. For example, a p -value near .05 taken by itself offers only weak evidence against the null hypothesis. Likewise, a relatively large p -value does not imply evidence in favor of the null hypothesis; many other hypotheses may be equally or more consistent with the observed data” (Wasserstein & Lazar, 2016, p. 132).

Confidence intervals

Because of the limitations of p -values, scientists can use other methods to determine whether their models of the world are true. One common approach is to use a confidence interval , or a range of values in which the true value is likely to be found. Confidence intervals are helpful because, as principal #5 above points out, p -values do not measure the size of an effect (Greenland et al., 2016). [8] Remember, something that has very little impact on the world can be statistically significant, and the values in a confidence interval would be helpful. In our example from Table 7.1, imagine our analysis produced a confidence interval that women are 1.2-3.4 times more likely to experience “staring or invasion of personal space” than men. As with p -values, calculation for a confidence interval compares what was found in one study with a hypothetical set of results if we repeated the study over and over again. If we calculated 95% confidence intervals for all of the hypothetical set of hundreds and hundreds of studies, that would be our confidence interval. 

Confidence intervals are pretty intuitive. As of this writing, my wife and are expecting our second child. The doctor told us our due date was December 11th. But the doctor also told us that December 11th was only their best estimate. They were actually 95% sure our baby might be born any time in the 30-day period between November 27th and December 25th. Confidence intervals are often listed with a percentage, like 90% or 95%, and a range of values, such as between November 27th and December 25th. You can read that as: “we are 95% sure your baby will be born between November 27th and December 25th because we’ve studied hundreds of thousands of fetuses and mothers, and we’re 95% sure your baby will be within these two dates.”

Notice that we’re hedging our bets here by using words like “best estimate.” When testing hypotheses, social scientists generally phrase their findings in a tentative way, talking about what results “indicate” or “support,” rather than making bold statements about what their results “prove.” Social scientists have humility because they understand the limitations of their knowledge. In a literature review, using a single study or fact to “prove” an argument right or wrong is often a signal to the person reading your literature review (usually your professor) that you may not have appreciated the limitations of that study or its place in the broader literature on the topic. Strong arguments in a literature review include multiple facts and ideas that span across multiple studies.

You can learn more about creating tables, reading tables, and tests of statistical significance in a class focused exclusively on statistical analysis. We provide links to many free and openly licensed resources on statistics in Chapter 16. For now, we hope this brief introduction to reading tables will improve your confidence in reading and understanding the results sections in quantitative empirical articles.

Key Takeaways

• The results section of empirical articles are often the most difficult to understand.
• To understand a quantitative results section, look for results that were statistically significant and examine the confidence interval, if provided.

Post-awareness check (Emotional)

On a scale of 1-10 (10 being excellent), how would you rate your confidence level in your ability to understand a quantitative results section in empirical articles on your topic of interest?

TRACK 1 (IF YOU ARE CREATING A RESEARCH PROPOSAL FOR THIS CLASS)

Select a quantitative empirical article related to your topic.

• Write down the results the authors identify as statistically significant in the results section.
• How do the authors interpret their results in the discussion section?
• Do the authors provide enough information in the introduction for you to understand their results?

TRACK 2 (IF YOU  AREN’T CREATING A RESEARCH PROPOSAL FOR THIS CLASS)

You are interested in researching the effects of race-based stress and burnout among social workers.

Select a quantitative empirical article related to this topic.

• It wouldn’t make any sense to say that people’s workplace experiences predict their gender, so in this example, the question of which is the independent variable and which are the dependent variables has a pretty obvious answer. ↵
• Cassidy, S. A., Dimova, R., Giguère, B., Spence, J. R., & Stanley, D. J. (2019). Failing grade: 89% of introduction-to-psychology textbooks that define or explain statistical significance do so incorrectly. Advances in Methods and Practices in Psychological Science ,  2 (3), 233-239. ↵
• Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p -values: context, process, and purpose. The American Statistician, 70 , p. 129-133. ↵
• Head, M. L., Holman, L., Lanfear, R., Kahn, A. T., & Jennions, M. D. (2015). The extent and consequences of p-hacking in science. PLoS biology, 13 (3). ↵
• Peng, R. (2015), The reproducibility crisis in science: A statistical counterattack. Significance , 12 , 30–32. ↵
• Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations.  European journal of epidemiology ,  31 (4), 337-350. ↵

report the results of a quantitative or qualitative data analysis conducted by the author

a quick, condensed summary of the report’s key findings arranged by row and column

causes a change in the dependent variable

a variable that depends on changes in the independent variable

(as in generalization) to make claims about a large population based on a smaller sample of people or items

"Assuming that the null hypothesis is true and the study is repeated an infinite number times by drawing random samples from the same populations(s), less than 5% of these results will be more extreme than the current result" (Cassidy et al., 2019, p. 233).

the assumption that no relationship exists between the variables in question

“a logical grouping of attributes that can be observed and measured and is expected to vary from person to person in a population” (Gillespie & Wagner, 2018, p. 9)

summarizes the incompatibility between a particular set of data and a proposed model for the data, usually the null hypothesis. The lower the p-value, the more inconsistent the data are with the null hypothesis, indicating that the relationship is statistically significant.

a range of values in which the true value is likely to be, to provide a more accurate description of their data

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• Knowledge Base

Methodology

• What Is Quantitative Research? | Definition, Uses & Methods

What Is Quantitative Research? | Definition, Uses & Methods

Published on June 12, 2020 by Pritha Bhandari . Revised on June 22, 2023.

Quantitative research is the process of collecting and analyzing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalize results to wider populations.

Quantitative research is the opposite of qualitative research , which involves collecting and analyzing non-numerical data (e.g., text, video, or audio).

Quantitative research is widely used in the natural and social sciences: biology, chemistry, psychology, economics, sociology, marketing, etc.

• What is the demographic makeup of Singapore in 2020?
• How has the average temperature changed globally over the last century?
• Does environmental pollution affect the prevalence of honey bees?
• Does working from home increase productivity for people with long commutes?

Table of contents

Quantitative research methods, quantitative data analysis, advantages of quantitative research, disadvantages of quantitative research, other interesting articles, frequently asked questions about quantitative research.

You can use quantitative research methods for descriptive, correlational or experimental research.

• In descriptive research , you simply seek an overall summary of your study variables.
• In correlational research , you investigate relationships between your study variables.
• In experimental research , you systematically examine whether there is a cause-and-effect relationship between variables.

Correlational and experimental research can both be used to formally test hypotheses , or predictions, using statistics. The results may be generalized to broader populations based on the sampling method used.

To collect quantitative data, you will often need to use operational definitions that translate abstract concepts (e.g., mood) into observable and quantifiable measures (e.g., self-ratings of feelings and energy levels).

Note that quantitative research is at risk for certain research biases , including information bias , omitted variable bias , sampling bias , or selection bias . Be sure that you’re aware of potential biases as you collect and analyze your data to prevent them from impacting your work too much.

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Once data is collected, you may need to process it before it can be analyzed. For example, survey and test data may need to be transformed from words to numbers. Then, you can use statistical analysis to answer your research questions .

Descriptive statistics will give you a summary of your data and include measures of averages and variability. You can also use graphs, scatter plots and frequency tables to visualize your data and check for any trends or outliers.

