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Introduction to Research Statistical Analysis: An Overview of the Basics

Christian vandever.

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Correspondence to: Christian Vandever, HCA Healthcare Graduate Medical Education, 2000 Health Park Drive, Brentwood TN, 37027, ( [email protected] )

Corresponding author.

Collection date 2020.

Description

This article covers many statistical ideas essential to research statistical analysis. Sample size is explained through the concepts of statistical significance level and power. Variable types and definitions are included to clarify necessities for how the analysis will be interpreted. Categorical and quantitative variable types are defined, as well as response and predictor variables. Statistical tests described include t-tests, ANOVA and chi-square tests. Multiple regression is also explored for both logistic and linear regression. Finally, the most common statistics produced by these methods are explored.

Keywords: statistical analysis, sample size, power, t-test, anova, chi-square, regression

Introduction

Statistical analysis is necessary for any research project seeking to make quantitative conclusions. The following is a primer for research-based statistical analysis. It is intended to be a high-level overview of appropriate statistical testing, while not diving too deep into any specific methodology. Some of the information is more applicable to retrospective projects, where analysis is performed on data that has already been collected, but most of it will be suitable to any type of research. This primer will help the reader understand research results in coordination with a statistician, not to perform the actual analysis. Analysis is commonly performed using statistical programming software such as R, SAS or SPSS. These allow for analysis to be replicated while minimizing the risk for an error. Resources are listed later for those working on analysis without a statistician.

After coming up with a hypothesis for a study, including any variables to be used, one of the first steps is to think about the patient population to apply the question. Results are only relevant to the population that the underlying data represents. Since it is impractical to include everyone with a certain condition, a subset of the population of interest should be taken. This subset should be large enough to have power, which means there is enough data to deliver significant results and accurately reflect the study’s population.

The first statistics of interest are related to significance level and power, alpha and beta. Alpha (α) is the significance level and probability of a type I error, the rejection of the null hypothesis when it is true. The null hypothesis is generally that there is no difference between the groups compared. A type I error is also known as a false positive. An example would be an analysis that finds one medication statistically better than another, when in reality there is no difference in efficacy between the two. Beta (β) is the probability of a type II error, the failure to reject the null hypothesis when it is actually false. A type II error is also known as a false negative. This occurs when the analysis finds there is no difference in two medications when in reality one works better than the other. Power is defined as 1-β and should be calculated prior to running any sort of statistical testing. Ideally, alpha should be as small as possible while power should be as large as possible. Power generally increases with a larger sample size, but so does cost and the effect of any bias in the study design. Additionally, as the sample size gets bigger, the chance for a statistically significant result goes up even though these results can be small differences that do not matter practically. Power calculators include the magnitude of the effect in order to combat the potential for exaggeration and only give significant results that have an actual impact. The calculators take inputs like the mean, effect size and desired power, and output the required minimum sample size for analysis. Effect size is calculated using statistical information on the variables of interest. If that information is not available, most tests have commonly used values for small, medium or large effect sizes.

When the desired patient population is decided, the next step is to define the variables previously chosen to be included. Variables come in different types that determine which statistical methods are appropriate and useful. One way variables can be split is into categorical and quantitative variables. ( Table 1 ) Categorical variables place patients into groups, such as gender, race and smoking status. Quantitative variables measure or count some quantity of interest. Common quantitative variables in research include age and weight. An important note is that there can often be a choice for whether to treat a variable as quantitative or categorical. For example, in a study looking at body mass index (BMI), BMI could be defined as a quantitative variable or as a categorical variable, with each patient’s BMI listed as a category (underweight, normal, overweight, and obese) rather than the discrete value. The decision whether a variable is quantitative or categorical will affect what conclusions can be made when interpreting results from statistical tests. Keep in mind that since quantitative variables are treated on a continuous scale it would be inappropriate to transform a variable like which medication was given into a quantitative variable with values 1, 2 and 3.

Categorical vs. Quantitative Variables

Both of these types of variables can also be split into response and predictor variables. ( Table 2 ) Predictor variables are explanatory, or independent, variables that help explain changes in a response variable. Conversely, response variables are outcome, or dependent, variables whose changes can be partially explained by the predictor variables.