Using inferential statistics , you can make predictions or generalizations based on your data. You can test your hypothesis or use your sample data to estimate the population parameter .

First, you use descriptive statistics to get a summary of the data. You find the mean (average) and the mode (most frequent rating) of procrastination of the two groups, and plot the data to see if there are any outliers.

You can also assess the reliability and validity of your data collection methods to indicate how consistently and accurately your methods actually measured what you wanted them to.

Quantitative research is often used to standardize data collection and generalize findings . Strengths of this approach include:

• Replication

Repeating the study is possible because of standardized data collection protocols and tangible definitions of abstract concepts.

• Direct comparisons of results

The study can be reproduced in other cultural settings, times or with different groups of participants. Results can be compared statistically.

• Large samples

Data from large samples can be processed and analyzed using reliable and consistent procedures through quantitative data analysis.

• Hypothesis testing

Using formalized and established hypothesis testing procedures means that you have to carefully consider and report your research variables, predictions, data collection and testing methods before coming to a conclusion.

Despite the benefits of quantitative research, it is sometimes inadequate in explaining complex research topics. Its limitations include:

• Superficiality

Using precise and restrictive operational definitions may inadequately represent complex concepts. For example, the concept of mood may be represented with just a number in quantitative research, but explained with elaboration in qualitative research.

• Narrow focus

Predetermined variables and measurement procedures can mean that you ignore other relevant observations.

• Structural bias

Despite standardized procedures, structural biases can still affect quantitative research. Missing data , imprecise measurements or inappropriate sampling methods are biases that can lead to the wrong conclusions.

• Lack of context

Quantitative research often uses unnatural settings like laboratories or fails to consider historical and cultural contexts that may affect data collection and results.

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If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square goodness of fit test
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Inclusion and exclusion criteria

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

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.

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How to present your data in quantitative research lecture (CC-BY, 2020)

CC BY is the correct license for this work. Ignore the ones in the slides: use this materials as you like, with attribution. (KW, 02-2020)

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Mastering the results chapter in quantitative research.

Article created from: https://youtu.be/9WFhfQAP6R4?si=5jzHlh_-A4umWDCx

Crafting the Perfect Results Chapter for Your Quantitative Study

Welcome to a comprehensive guide on how to approach the results chapter in a quantitative study, whether it is part of a dissertation, thesis, or any other academic research project. Understanding the distinction between the results and discussion chapters and knowing how to present your data correctly is crucial for conveying your findings effectively.

Understanding the Results Chapter

At its core, the results chapter is designed to showcase the outcomes of your quantitative analysis. It systematically presents the statistical data you've generated, using a clear text-based narrative supported by tables, graphs, and charts. This chapter is critical as it demonstrates what you have discovered through your data collection and analysis, without delving into subjective interpretation or linking findings to existing literature—that's the job for the discussion chapter.

Key Differences Between Results and Discussion

Results Chapter : Focuses solely on presenting statistical findings, including any issues like statistical outliers or unusual findings, without interpretation.

Discussion Chapter : Interprets the findings, linking them back to the literature review, research objectives, and questions, thus painting a broader picture of the research implications.

Structuring Your Results Chapter

Revisit Research Objectives and Questions : Begin by aligning your analyses with your research objectives and questions. This step ensures you only include relevant data in your chapter.

Sample Demographics : Present an overview of your sample's demographics to assess representativeness and contextualize findings accurately.

Data Suitability Checks : Before diving into the core statistical analysis, ensure your data meets the necessary assumptions for your chosen methods.

Descriptive Statistics : Start your actual analysis by presenting descriptive statistics for your variables, laying a foundation for inferential statistics.

Inferential Statistics : Use inferential statistics to make predictions about the population based on your sample, focusing on comparing measurements between groups or assessing relationships between variables.

Hypothesis Testing : If applicable, test your hypotheses using your statistical data, clearly supporting or rejecting each hypothesis based on your findings.

Conclusion : Conclude the chapter with a brief summary of the key findings relevant to your research objectives and questions, setting the stage for the discussion chapter.

Tips for Writing Your Results Chapter

Ensure that every piece of analysis directly addresses your research objectives and questions.

Use tables, graphs, and charts effectively to present your data, but make sure your narrative can stand on its own without relying solely on these visual aids.

Be selective with your analysis methods to avoid overwhelming your chapter with unnecessary data.

Clearly label all figures and tables for easy understanding.

Keep your conclusion brief, highlighting only the most crucial findings.

By following these guidelines, you can craft a results chapter that not only presents your data effectively but also lays a solid foundation for your discussion chapter. Remember, the goal is to present the hard facts and figures clearly and systematically, without interpretation.

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Original research article, how to manifest the fertilizer reduction effect of pro-environmental agricultural technologies from the perspective of farmers’ perception and behavioral adoption.

• 1 School of Economics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, China
• 2 State Key Laboratory of Earth Surface Processes and Resource Ecology (ESPRE), Beijing Normal University, Beijing, China
• 3 School of Natural Resources, Faculty of Geographical Science, Beijing Normal University, Beijing, China
• 4 School of Economics and Management, Nanchang Hangkong University, Nanchang, Jiangxi, China

Introduction: The ecological and environmental pollution problem at the source of agriculture cannot be ignored, and the manifestation of the fertilizer reduction effect of pro-environmentally agricultural technologies (PEATs) will help motivate farmers to adopt technology, thereby promoting sustainable agricultural development.

Methods: From the dual perspectives of farmers’ perception and behavior effects, this paper uses 607 survey data of Chinese farmers, and an endogenous switching regression model is employed to identify the influencing factors of farmers’ adoption of PEATs and manifest its fertilizer reduction effect.

Results and discussion: The results of the perception survey show that the farmers’ recognition of the fertilizer reduction effect of PEATs is not high, and the technical effect needs to be further demonstrated. Moreover, the estimated results suggest that PEATs can significantly reduce the fertilizer application of farmers. Specifically, if farmers who have adopted PEATs do not adopt them, they will apply more chemical fertilizers, the farmers who have not adopted PEATs will use less chemical fertilizer if they do. Overall, the main influencing factors for farmers adopting PEATs include education level, government officials, cultivated land area, soil fertility, information access channels, and the distance of home-agricultural technology station. This study aims to provide empirical evidence for the formulation of strategies and plans to promote sustainable agricultural development.

1 Introduction

There is a consensus that chemical fertilizers play an important role in addressing global hunger and malnutrition, achieving increased production and income for farmers, and effectively ensuring food security ( Erisman et al., 2008 ; Guo et al., 2022 ; Schulte-Uebbing et al., 2022 ), especially for developing countries ( Wang et al., 2018 ; Shahzad et al., 2019 ; Lin et al., 2022 ). For example, fertilizer contributes over 40% of China’ s crop yields growth, making it possible for China to feed 22% of the world’s population with 9% of the world’s cultivated land ( Huang et al., 2010 ; Lu et al., 2015 ; Hu et al., 2019 ). Nevertheless, the excessive and uncontrolled use of chemical fertilizers has led to serious environmental problems, such as non-point source pollution, water pollution, soil quality degradation, greenhouse gas emissions ( Trimpler et al., 2016 ; Wang et al., 2018 ; Guo et al., 2022 ; Anik et al., 2023 ). As the world’s largest consumer of chemical fertilizers, China’s use of agricultural chemical fertilizer application increased from 8.84 million tons to 50.79 million tons between 1978 and 2023 ( National Bureau of Statistics of China (NBSC), 2023 ), with fertilizer application intensity far exceeding international standards ( Guo et al., 2022 ). Furthermore, the chemical fertilizer utilization rate for major food crops was only 40.2%, lower than in the EU and other developed countries. Therefore, how to reduce fertilizer application requires more policy intervention and empirical study.

In order to address the adverse effects of excessive use of chemical fertilizers, a global consensus has been reached on promoting sustainable agricultural development strategies ( Shahzad et al., 2019 ; Schulte-Uebbing et al., 2022 ; Zhou et al., 2023 ). In view of this, policy-and technology-led solutions are designed to reduce fertilizer use. On the one hand, subsidies and tax tools are used to advocate for farmers to reduce fertilization, while laws and regulations are designed to regulate and restrict the use of fertilizer to farmers ( Brady, 2003 ; Wang et al., 2018 ; Lin et al., 2022 ). In such cases, in 2015, China released a detailed document entitled “action plan for zero-growth in fertilizer use by 2020 ” (see Jin and Zhou, 2018 ). On the other hand, some PEATs dedicated to improving soil fertility and improving fertilizer utilization efficiency have been developed and promoted by relevant departments and institutions ( Egodawatta et al., 2012 ; Jordan-Meille et al., 2012 ; Kuang et al., 2023 ).

It is worth noting that the implementation of policies and technical solutions to reduce fertilizers application cannot be separated from farmers. As the user of cultivated land, farmers are also the decision-making subject of chemical fertilizer reduction, and play an important role in promoting the sustainable development of agriculture ( Bopp et al., 2019 ; Lai et al., 2020 ; Kuang et al., 2023 ). In China, lots of work and effort have been put into promoting PEATs, but the actual promotion effect is not satisfactory. Specifically, farmers still follow the “heavy utilization, light protection” approach to cultivated land utilization, and the actual adoption rate of PEATs is not high ( Lai et al., 2020 ; Kuang et al., 2023 ; Qing et al., 2023 ), even stay at the cognitive level of “whether they have heard of it” ( Liu et al., 2019 ; Rust et al., 2021 ). Undoubtedly, this goes against the original intention of designing a plan to reduce fertilizer use. So, what exactly is the reason that inhibits farmers from adopting PEATs?

After reviewing previous studies, we found that existing studies mainly reveal the reasons why farmers are unwilling to adopt PEAT from two aspects. For one thing, the transformation of farmers from the traditional agricultural production mode to the sustainable agriculture is a complex behavioral decision-making process ( Baumgart-Getz et al., 2012 ; Ward et al., 2018 ; Kuang et al., 2023 ), which is influenced by multi-dimensional factors ( Burton, 2014 ; Wang et al., 2018 ; Pham et al., 2022 ). However, existing studies do not agree on the influence mechanism of PEATs adoption, and even have opposite results. For another thing, farmers do not agree that PEATs are effective, and even have doubts about this ( Abdallah et al., 2021 ).

Therefore, the potential contribution of this article lies in answering the question of whether adopting PEATs can reduce chemical fertilizer application from the perspectives of farmer perception and behavioral adoption. Furthermore, an endogenous switching regression model that can solve the problems of sample selection and endogeneity is employed for unbiased estimation, revealing the impact mechanism of PEATs adoption by farmers.

2 Methodology

2.1 study area.

The Poyang Lake Plain is mainly distributed in the northern part of Jiangxi Province, China, located at 27°32′-30°06′ N and 115°01′-117°34′ E. The Poyang Lake Plain is formed by the impact of the Poyang Lake water body, covering a land area of 38760.6 km 2 , accounting for 23.2% of Jiangxi Province, while the cultivated land area accounts for 37.3% of Jiangxi Province. The humid subtropical monsoon climate brings abundant rainfall and sufficient heat and light, convenient irrigation resources and long farming culture create favorable agricultural development conditions for the region, which also brings wealth to the local farmers ( Kuang et al., 2023 ). The Poyang Lake Plain has always been a major grain producing area in Jiangxi Province and one of the important rice producing areas in China ( Li et al., 2012 ). The rice planting area in this region accounts for more than half of the total crop planting area in Jiangxi Province, and 86% of the grain crop planting area in Jiangxi Province is concentrated here ( Kuang et al., 2023 ).

2.2 Sampling procedure

The sampling procedure was carried out in accordance with the four stages shown in Figure 1 . The first stage, the preliminary questionnaire was designed. After literature review and expert consultation, we designed the preliminary survey questionnaire. In the second stage, the final survey questionnaire was determined. In October 2020, 50 farmers in Poyang County were selected to test the preliminary questionnaire. Local government officials and villagers were invited to participate in the focus group discussion (FGDs). After FGDs and pre-survey, the preliminary questionnaire was modified and improved, and the final survey questionnaire was determined. The third stage, a formal survey is conducted. In December 2020, we organized a field survey of farmers in the Poyang Lake Plain. The fourth stage, data review and analysis was carried out. We conducted a logical relationship check on the collected survey data, eliminating incomplete and contradictory questionnaire data, and the valid data was used for subsequent analysis.

Figure 1 . The schematic flow chart of questionnaire survey.

In field investigation, the method of combining simple random sampling and stratified random sampling is used to obtain the survey data of farmers. Specifically, based on the results of advanced grain production counties in China and Jiangxi Province from 2004 to 2014, 1 we preferentially selected six Counties around the Poyang Lake as sample points. Moreover, township population, size, and geographical location were considered as a sampling basis, and 2 sample townships were selected from each county. Then, 3 sample villages were randomly selected from each township, 15–20 farmers in each selected village were randomly invited to participate in the questionnaire. As mentioned above, we conducted this survey in October 2020 and distributed 630 questionnaires. After reviewing the questionnaire data, we finally obtained 607 valid farmer survey data.

2.3 Econometric model

In Eq. (1) , where Y j represents the amount of chemical fertilizer applied by farmers in planting rice; X j ' indicates the influencing factors of chemical fertilizer application (e.g., personal, household and cultivated land resource characteristics); D j is set as the production decision of whether farmers adopt PEATs, D j = 1 indicates that farmers have adopted PEATs, and D j = 0 indicates that farmers have not adopted PEATs; β 0 and γ 0 are the corresponding estimated coefficients; ε j is the random error term.

If the decision of farmers adopting PEATs is exogenous, then γ 0 can accurately assess the impact of PEATs. However, farmers’ adoption behavior decision-making of PEATs is also affected by factors (e.g., personal, household and cultivated land resource characteristics), making farmers’ PEATs adoption behavior not entirely exogenous, leading to the existence of self selection problems in the model. If the problem of sample self selection is ignored and the ordinary least square method (OLS) is continued for estimation, it will easily lead to biased estimation ( Lokshin and Sajaia, 2004 ; Kuang et al., 2023 ).