Response vs. Predictor Variables

Choosing the correct statistical test depends on the types of variables defined and the question being answered. The appropriate test is determined by the variables being compared. Some common statistical tests include t-tests, ANOVA and chi-square tests.

T-tests compare whether there are differences in a quantitative variable between two values of a categorical variable. For example, a t-test could be useful to compare the length of stay for knee replacement surgery patients between those that took apixaban and those that took rivaroxaban. A t-test could examine whether there is a statistically significant difference in the length of stay between the two groups. The t-test will output a p-value, a number between zero and one, which represents the probability that the two groups could be as different as they are in the data, if they were actually the same. A value closer to zero suggests that the difference, in this case for length of stay, is more statistically significant than a number closer to one. Prior to collecting the data, set a significance level, the previously defined alpha. Alpha is typically set at 0.05, but is commonly reduced in order to limit the chance of a type I error, or false positive. Going back to the example above, if alpha is set at 0.05 and the analysis gives a p-value of 0.039, then a statistically significant difference in length of stay is observed between apixaban and rivaroxaban patients. If the analysis gives a p-value of 0.91, then there was no statistical evidence of a difference in length of stay between the two medications. Other statistical summaries or methods examine how big of a difference that might be. These other summaries are known as post-hoc analysis since they are performed after the original test to provide additional context to the results.

Analysis of variance, or ANOVA, tests can observe mean differences in a quantitative variable between values of a categorical variable, typically with three or more values to distinguish from a t-test. ANOVA could add patients given dabigatran to the previous population and evaluate whether the length of stay was significantly different across the three medications. If the p-value is lower than the designated significance level then the hypothesis that length of stay was the same across the three medications is rejected. Summaries and post-hoc tests also could be performed to look at the differences between length of stay and which individual medications may have observed statistically significant differences in length of stay from the other medications. A chi-square test examines the association between two categorical variables. An example would be to consider whether the rate of having a post-operative bleed is the same across patients provided with apixaban, rivaroxaban and dabigatran. A chi-square test can compute a p-value determining whether the bleeding rates were significantly different or not. Post-hoc tests could then give the bleeding rate for each medication, as well as a breakdown as to which specific medications may have a significantly different bleeding rate from each other.

A slightly more advanced way of examining a question can come through multiple regression. Regression allows more predictor variables to be analyzed and can act as a control when looking at associations between variables. Common control variables are age, sex and any comorbidities likely to affect the outcome variable that are not closely related to the other explanatory variables. Control variables can be especially important in reducing the effect of bias in a retrospective population. Since retrospective data was not built with the research question in mind, it is important to eliminate threats to the validity of the analysis. Testing that controls for confounding variables, such as regression, is often more valuable with retrospective data because it can ease these concerns. The two main types of regression are linear and logistic. Linear regression is used to predict differences in a quantitative, continuous response variable, such as length of stay. Logistic regression predicts differences in a dichotomous, categorical response variable, such as 90-day readmission. So whether the outcome variable is categorical or quantitative, regression can be appropriate. An example for each of these types could be found in two similar cases. For both examples define the predictor variables as age, gender and anticoagulant usage. In the first, use the predictor variables in a linear regression to evaluate their individual effects on length of stay, a quantitative variable. For the second, use the same predictor variables in a logistic regression to evaluate their individual effects on whether the patient had a 90-day readmission, a dichotomous categorical variable. Analysis can compute a p-value for each included predictor variable to determine whether they are significantly associated. The statistical tests in this article generate an associated test statistic which determines the probability the results could be acquired given that there is no association between the compared variables. These results often come with coefficients which can give the degree of the association and the degree to which one variable changes with another. Most tests, including all listed in this article, also have confidence intervals, which give a range for the correlation with a specified level of confidence. Even if these tests do not give statistically significant results, the results are still important. Not reporting statistically insignificant findings creates a bias in research. Ideas can be repeated enough times that eventually statistically significant results are reached, even though there is no true significance. In some cases with very large sample sizes, p-values will almost always be significant. In this case the effect size is critical as even the smallest, meaningless differences can be found to be statistically significant.