Due to the fact that deciding whether to adopt PEATs is a self choice made by farmers after analyzing expected benefits, there are some unobservable factors such as personal preferences and management skills of farmers, which simultaneously affect their adoption behavior and the level of behavioral effects. In other words, there is a problem of sample self selection. Therefore, we cannot consider the decision variable PEAT in model (1) as an exogenous variable. If the problem of sample self selection is ignored, model (1) uses the least squares method (OLS) to estimate, and the estimated results of the model will be biased. After reviewing existing literature, many scholars have used propensity score matching (PSM) to solve the problem of selectivity bias. However, this method cannot solve the endogeneity problem of omitted variables caused by unobservable factors. In addition, some scholars have attempted to use instrumental variable method (IV) to estimate, but this method did not consider the heterogeneity of treatment effects. Many scholars use the endogenous switching regression (ESR) model to explore the behavioral effects of farmers. Besides inheriting the advantages of the propensity score matching (PSM) method and instrumental variable method, ESR model also has its unique advantages. Specifically, it not only addresses the sample selectivity bias and endogenous problems resulting from both observable and unobservable factors, but also corrects the setting bias or missing variables in the equation by introducing inverse Mills ratio coefficients ( Lokshin and Sajaia, 2004 ; Ma and Abdulai, 2016 ). Furthermore, the full information maximum likelihood estimation is employed to implement counterfactual analysis, which will ameliorate the problem of models missing valid information ( Khanal et al., 2018 ). ESR model includes the following equations:

In Eqs. (2–4) , where Q j indicates the influencing factor of farmers’ response to PEATs; V j represents identification variable; Y j n and Y j a represent the behavioral effects of farmers who did not adopt and adopt PEATs, respectively; X j n and X j y are the influencing factors of behavioral effects; π , δ , β n , β y are the corresponding coefficients to be estimated; ξ j , μ j n , μ j a are the random standard error terms for each equation.

Based on the construction of the counterfactual analysis framework, the average treatment effect of the behavioral effect of farmers adopting PEATs in both the real and counterfactual scenarios was estimated.

2.4 Selection of variables

Dependent variable. Given that it is not possible for farmers to apply only single element fertilizers (e.g., Nitrogen, Phosphorus and Potassium fertilizer) when planting rice, exploring only single element fertilizers often masks the true effect of PEATs in reducing chemical fertilizer application. Therefore, the amount of pure chemical fertilization was set as the explanatory variable.

Key independent variables. PEATs are a generic term that includes multiple types of agricultural technologies, and farmers may also adopt more than one of these agricultural technologies. Learning from the processing method of Kuang et al. (2023) , this study will focus on three production stages of growing rice (before, during and postpartum), and select a PEATs commonly used by farmers in each production stage. Therefore, three kinds of PEATs, namely green manure (GM), soil testing and formula fertilization (STFF) and straw returning to field (SR), were set as the key independent variables.

Control variables. According to existing studies ( Khonje et al., 2018 ; Wossen et al., 2019 ; Xie and Huang, 2021 ; Kuang et al., 2023 ), this study selected 3–4 control variables from three aspects: personal characteristics, family characteristics, and farm characteristics of the surveyed farmers. Specifically, age, gender, education (personal characteristics), population, income, government officials (family characteristics), cultivated land area, cultivated land fragmentation, soil fertility, and cultivation distance (farm characteristics) were set as control variables.

Identification variables. “Information acquisition channels” and “the distance to agricultural technology station” are set as identification variables. The reason is that information channels such as agricultural technology stations are the main sources for farmers to receive the latest agricultural information, especially for new agricultural technologies such as PEATs. In other words, these two identification variables have a direct and important impact on farmers’ adoption of PEATs. Moreover, the commuting distance from home to the agricultural technology stations is objectively exists, and the impact on fertilizer application is weak. The variable setting and descriptive statistical results were shown in Table 1 .

Table 1 . Variable setting and descriptive statistics.

3.1 Farmers’ perceived benefits of PEATs

Each interviewed farmer was asked to evaluate the fertilizer reduction effects of three types of PEATs separately, and an evaluation option with five levels of agreement was designed. As shown in Figure 2 , farmers feel that the proportion of GM in reducing fertilizer application is not obvious (including “disagree” and “strongly disagree,” similarly hereinafter), general, and obvious (including “agree” and “strongly agree,” similarly hereinafter) is 34.60, 25.86, and 39.54%, respectively. Moreover, 34.43% of farmers believe that STFF has a poor effect on reducing chemical fertilizer application, 42.67% of farmers believe that the effect is good, and 22.90% of farmers still believe that the effect is general. Similarly, farmers believe that the proportion of SR in reducing fertilizer application is not obvious, general, and obvious is 35.25, 23.89, and 40.86%, respectively. Overall, about 40% of farmers believe that PEATs can significantly reduce fertilizer usage, while the proportion of those who consider the effect to be average and insignificant is about 25 and 35%, respectively.

Figure 2 . Farmers’ perception of the fertilizer reduction effect of PEATs.

3.2 Difference test of fertilizer application among rice farmers

According to the statistical results of fertilizer application of rice farmers, overall, the pure amount of chemical fertilizer applied by most rice farmers is 25 ~ 40 kg/mu, with a small number of farmers applying less than 25 kg/mu, while a large number of farmers applying more than 40 kg/mu, or even more than 60 kg/mu. Table 2 presents the statistical results of mean difference in chemical fertilizer application under different adoption scenarios. The chemica fertilizer application level of farmers who did not adopt PEATs was significantly higher than the sample average. According to the T -test results of independent samples, farmers who adopted different types or degrees of PEATs can reduce the application of nitrogen, phosphorus, and potassium fertilizers. However, the results in Table 2 do not infer that PEATs have an impact on fertilizer application. The influence of observable factors (such as the personal, family and land characteristics of farmers) and unobservable factors still needs to be further explored.

Table 2 . Farmers’ fertilizer application under different adoption scenarios.

3.3 The econometric results of ESR model

Tables 3 – 5 present the econometric regression results of the model. The 2–3 columns of each table provide the estimated results of the selection equation, while the 4–7 columns provide the result equations for the farmer groups who did not adopt or adopted PEATs. Specifically, both identified variables were significant in all three models, indicating that the identification effect of the variables is good. The estimation results of ρ μ a or ρ μ n are significant, which proves the existence of sample self selection problem ( Lokshin and Sajaia, 2004 ; Ma and Abdulai, 2016 ; Kuang et al., 2023 ). In other words, ignoring this issue may lead to biased estimation results.In other words, the problem needs to be addressed with the ESR model to obtain more plausible estimation results.

Table 3 . The estimation results of farmers’ response to GM.

Table 4 . The estimation results of farmers’ response to STFF.

Table 5 . The estimation results of farmers’ response to SR.

3.4 Quantitative analysis of farmers’ response to GM

Table 3 presents the estimated results of farmers adopting GM and its impact on chemical fertilizer application. The results show that gender, education level, government officials, cultivated land area, soil fertility, information access channels, and the distance from home to agricultural technology stations are the main influencing factors for farmers to adopt GM. Specifically, farmers with male, higher education, better soil fertility and more diverse information acquisition channels are more likely to adopt GM. Conversely, farmers with family members including government officials, large-scale planting and homes farther away from agricultural stations are less likely to adopt GM.

As shown in Table 3 , the impact of GM adoption by farmers on chemical fertilizer application was estimated. The estimated results of the cultivated land fragmentation variable indicate that farmers with a higher degree of farmland fragmentation use more chemical fertilizers. Similarly, this significant positive impact also occurs in the variables of education and the distance from home to farmland. Conversely, the negative effect of the cultivated land area variable on fertilizer application indicates that farmers with larger farm areas are more inclined to use more chemical fertilizer. Moreover, soil fertility has a positive driving effect on farmers to reduce the application of chemical fertilizer.

3.4.1 Quantitative analysis of farmers’ response to STFF

The influencing factors of farmers adopting STFF and its impact on fertilizer application are estimated in Table 4 . In the selection equation, the main influencing factors for farmers to adopt STFF include cultivated land area, information acquisition channels, and distance from home to agricultural technology stations. In other words, farmers with larger cultivated land area, more information access channels, and closer homes to agricultural technology stations are more likely to adopt STFF.

Table 4 also presents the estimation results of the result equations for different adoption groups of STFF. For all farmers (adopted or not adopted), the cultivated land fragmentation and soil fertility variables have significant positive and negative effects on fertilizer application, respectively. In other words, farmers with greater cultivated land fragmentation or poorer soil are more inclined to use more chemical fertilizer. In addition, for farmers who adopt STFF, men are more likely to apply more chemical fertilizer. For unadopted farmers, farmers with larger household populations or farther away from the cultivated land tend to apply more chemical fertilizer.

3.4.2 Quantitative analysis of farmers’ response to SR

Table 5 shows the estimated results of the farmers’ responses to SR. The results indicate that farmers adopting was mainly influenced by education, cultivated land area, family population, income, soil fertility, officials, the distance from home to land, information acquisition channels, and the distance from home to agricultural technology stations. Specifically, farmers with higher income, greater cultivated land area, more information access channels, and better soil fertility are more inclined to adopt SR. Conversely, farmers with high education, large family population, government officials in families, farther away from land, and farther away from agricultural technology stations have lower probability of adopting SR.

From Table 5 , we also found the results of farmers’ response to SR on fertilizer application. Soil fertility has a significant negative effect on chemical fertilizers application, indicating that farmers with more fertile land have a higher probability of using less chemical fertilizer. For unadopted farmers, the distance from home to cultivated land has a significant positive influence on chemical fertilizer application, suggesting that farmers who are farther away from farmland use more fertilizer. For adopted farmers, farmers with greater age and cultivated land fragmentation use more chemical fertilizer, while farmers with larger cultivation areas use less chemical fertilizer.

3.5 Estimating the behavioral effects of farmers adopting PEATs

The effect results of PEATs on chemical fertilizer application is presented in Table 6 . Overall, the adoption of PEATs will help farmers reduce chemical fertilizer use. Specifically, the estimation results indicate that if farmers who have adopted GM, STFF, and SR choose not to adopt the corresponding types of PEATs, the chemical fertilizer application will increase by 4.84, 2.14, and 7.20%, respectively. Furthermore, for farmers who have not actually adopted PGM, STFFT and SRT, if they adopt the corresponding types of PEATs in the future, the chemical fertilizer application will reduce by 3.16, 1.00 and 4.91%, respectively.

Table 6 . Average treatment effect of farmers’ behavior under different PAETs adoption scenarios.

Is the robustness of the results of PEATs having significant fertilizer reduction effects? This is a key issue that this study focuses on. In addition, since farmers may not only adopt one PEATs, this study will again explore the effect of adoption behavior on chemical fertilizer application from the “adoption degree” dimension. As shown in Table 6 , the three adoption degree of PEATs have been verified to have significant fertilizer reduction effects, indicating that farmers adopting one or more PEATs can achieve the effect of reduced chemical fertilizer application. Specifically, for farmers who have already adopted one, two, and three types of PEATs, if they do not adopt the corresponding degree of PEATs, the chemical fertilizer application will increase by 4.84, 4.42, and 0.60%, respectively. Correspondingly, for farmers who have not actually adopted one kind, two kinds, and three kinds, if they adopt the corresponding degree of PEATs in the future, their chemical fertilizer will increase by 3.16, 5.42 and 2.96%, respectively. Farmers who did not adopt one, two and three types of PEATs, if they decided to adopt the corresponding degree of PEATs, fertilizer use would increase by 3.16, 5.42 and 2.96%, respectively.

4 Discussion

The results indicate that adopting PEATs by farmers can effectively reduce the use of chemical fertilizers. Specifically, green manure can improve surface coverage, enhance the gas regulation function of the farmland system, reduce nutrient loss to the environment, and improve soil organic matter content, thereby achieving chemical fertilizer reduction ( Egodawatta et al., 2012 ; Hong et al., 2019 ; Chang et al., 2022 ). Based on the results of soil testing, STFF achieves precision fertilization, improves soil fertility, meets the needs of crops for various nutrients, and improves the utilization rate of fertilizers by crops, so as to realize the reduction of chemical fertilizer usage ( Jordan-Meille et al., 2012 ; Zebarth et al., 2012 ; Wu et al., 2022 ). SR can release rich nutrient elements from crop straw, maintain a balance of nutrients, increase soil organic matter, improve soil nutrient content, and enhance soil fertility, thereby reducing chemical fertilizer application ( Malhi et al., 2011 ; Islam et al., 2022 ; Liu et al., 2023 ). In addition, we also need to note that the perception level of farmers that PEATs can significantly reduce fertilizer use still needs to be improved. Descriptive statistical results indicate that a large proportion of farmers still believe that the reduction effect of PEATs on fertilizer is not significant, which is also the reason why Chinese farmers generally have low enthusiasm for adopting PEATs.

Our results suggest that different factors influence different PEATs. Due to the different application conditions of different PEATs, farmers have different preferences for technology ( Zhao and Zhou, 2021 ; Kotu et al., 2022 ; Pham et al., 2022 ), which is very normal and easy to understand. Nevertheless, we have found some similar results, which will help us reveal the regularity of farmers’ adoption of PEATs behavior decision-making. Specifically, farmers with easier access to information or closer to agricultural technical stations have a higher probability of adopting PEATs. Similar studies have pointed out that information asymmetry is an important reason why farmers are reluctant or afraid to adopt new agricultural technologies ( Aker et al., 2016 ; Ullah et al., 2020 ). Therefore, providing more farmers with timely agricultural information and technical guidance is an important task for the agricultural technology extension department, which will encourage farmers to actively adopt PEATs ( Shikuku, 2019 ; Campenhout et al., 2021 ; Li et al., 2021 ).

Generally speaking, expanding farm size drives farmers to achieve economies of scale, internalizes the cost of farmland construction, motivate farmers to improve soil fertility through increasing investment, and thus increase the adoption rate of PEATs ( Cao et al., 2020 ; Xie and Huang, 2021 ). Interestingly, The results show that expanding cultivated land area does not necessarily promote farmers to adopt PEATs, and even has an inhibitory effect. This finding is supported by Gong et al. (2016) , Abera et al. (2020) , and Kuang et al. (2023) , suggesting that expanding farmland scale cannot achieve economies of scale, but has negative scale effects, and does not promote farmers to adopt PEATs. The possible reason is that almost all large-scale farmers choose agricultural machinery to reduce the expensive labor input, while some PEATs (such as GM) are easy to damage agricultural machinery, resulting in incompatibility with agricultural mechanization ( Kuang et al., 2023 ). Furthermore, as the results of this study show, farmers’ perceived benefits of PEATs need to be improved, and some farmers do not recognize the effectiveness of the technology.