These variables and tests are just some things to keep in mind before, during and after the analysis process in order to make sure that the statistical reports are supporting the questions being answered. The patient population, types of variables and statistical tests are all important things to consider in the process of statistical analysis. Any results are only as useful as the process used to obtain them. This primer can be used as a reference to help ensure appropriate statistical analysis.

the significance level and probability of a type I error, the probability of a false positive

test observing mean differences in a quantitative variable between values of a categorical variable, typically with three or more values to distinguish from a t-test

the probability of a type II error, the probability of a false negative

place patients into groups, such as gender, race or smoking status

examines association between two categorical variables

a range for the correlation with a specified level of confidence, 95% for example

variables likely to affect the outcome variable that are not closely related to the other explanatory variables

the idea being tested by statistical analysis

regression used to predict differences in a quantitative, continuous response variable, such as length of stay

regression used to predict differences in a dichotomous, categorical response variable, such as 90-day readmission

regression utilizing more than one predictor variable

the hypothesis that there are no significant differences for the variable(s) being tested

the population the data is collected to represent

analysis performed after the original test to provide additional context to the results

1-beta, the probability of avoiding a type II error, avoiding a false negative

explanatory, or independent, variables that help explain changes in a response variable

a value between zero and one, which represents the probability that the null hypothesis is true, usually compared against a significance level to judge statistical significance

variable measuring or counting some quantity of interest

outcome, or dependent, variables whose changes can be partially explained by the predictor variables

a study using previously existing data that was not originally collected for the purposes of the study

the number of patients or observations used for the study

alpha, the probability of a type I error, usually compared to a p-value to determine statistical significance

analysis of data using statistical testing to examine a research hypothesis

testing used to examine the validity of a hypothesis using statistical calculations

determine whether to reject the null hypothesis, whether the p-value is below the threshold of a predetermined significance level

test comparing whether there are differences in a quantitative variable between two values of a categorical variable

Funding Statement

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity.

Conflicts of Interest

The author declares he has no conflicts of interest.

Christian Vandever is an employee of HCA Healthcare Graduate Medical Education, an organization affiliated with the journal’s publisher.

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity. The views expressed in this publication represent those of the author(s) and do not necessarily represent the official views of HCA Healthcare or any of its affiliated entities.

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How To Write The Results/Findings Chapter

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

Overview: Quantitative Results Chapter

• What exactly the results chapter is
• What you need to include in your chapter
• How to structure the chapter
• Tips and tricks for writing a top-notch chapter
• Free results chapter template

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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The Data Deep Dive: Statistical Analysis Guide

Table of contents

• 1 What Is Statistical Analysis and Its Role?
• 2 Preparing for Statistical Analysis
• 3 Data Collection and Management
• 4 Performing Descriptive Statistical Analysis
• 5 Performing Inferential Statistics Analysis
• 6 Writing the Statistical Research Paper
• 7 Common Mistakes in Statistical Analysis
• 8 Ethical Considerations
• 9 Concluding the Research Paper
• 10 Examples of Good and Poor Statistical Analysis in Research Paper
• 11 Key Insights: Navigating Statistical Analysis

Statistical analysis is fundamental if you need to reveal patterns or identify trends in datasets, employing numerical data analysis to eliminate bias and extract meaningful vision. Accordingly, it is crucial in research explanation, model evolution, and survey planning.

Statistical analysts make valuable results from the raw data, facilitating informed decision-making and predictive statistical analytics based on historical information.

Do you need to make a statistical analysis for your university studies? In this statistical study article, you will find instructions on how to write statistical analysis, as well as types of statistical analysis, statistical tools, and common mistakes students face.

What Is Statistical Analysis and Its Role?

Statistical analysis is the systematic process of collecting, organizing, and interpreting numbers to reveal patterns and identify trends and relationships. It plays a crucial role in research by providing tools to analyze data objectively, remove bias, and draw conclusions. Moreover, statistical analysis aids in identifying correlations, testing hypotheses, and making predictions, thereby informing decision-making in various fields such as computer science, medicine, economics, and social sciences. Thus, it enables quantitative data and statistical analytics researchers to assess results.

Struggling with how to analyze data in research? Feel free to address our specialists to get skilled and qualified help with research paper data analysis.

Preparing for Statistical Analysis

Preparing for statistical analysis requires some essential steps to ensure the validity and reliability of results. Working with a recruiting business intelligence agency can ensure you have the right talent to navigate these critical processes effectively.

• Firstly, formulating understandable and measurable questions is critical for valid statistics in a research paper. Questions lead the entire data analysis process and help define the scope of the study. Accordingly, scientists should develop specific, relevant, and capable issues that can be answered through statistical methods.
• Secondly, identifying appropriate data is vital. Picking an accordant data set that aligns with the investigations guarantees the analysis and business intelligence are focused and meaningful. For this purpose, researchers should consider data origin, quality, and responsibility when selecting data for analysis.

By scrupulously formulating problems and selecting appropriate statistical analytics data, researchers can lay a solid foundation for statistical analysis, guiding to strong and prudent results.

Data Collection and Management

Information collection and management are integral components of the statistical analysis process, ensuring the accuracy and reliability of results. Firstly, considering the techniques of data collection is essential. Here, researchers may employ primary approaches, such as examinations, interviews, or experiments, to gather direct information. Secondary methods involve utilizing existing data sources like databases, statistical analysis software, literature reviews, or archival records.

To collect data, specialists need to analyze:

• dependent variable;
• categorical variables;
• outcome variable;
• patterns and trends;
• alternative hypothesis states.

Once data is collected, organizing it is crucial for efficient analysis. As a rule, researchers utilize statistical analysis software tools or spreadsheets to manage data systematically, ensuring clarity and accessibility. Besides, proper organization includes labeling variables, formatting data consistently, and documenting any transformations or cleaning statistical procedures undertaken.

Effective data management also facilitates coherent analysis, empowering scientists to get meaningful insights and draw valid conclusions. By using suitable data collection approaches and organizing data systematically, researchers can unlock the full potential of statistical analysis, advancing knowledge and driving proof-based replies.

Performing Descriptive Statistical Analysis

Performing descriptive statistics is essential in knowing and summarizing data sets for statistics in research. Usually, it involves exploring the crucial characteristics of the data to gain insights into its normal allotting and changeability.

The basics of descriptive statistics encompass measures of central tendency, dispersion, and graphical representations.

• Measures of main bias , such as mean, median, and mode, summarize a dataset’s typical or main value.
• Dispersion repeated measures , including range, variance, and standard deviation, quantify the spread or variability of the data points.
• Graphical representations , such as histograms, box plots, and scatter plots, offer visual insights into the distribution and patterns within the data based on statistical observations.

Explaining descriptive statistical analysis results involves understanding and presenting the findings effectively. Accordingly, researchers should show understandable explanations of the descriptive statistics in the research paper calculated, highlighting key insights and trends within the data. Indeed, visual representations can enhance understanding by illustrating the distribution and relationships in the data. Hence, it’s essential to consider the context of the analysis and the questions when interpreting the results, ensuring that the conclusions drawn are suggestive and relevant.

Overall, performing descriptive statistical data analysis enables researchers to summarize and derive the crucial characteristics after collecting data. It is vital to provide a foundation for further research study and interpretation. By mastering the basics of different types of statistical analysis and correctly explaining the results, experimentals can uncover valuable insights and communicate their findings clearly and precisely.

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Performing Inferential Statistics Analysis

When students perform statistical analysis, it involves making statistical inference and drawing conclusions about a population based on sample data. For this reason, the inferential statistical tool in research revolves around hypothesis testing, confidence intervals, and significance levels.

On the one side, hypothesis testing allows researchers to assess the validity of assumptions underlying entire population parameters by comparing one sample data to theoretical expectations. On the other side, sample data, null hypothesis, and confidence intervals provide a range of normal and extreme values within which the proper population parameter will likely fall. Lastly, significance levels indicate the probability of obtaining the observed results by chance alone, helping researchers determine the reliability of their findings.

Choosing the proper approach is crucial for conducting meaningful inferential statistics analysis. Accordingly, researchers must select appropriate parametric tests based on the research design, collect data type, null hypothesis, and hypothesis being tested. For example, standard parametric tests and non parametric tests include:

• T-tests: a parametric statistical test used to determine if there is a significant difference between the means of two groups. It is commonly used when the sample size is small, and the population standard deviation is unknown.
• Z test: similar to the t-test, the z-test is a parametric test used to compare means, but it is typically employed when the sample size is large and/or the population standard deviation is known.
• ANOVA: this parametric statistical test compares the means of three or more groups simultaneously. It assesses whether there are any statistically significant differences between the means of the groups.
• Regression: a statistical method used to examine the relationship between one dependent variable (often denoted as Y) and one or more independent variables (often denoted as X) within one case study analysis . Thus, it helps in understanding how the value of the dependent variable changes when one or more independent variables are varied. Here, case study analysis refers to applying regression analysis in specific scenarios or case studies to explore relationships between quantitative variables.