Finally, although this article reveals some important findings, it cannot be ignored that there are still some limitations. The estimated results of farmers adopting PEAT to reduce fertilizer use may be overestimated. Because farmers may adopt more than these three types of PEATs when planting rice. In other words, some farmers have also adopted other PEATs, which has an impact on chemical fertilizer application. Therefore, this article has done the following three tasks. Firstly, three commonly used PEATs by farmers were selected from the three production stages (before, middle and after) of planting rice. Secondly, examine the impact of PEATs on fertilizer reduction from the dimensions of “adoption or non adoption” and “degree of adoption.” Thirdly, this article explores the fertilizer reduction effects of farmers adopting PEATs from two perspectives: perception surveys and behavioral effect estimation. In general, how to scientifically and reasonably reveal the driving mechanism of farmers’ response to PEATs and demonstrate technology benefits are still the focus of follow-up research ( Kuang et al., 2023 ), which will be related to how to get through the last kilometer of farmers adopting PEATs.

5 Conclusions and policy suggestions

By highlighting the chemical fertilizer reduction effect of PEATs and identifying obstacle factors, we aim to incentivize farmers to adopt PEATs, thereby achieving green and sustainable agricultural development. Our perception survey results indicate that some farmers acknowledge that PEATs have good fertilizer reduction effects, while a large proportion of farmers still hold a skeptical attitude towards this. The estimated results indicate that the adoption of PEATs can significantly reduce the use of chemical fertilizer by farmers. Specifically, if farmers who actually adopt PEATs do not adopt them in the future, the chemical fertilizer application will increase; If farmers who have not actually adopted PEATs adopt them in the future, the chemical fertilizer application will be reduced. Furthmore, there are differences in the influencing factors of different types of PEATs. Overall, farmers’ adoption of PEATs is mainly influenced by factors such as education level, government officials, cultivated land area, soil fertility, information access channels and distance from home to agricultural machinery stations. Finally, the effect of PEATs on chemical fertilizer reduction was different among farmers’ endowments, which is mainly manifested as farmers with higher cultivated land fragmentation, more distant their homes from the cultivated land will choose to apply more chemical fertilizer, and farmers with better soil fertility apply less chemical fertilizer.

Therefore, the following three policy suggestions are proposed. Firstly, increase technical publicity and reduce the threshold for information acquisition. Cognition is the precursor of behavior, and solving the problem of information asymmetry is a key issue for agricultural technology promotion. Therefore, it is recommended to establish a PEATs promotion and publicity system led by the technology promotion department and participated by multiple entities. Secondly, promote the moderate scale management of cultivated land. It is suggested that government departments take the lead, taking villages as a unit, reduce the cultivated land fragmentation through land adjustment and land leveling, and encourage farmers to conduct moderate scale operations through land transfer. Thirdly, manifest the behavioral effects of PEATs. It is suggested to select a group of farmers or new agricultural business entities with high grain production efficiency under the leadership of the government, establish PEATs promotion and demonstration bases, organize farmers to visit and experience the benefits of PEATs, so as to encourage farmers to actively adopt PEATs.

Data availability statement

The data analyzed in this study is subject to the following licenses/restrictions: Data will be made available on request. Requests to access these datasets should be directed to [email protected] .

Author contributions

FK: Conceptualization, Funding acquisition, Investigation, Project administration, Writing – original draft, Writing – review & editing. JL: Software, Visualization, Writing – original draft, Writing – review & editing. JJ: Conceptualization, Funding acquisition, Project administration, Supervision, Writing – review & editing. CL: Conceptualization, Funding acquisition, Writing – review & editing. XQ: Investigation, Methodology, Writing – review & editing.

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This research was supported by the National Natural Science Foundation of China Fund Project (grant number: 72304132; 42271203; 72064030).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

1. ^ According to the available information, China conducted the selection of national and provincial advanced counties in grain production every year since 2004, and 2014 was the last year.

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Keywords: sustainable agriculture, PEATs, the fertilizer reduction effect, Chinese farmers, endogenous switching regression model

Citation: Kuang F, Li J, Jin J, Liu C and Qiu X (2024) How to manifest the fertilizer reduction effect of pro-environmental agricultural technologies? From the perspective of farmers’ perception and behavioral adoption. Front. Sustain. Food Syst . 8:1377040. doi: 10.3389/fsufs.2024.1377040

Received: 26 January 2024; Accepted: 08 April 2024; Published: 17 April 2024.

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Copyright © 2024 Kuang, Li, Jin, Liu and Qiu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Jianjun Jin, [email protected]

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How to Present Results in a Research Paper

• Aparna Mukherjee 4 ,
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The results section is the core of a research manuscript where the study data and analyses are presented in an organized, uncluttered manner such that the reader can easily understand and interpret the findings. This section is completely factual; there is no place for opinions or explanations from the authors. The results should correspond to the objectives of the study in an orderly manner. Self-explanatory tables and figures add value to this section and make data presentation more convenient and appealing. The results presented in this section should have a link with both the preceding methods section and the following discussion section. A well-written, articulate results section lends clarity and credibility to the research paper and the study as a whole. This chapter provides an overview and important pointers to effective drafting of the results section in a research manuscript and also in theses.

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Acknowledgments

The book chapter is derived in part from our article “Mukherjee A, Lodha R. Writing the Results. Indian Pediatr. 2016 May 8;53(5):409-15.” We thank the Editor-in-Chief of the journal “Indian Pediatrics” for the permission for the same.

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Mukherjee, A., Kumar, G., Lodha, R. (2023). How to Present Results in a Research Paper. In: Jagadeesh, G., Balakumar, P., Senatore, F. (eds) The Quintessence of Basic and Clinical Research and Scientific Publishing. Springer, Singapore. https://doi.org/10.1007/978-981-99-1284-1_44

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• v.89(2); Mar-Apr 2014

Presenting data in tables and charts *

Rodrigo pereira duquia.

1 Universidade Federal de Ciências da Saúde de Porto Alegre (UFCSPA) - Porto Alegre (RS), Brazil.

João Luiz Bastos

2 Universidade Federal de Santa Catarina (UFSC) - Florianópolis (SC) Brazil.

Renan Rangel Bonamigo

David alejandro gonzález-chica, jeovany martínez-mesa.

3 Latin American Cooperative Oncology Group (LACOG) - Porto Alegre (RS) Brazil.

The present paper aims to provide basic guidelines to present epidemiological data using tables and graphs in Dermatology. Although simple, the preparation of tables and graphs should follow basic recommendations, which make it much easier to understand the data under analysis and to promote accurate communication in science. Additionally, this paper deals with other basic concepts in epidemiology, such as variable, observation, and data, which are useful both in the exchange of information between researchers and in the planning and conception of a research project.

INTRODUCTION

Among the essential stages of epidemiological research, one of the most important is the identification of data with which the researcher is working, as well as a clear and synthetic description of these data using graphs and tables. The identification of the type of data has an impact on the different stages of the research process, encompassing the research planning and the production/publication of its results. For example, the use of a certain type of data impacts the amount of time it will take to collect the desired information (throughout the field work) and the selection of the most appropriate statistical tests for data analysis.