Importantly to note, interpreting results from inferential studies requires a nuanced understanding of statistical concepts and diligent consideration of the context. Here, investigators should assess the strength of evidence supporting their conclusions, considering factors such as effect size, statistical power, and potential biases. Besides, communicating inferential statistics results involves presenting findings and standard deviation to highlight the implications for the research question or troublesome under investigation.

Writing the Statistical Research Paper

Writing a research paper involves integrating and presenting your findings coherently. You need to know the answers to the questions: “What is statistical analysis?” and “How do you do a statistical analysis?”. As a rule, the typical structure includes several essential sections:

• Introduction : This section provides backdrop information on the research theme, states the research questions or null hypothesis, patterns, and trends, and outlines the study’s objectives and statistical attention.
• Methodology : Here, researchers detail the methods and procedures for analyzing and collecting data. This section should be thorough enough for other researchers to replicate the study.
• Results : This section presents the study’s findings, often through descriptive and inferential statistical data analysis. It’s essential to present results objectively and accurately, using appropriate statistical study measures and techniques.
• Discussion : In this segment, investigators interpret statistics and the results, discuss their implications, and compare them to existing literature. It’s an opportunity to critically evaluate the findings and address any limitations or potential biases.
• Conclusion : The conclusion summarizes the study’s key findings, discusses their significance, and suggests avenues for future research.

When you present or write a statistical report in each section, it’s crucial to clearly and concisely explain the methods, results, and research design. Therefore, students usually need to test it in the sample group. In the methodology section, describe the statistical techniques used and justify their appropriateness for the research question. Otherwise, use descriptive statistics to summarize data and inferential statistics to test hypotheses or explore relationships between variables.

Whereas, graphics and tables are potent statistical instruments for presenting data effectively. Choose the most appropriate format for your data, whether it’s a bar graph, scatter plot, or table of descriptive statistics for research.

As a result, writing your research essay must involve such steps:

• Arranging your decisions analytically;
• Integrating statistical analysis throughout;
• Using visuals and tables to enhance clarity and understanding.

Common Mistakes in Statistical Analysis

Common mistakes in statistical analysis can undermine the validity and reliability of research findings. Here are some key pitfalls to avoid:

• Confusing terms like ‘mean’ and ‘median’ or misinterpreting p value and confidence intervals can lead to incorrect conclusions.
• Selecting the wrong test for the research question or ignoring test assumptions can compromise the accuracy of the results.
• Ignoring missing data and outliers or failing to preprocess data properly can introduce bias and skew results.
• Focusing solely on statistical significance without considering practical significance or engaging in p-hacking practices can lead to misleading conclusions.
• Failing to share facts or selectively report results can hinder research reproducibility and transparency.
• Both small and large sample sizes can impact the reliability and generalizability of findings.
• Repeatedly testing hypotheses on the same data set or creating overly complicated models can result in spurious decisions.
• Failing to interpret statistical results within the broader context or generalize findings appropriately can limit the practical relevance of research.
• Misrepresenting graphics or neglecting to label and interval scale graphs correctly can distort the statistical analysis of data.
• Managing redundant analyses or ignoring existing knowledge in the field can hinder the promotion of research.

Avoiding common mistakes in statistical analysis requires diligence and attention to detail. Consequently, researchers should prioritize understanding statistical concepts systematically and using appropriate methods for exploratory data analysis. Thus, it’s essential to double-check calculations, verify assumptions, and seek guidance from statistical analysts if needed.

Furthermore, maintaining transparency and reproducibility in research practices is leading. It includes sharing data, code, and methodology details to facilitate equivalent surveys and replication of findings.

Continuous data learning and staying updated on best practices in statistical analysis are also vital for avoiding pitfalls and improving the quality of research. By addressing these common mistakes and adopting robust practices, researchers can ensure the morality and reliability of their findings, contributing to advancing knowledge in their respective fields.