On the other hand, the preparation of tables and graphs is a crucial tool in the analysis and production/publication of results, given that it organizes the collected information in a clear and summarized fashion. The correct preparation of tables allows researchers to present information about tens or hundreds of individuals efficiently and with significant visual appeal, making the results more easily understandable and thus more attractive to the users of the produced information. Therefore, it is very important for the authors of scientific articles to master the preparation of tables and graphs, which requires previous knowledge of data characteristics and the ability of identifying which type of table or graph is the most appropriate for the situation of interest.

BASIC CONCEPTS

Before evaluating the different types of data that permeate an epidemiological study, it is worth discussing about some key concepts (herein named data, variables and observations):

Data - during field work, researchers collect information by means of questions, systematic observations, and imaging or laboratory tests. All this gathered information represents the data of the research. For example, it is possible to determine the color of an individual's skin according to Fitzpatrick classification or quantify the number of times a person uses sunscreen during summer. 1 , 2 All the information collected during research is generically named "data." A set of individual data makes it possible to perform statistical analysis. If the quality of data is good, i.e., if the way information was gathered was appropriate, the next stages of database preparation, which will set the ground for analysis and presentation of results, will be properly conducted.

Observations - are measurements carried out in one or more individuals, based on one or more variables. For instance, if one is working with the variable "sex" in a sample of 20 individuals and knows the exact amount of men and women in this sample (10 for each group), it can be said that this variable has 20 observations.

Variables - are constituted by data. For instance, an individual may be male or female. In this case, there are 10 observations for each sex, but "sex" is the variable that is referred to as a whole. Another example of variable is "age" in complete years, in which observations are the values 1 year, 2 years, 3 years, and so forth. In other words, variables are characteristics or attributes that can be measured, assuming different values, such as sex, skin type, eye color, age of the individuals under study, laboratory results, or the presence of a given lesion/disease. Variables are specifically divided into two large groups: (a) the group of categorical or qualitative variables, which is subdivided into dichotomous, nominal and ordinal variables; and (b) the group of numerical or quantitative variables, which is subdivided into continuous and discrete variables.

Categorical variables

• Dichotomous variables, also known as binary variables: are those that have only two categories, i.e., only two response options. Typical examples of this type of variable are sex (male and female) and presence of skin cancer (yes or no).
• Ordinal variables: are those that have three or more categories with an obvious ordering of the categories (whether in an ascending or descending order). For example, Fitzpatrick skin classification into types I, II, III, IV and V. 1
• Nominal variables: are those that have three or more categories with no apparent ordering of the categories. Example: blood types A, B, AB, and O, or brown, blue or green eye colors.

Numerical variables

• Discrete variables: are observations that can only take certain numerical values. An example of this type of variable is subjects' age, when assessed in complete years of life (1 year, 2 years, 3 years, 4 years, etc.) and the number of times a set of patients visited the dermatologist in a year.
• Continuous variables: are those measured on a continuous scale, i.e., which have as many decimal places as the measuring instrument can record. For instance: blood pressure, birth weight, height, or even age, when measured on a continuous scale.

It is important to point out that, depending on the objectives of the study, data may be collected as discrete or continuous variables and be subsequently transformed into categorical variables to suit the purpose of the research and/or make interpretation easier. However, it is important to emphasize that variables measured on a numerical scale (whether discrete or continuous) are richer in information and should be preferred for statistical analyses. Figure 1 shows a diagram that makes it easier to understand, identify and classify the abovementioned variables.

Types of variables

DATA PRESENTATION IN TABLES AND GRAPHS

Firstly, it is worth emphasizing that every table or graph should be self-explanatory, i.e., should be understandable without the need to read the text that refers to it refers.

Presentation of categorical variables

In order to analyze the distribution of a variable, data should be organized according to the occurrence of different results in each category. As for categorical variables, frequency distributions may be presented in a table or a graph, including bar charts and pie or sector charts. The term frequency distribution has a specific meaning, referring to the the way observations of a given variable behave in terms of its absolute, relative or cumulative frequencies.

In order to synthesize information contained in a categorical variable using a table, it is important to count the number of observations in each category of the variable, thus obtaining its absolute frequencies. However, in addition to absolute frequencies, it is worth presenting its percentage values, also known as relative frequencies. For example, table 1 expresses, in absolute and relative terms, the frequency of acne scars in 18-year-old youngsters from a population-based study conducted in the city of Pelotas, Southern Brazil, in 2010. 3

Absolute and relative frequencies of acne scar in 18- year-old adolescents (n = 2.414). Pelotas, Brazil, 2010

The same information from table 1 may be presented as a bar or a pie chart, which can be prepared considering the absolute or relative frequency of the categories. Figures 2 and ​ and3 3 illustrate the same information shown in table 1 , but present it as a bar chart and a pie chart, respectively. It can be observed that, regardless of the form of presentation, the total number of observations must be mentioned, whether in the title or as part of the table or figure. Additionally, appropriate legends should always be included, allowing for the proper identification of each of the categories of the variable and including the type of information provided (absolute and/or relative frequency).

Absolute frequencies of acne scar in 18-year-old adolescents (n = 2.414). Pelotas, Brazil, 2010

Relative frequencies of acne scar in 18-year-old adolescents (n = 2.414). Pelotas, Brazil, 2010

Presentation of numerical variables

Frequency distributions of numerical variables can be displayed in a table, a histogram chart, or a frequency polygon chart. With regard to discrete variables, it is possible to present the number of observations according to the different values found in the study, as illustrated in table 2 . This type of table may provide a wide range of information on the collected data.

Educational level of 18-year-old adolescents (n = 2,199). Pelotas, Brazil, 2010

Table 2 shows the distribution of educational levels among 18-year-old youngsters from Pelotas, Southern Brazil, with absolute, relative, and cumulative relative frequencies. In this case, absolute and relative frequencies correspond to the absolute number and the percentage of individuals according to their distribution for this variable, respectively, based on complete years of education. It should be noticed that there are 450 adolescents with 8 years of education, which corresponds to 20.5% of the subjects. Tables may also present the cumulative relative frequency of the variable. In this case, it was found that 50.6% of study subjects have up to 8 years of education. It is important to point that, although the same data were used, each form of presentation (absolute, relative or cumulative frequency) provides different information and may be used to understand frequency distribution from different perspectives.

When one wants to evaluate the frequency distribution of continuous variables using tables or graphs, it is necessary to transform the variable into categories, preferably creating categories with the same size (or the same amplitude). However, in addition to this general recommendation, other basic guidelines should be followed, such as: (1) subtracting the highest from the lowest value for the variable of interest; (2) dividing the result of this subtraction by the number of categories to be created (usually from three to ten); and (3) defining category intervals based on this last result.

For example, in order to categorize height (in meters) of a set of individuals, the first step is to identify the tallest and the shortest individual of the sample. Let us assume that the tallest individual is 1.85m tall and the shortest, 1.55m tall, with a difference of 0.3m between these values. The next step is to divide this difference by the number of categories to be created, e.g., five. Thus, 0.3m divided by five equals 0.06m, which means that categories will have exactly this range and will be numerically represented by the following range of values: 1st category - 1.55m to 1.60m; 2nd category - 1.61m to 1.66m; 3rd category - 1.67m to 1.72m; 4th category - 1.73m to 1.78m; 5th category - 1.79m to 1.85m.