Ethical Considerations

Ethical considerations in statistical analysis encompass safeguarding data privacy and integrity. That being said, researchers must uphold ethical practices in handling data, ensuring confidentiality, and respecting participants’ rights. Indeed, transparent reporting of results is vital, as is disclosing potential conflicts of passion and holding to moral guidelines data dedicated to relevant institutions and controlling bodies. By prioritizing ethical principles, researchers can maintain trust and integrity in their work, fostering a culture of responsible data analysis in research and decision-making.

Concluding the Research Paper

Concluding a research paper involves summarizing key findings and suggesting future research directions. Here, reiterating the paper’s main points and highlighting the significance of the results is essential. Statistical analysts can also discuss limitations and areas for further investigation, providing context for future studies. By showing insightful outcomes and figuring out avenues for future research, scientists can contribute to the ongoing discourse in their field and inspire further inquiry and exploration.

Examples of Good and Poor Statistical Analysis in Research Paper

Good statistical analysis examples in research:

• A study on the effectiveness of a new drug uses appropriate parametric tests, presents results clearly with confidence intervals, and discusses both statistical and practical significance.
• A survey-based research project employs stratified random sampling, ensuring a representative sample, and utilizes advanced regression analysis to explore complex relationships between variables.
• An experiment investigating the impact of a teaching method on student performance controls for potential confounding variables and conducts power statistical analysis basics to determine sample size, ensuring adequate statistical power.

Examples of poor stat analysis in research:

• A study fails to report key details about information collection and statistical methods, making it impossible to evaluate the validity of the findings.
• A research paper relies solely on p value to conclude without considering effect sizes or practical significance, leading to misleading interpretations.
• An analysis uses an inappropriate statistical test for the research question, resulting in flawed conclusions and misinterpretation of the data.

Here are two good examples.

Example 1: The Effect of Regular Exercise on Anxiety Levels among College Students

Introduction: In recent years, mental health issues among college students have become a growing concern. Anxiety, in particular, is prevalent among this demographic. This study aims to investigate the potential impact of regular exercise on anxiety levels among college students. Understanding this relationship could inform interventions aimed at improving mental well-being in this population.

Methodology: Participants (N = 100) were recruited from a local university and randomly assigned to either an exercise or control group. The exercise group engaged in a supervised 30-minute aerobic exercise session three times a week for eight weeks, while the control group maintained regular activities. Anxiety levels were assessed using the State-Trait Anxiety Inventory (STAI) before and after the intervention period.

Results: The results revealed a significant decrease in anxiety levels among participants in the exercise group compared to the control group (t(98) = -2.45, p < 0.05). Specifically, the mean anxiety score decreased from 45.2 (SD = 7.8) to 38.6 (SD = 6.4) in the exercise group, while it remained relatively stable in the control group (mean = 44.5, SD = 8.2).

Discussion: These findings suggest that regular aerobic exercise may have a beneficial effect on reducing anxiety levels among college students. Engaging in physical activity could serve as a potential non-pharmacological intervention for managing anxiety symptoms in this population. Further research is warranted to explore this relationship’s underlying mechanisms and determine optimal exercise duration and intensity for maximum mental health benefits.

Example 2: The Relationship between Service Quality, Customer Satisfaction, and Loyalty in Retail Settings

Introduction: Maintaining high levels of customer satisfaction and loyalty is essential for the success of retail businesses. This study investigates the relationship between service quality, customer satisfaction, and loyalty in a local retail chain context. Understanding these dynamics can help businesses identify areas for improvement and develop strategies to enhance customer retention.

Methodology: A survey was conducted among the retail chain’s customers (N = 300) to assess their perceptions of service quality, satisfaction with their shopping experience, and intention to repurchase from the store. Service quality was measured using the SERVQUAL scale, while customer satisfaction and loyalty were assessed using Likert-type scales.

Results: The results indicated a strong positive correlation between service quality, customer satisfaction, and loyalty (r = 0.75, p < 0.001). Furthermore, regression analysis revealed that service quality significantly predicted both customer satisfaction (β = 0.60, p < 0.001) and loyalty (β = 0.45, p < 0.001). Additionally, customer satisfaction emerged as a significant predictor of loyalty (β = 0.50, p < 0.001), indicating its mediating role in the relationship between service quality and loyalty.

Discussion: These findings underscore the importance of high-quality service in enhancing customer satisfaction and fostering loyalty in retail settings. Businesses should prioritize investments in service training, infrastructure, and customer relationship management to ensure positive shopping experiences and promote repeat patronage. Future research could explore additional factors influencing customer loyalty and examine the effectiveness of specific loyalty programs and incentives in driving repeat business.

Key Insights: Navigating Statistical Analysis

To sum up, mastering a statistical analysis system is essential for researchers to derive meaningful insights from data. Understanding statistical concepts, choosing appropriate methods, and adhering to ethical guidelines are paramount.

Additionally, transparent reporting, rigorous methodology, and careful interpretation ensure the integrity and reliability of research findings. By avoiding common pitfalls and embracing best practices, researchers can contribute to advancing knowledge and making informed decisions across various fields. Statistical Analysis is one of the most in-demand hard skills that employers look for in potential candidates. So, you may even look for  online study courses that can help you upskill and master this skill.

Ultimately, statistical analysis is a powerful tool for unlocking the mysteries hidden within data, guiding us toward more profound understanding and innovation.

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• How to Write a Results Section | Tips & Examples

How to Write a Results Section | Tips & Examples

Published on August 30, 2022 by Tegan George . Revised on July 18, 2023.

A results section is where you report the main findings of the data collection and analysis you conducted for your thesis or dissertation . You should report all relevant results concisely and objectively, in a logical order. Don’t include subjective interpretations of why you found these results or what they mean—any evaluation should be saved for the discussion section .

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Table of contents

How to write a results section, reporting quantitative research results, reporting qualitative research results, results vs. discussion vs. conclusion, checklist: research results, other interesting articles, frequently asked questions about results sections.

When conducting research, it’s important to report the results of your study prior to discussing your interpretations of it. This gives your reader a clear idea of exactly what you found and keeps the data itself separate from your subjective analysis.

Here are a few best practices:

• Your results should always be written in the past tense.
• While the length of this section depends on how much data you collected and analyzed, it should be written as concisely as possible.
• Only include results that are directly relevant to answering your research questions . Avoid speculative or interpretative words like “appears” or “implies.”
• If you have other results you’d like to include, consider adding them to an appendix or footnotes.
• Always start out with your broadest results first, and then flow into your more granular (but still relevant) ones. Think of it like a shoe store: first discuss the shoes as a whole, then the sneakers, boots, sandals, etc.

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If you conducted quantitative research , you’ll likely be working with the results of some sort of statistical analysis .

Your results section should report the results of any statistical tests you used to compare groups or assess relationships between variables . It should also state whether or not each hypothesis was supported.

The most logical way to structure quantitative results is to frame them around your research questions or hypotheses. For each question or hypothesis, share:

• A reminder of the type of analysis you used (e.g., a two-sample t test or simple linear regression ). A more detailed description of your analysis should go in your methodology section.
• A concise summary of each relevant result, both positive and negative. This can include any relevant descriptive statistics (e.g., means and standard deviations ) as well as inferential statistics (e.g., t scores, degrees of freedom , and p values ). Remember, these numbers are often placed in parentheses.
• A brief statement of how each result relates to the question, or whether the hypothesis was supported. You can briefly mention any results that didn’t fit with your expectations and assumptions, but save any speculation on their meaning or consequences for your discussion  and conclusion.

A note on tables and figures

In quantitative research, it’s often helpful to include visual elements such as graphs, charts, and tables , but only if they are directly relevant to your results. Give these elements clear, descriptive titles and labels so that your reader can easily understand what is being shown. If you want to include any other visual elements that are more tangential in nature, consider adding a figure and table list .

As a rule of thumb:

• Tables are used to communicate exact values, giving a concise overview of various results
• Graphs and charts are used to visualize trends and relationships, giving an at-a-glance illustration of key findings

Don’t forget to also mention any tables and figures you used within the text of your results section. Summarize or elaborate on specific aspects you think your reader should know about rather than merely restating the same numbers already shown.