Table 3 illustrates weight values at 18 years of age in kg (continuous numerical variable) obtained in a study with youngsters from Pelotas, Southern Brazil. 4 , 5 Figure 4 shows a histogram with the variable weight categorized into 20-kg intervals. Therefore, it is possible to observe that data from continuous numerical variables may be presented in tables or graphs.

Weight distribution among 18-year-old young male sex (n = 2.194). Pelotas, Brazil, 2010

Weight distribution at 18 years of age among youngsters from the city of Pelotas. Pelotas (n = 2.194), Brazil, 2010

Assessing the relationship between two variables

The forms of data presentation that have been described up to this point illustrated the distribution of a given variable, whether categorical or numerical. In addition, it is possible to present the relationship between two variables of interest, either categorical or numerical.

The relationship between categorical variables may be investigated using a contingency table, which has the purpose of analyzing the association between two or more variables. The lines of this type of table usually display the exposure variable (independent variable), and the columns, the outcome variable (dependent variable). For example, in order to study the effect of sun exposure (exposure variable) on the development of skin cancer (outcome variable), it is possible to place the variable sun exposure on the lines and the variable skin cancer on the columns of a contingency table. Tables may be easier to understand by including total values in lines and columns. These values should agree with the sum of the lines and/or columns, as appropriate, whereas relative values should be in accordance with the exposure variable, i.e., the sum of the values mentioned in the lines should total 100%.

It is such a display of percentage values that will make it possible for risk or exposure groups to be compared with each other, in order to investigate whether individuals exposed to a given risk factor show higher frequency of the disease of interest. Thus, table 4 shows that 75.0%, 9.0%, and 0.3% of individuals in the study sample who had been working exposed to the sun for 20 years or more, for less than 20 years, and had never been working exposed to the sun, respectively, developed non-melanoma skin cancer. Another way of interpreting this table is observing that 25.0%, 91%,.0%, and 99.7% of individuals who had been working exposed to the sun for 20 years of more, for less than 20 years, and had never been working exposed to the sun did not develop non-melanoma skin cancer. This form of presentation is one of the most used in the literature and makes the table easier to read.

Sun exposure during work and non-melanoma skin cancer (hypothetical data).

The relationship between two numerical variables or between one numerical variable and one categorical variable may be assessed using a scatter diagram, also known as dispersion diagram. In this diagram, each pair of values is represented by a symbol or a dot, whose horizontal and vertical positions are determined by the value of the first and second variables, respectively. By convention, vertical and horizontal axes should correspond to outcome and exposure variables, respectively. Figure 5 shows the relationship between weight and height among 18-year-old youngsters from Pelotas, Southern Brazil, in 2010. 3 , 4 The diagram presented in figure 5 should be interpreted as follows: the increase in subjects' height is accompanied by an increase in their weight.

Point diagram for the relationship between weight (kg) and height (cm) among 18-year-old youngsters from the city of Pelotas (n = 2.194). Pelotas, Brazil, 2010.

BASIC RULES FOR THE PREPARATION OF TABLES AND GRAPHS

Ideally, every table should:

• Be self-explanatory;
• Present values with the same number of decimal places in all its cells (standardization);
• Include a title informing what is being described and where, as well as the number of observations (N) and when data were collected;
• Have a structure formed by three horizontal lines, defining table heading and the end of the table at its lower border;
• Not have vertical lines at its lateral borders;
• Provide additional information in table footer, when needed;
• Be inserted into a document only after being mentioned in the text; and
• Be numbered by Arabic numerals.

Similarly to tables, graphs should:

• Include, below the figure, a title providing all relevant information;
• Be referred to as figures in the text;
• Identify figure axes by the variables under analysis;
• Quote the source which provided the data, if required;
• Demonstrate the scale being used; and
• Be self-explanatory.

The graph's vertical axis should always start with zero. A usual type of distortion is starting this axis with values higher than zero. Whenever it happens, differences between variables are overestimated, as can been seen in figure 6 .

Figure showing how graphs in which the Y-axis does not start with zero tend to overestimate the differences under analysis. On the left there is a graph whose Y axis does not start with zero and on the right a graph reproducing the same data but with the Y axis starting with zero.

Understanding how to classify the different types of variables and how to present them in tables or graphs is an essential stage for epidemiological research in all areas of knowledge, including Dermatology. Mastering this topic collaborates to synthesize research results and prevents the misuse or overuse of tables and figures in scientific papers.

Conflict of Interest: None

Financial Support: None

How to cite this article: Duquia RP, Bastos JL, Bonamigo RR, González-Chica DA, Martínez-Mesa J. Presenting data in tables and charts. An Bras Dermatol. 2014;89(2):280-5.

* Work performed at the Dermatology service, Universidade Federal de Ciências da Saúde de Porto Alegre (UFCSPA), Departamento de Saúde Pública e Departamento de Nutrição da UFSC.

Invasive species, pandemic prevention research presented to Board of Visitors committee

• Virginia Tech News

11 Apr 2024

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The Board of Visitors’ Academic, Research, and Student Affairs Committee heard a presentation this month on two transdisciplinary research projects funded through the university’s Destination Area 2.0 grants.

Jacob Barney, a professor of invasive plant ecology and principal investigator for the Invasive Species Destination Area , talked about the team’s work to mitigate the global threat of biological invasions.

The invasive species crisis is as costly as natural disasters, leads to animal extinctions, exacerbates droughts/wildfires, and leads to increased disease and food insecurity, Barney told the committee. It can lead to social conflict as well – what’s invasive to one person may be desirable to another person, Barney told the committee.

The work spans across the university, involving five colleges, three institutes, 11 Agricultural Research and Extension Centers, and a strong connection to the greater Washington, D.C., area. 

Barney praised the university’s decision to invest in key topics and solve important problems. He said the invasive species team wants to take “moonshots” to help solve the problem. “We want to be ambitious, not just make incremental improvements.”

T.M. Murali, professor of computer science and principal investigator for the Pandemic Prediction and Prevention Destination Area , briefed the committee on his team’s work to forecast and control future viral pandemics.

The team, which includes more than 20 faculty members from seven colleges and 13 departments, is working with nine external partners and has more than $37 million in external awards.

Working across diverse disciplines is key, Murali said, because the solution to the problem requires addressing moral, ethical, social, and policy considerations.

Associate Vice Provost Catherine Amelink, who opened the panel and introduced the speakers, told the committee the Destination Area grants are unique because they require faculty to focus on Virginia Tech’s three-part mission – student learning, research, and outreach/impact into our communities. Both projects, too, will fuel the Virginia Tech Global Distinction priority, designed to expand the university’s ability to tackle global-scale challenges. 

Providing support for these highly collaborative teams – which include STEM and non-STEM disciplines – is key to attracting and retaining talent and helping the university raise its profile around the world, Amelink said. 

The university is soliciting proposals for the next round of DA 2.0 Phase 1 projects.

Michael Stowe

540-392-4218

• College of Agriculture and Life Sciences
• College of Engineering
• Destination Areas
• Global Change Center
• Invasive Species
• Pandemic Prediction and Prevention
• Virginia Tech Board of Visitors
• Virginia Tech Global Distinction

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