A two-sample t test was used to test the hypothesis that higher social distance from environmental problems would reduce the intent to donate to environmental organizations, with donation intention (recorded as a score from 1 to 10) as the outcome variable and social distance (categorized as either a low or high level of social distance) as the predictor variable.Social distance was found to be positively correlated with donation intention, t (98) = 12.19, p < .001, with the donation intention of the high social distance group 0.28 points higher, on average, than the low social distance group (see figure 1). This contradicts the initial hypothesis that social distance would decrease donation intention, and in fact suggests a small effect in the opposite direction.

Figure 1: Intention to donate to environmental organizations based on social distance from impact of environmental damage.

In qualitative research , your results might not all be directly related to specific hypotheses. In this case, you can structure your results section around key themes or topics that emerged from your analysis of the data.

For each theme, start with general observations about what the data showed. You can mention:

• Recurring points of agreement or disagreement
• Patterns and trends
• Particularly significant snippets from individual responses

Next, clarify and support these points with direct quotations. Be sure to report any relevant demographic information about participants. Further information (such as full transcripts , if appropriate) can be included in an appendix .

When asked about video games as a form of art, the respondents tended to believe that video games themselves are not an art form, but agreed that creativity is involved in their production. The criteria used to identify artistic video games included design, story, music, and creative teams.One respondent (male, 24) noted a difference in creativity between popular video game genres:

“I think that in role-playing games, there’s more attention to character design, to world design, because the whole story is important and more attention is paid to certain game elements […] so that perhaps you do need bigger teams of creative experts than in an average shooter or something.”

Responses suggest that video game consumers consider some types of games to have more artistic potential than others.

Your results section should objectively report your findings, presenting only brief observations in relation to each question, hypothesis, or theme.

It should not  speculate about the meaning of the results or attempt to answer your main research question . Detailed interpretation of your results is more suitable for your discussion section , while synthesis of your results into an overall answer to your main research question is best left for your conclusion .

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I have completed my data collection and analyzed the results.

I have included all results that are relevant to my research questions.

I have concisely and objectively reported each result, including relevant descriptive statistics and inferential statistics .

I have stated whether each hypothesis was supported or refuted.

I have used tables and figures to illustrate my results where appropriate.

All tables and figures are correctly labelled and referred to in the text.

There is no subjective interpretation or speculation on the meaning of the results.

You've finished writing up your results! Use the other checklists to further improve your thesis.

If you want to know more about AI for academic writing, AI tools, or research bias, make sure to check out some of our other articles with explanations and examples or go directly to our tools!

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The results chapter of a thesis or dissertation presents your research results concisely and objectively.

In quantitative research , for each question or hypothesis , state:

• The type of analysis used
• Relevant results in the form of descriptive and inferential statistics
• Whether or not the alternative hypothesis was supported

In qualitative research , for each question or theme, describe:

• Recurring patterns
• Significant or representative individual responses
• Relevant quotations from the data

Don’t interpret or speculate in the results chapter.

Results are usually written in the past tense , because they are describing the outcome of completed actions.

The results chapter or section simply and objectively reports what you found, without speculating on why you found these results. The discussion interprets the meaning of the results, puts them in context, and explains why they matter.

In qualitative research , results and discussion are sometimes combined. But in quantitative research , it’s considered important to separate the objective results from your interpretation of them.

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How do I write a dissertation data analysis plan?

How do I do dissertation data analysis?

Data Analysis Plan Overview

Dissertation methodologies require a data analysis plan . Your dissertation data analysis plan should clearly state the statistical tests and assumptions of these tests to examine each of the research questions, how scores are cleaned and created, and the desired sample size for that test. The selection of statistical tests depend on two factors: (1) how the research questions and hypotheses are phrased and (2) the level of measurement of the variables. For example, if the question examines the impact of variable x on variable y, we are talking about regressions, if the question seeks associations or relationships, we are into correlation and chi-square tests, if differences are examined, then t-tests and ANOVA’s are likely the correct test.

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Level of Measurement

The level of measurement is the second factor used in selecting the correct statistical test. If the research question will examine the impact of X on Y variable, and that outcome variable Y is scale, a linear regression is the correct test. For example, what is the impact of Income on Savings (as a scale variable), the linear regression is the test.  If that outcome variable Y is ordinal, then an ordinal regression is the correct test (e.g., what is the impact of Income on Savings (with Savings as an ordinal $0-$100, $101-$1000, $1001-$10,000, variable), then an ordinal regression is the correct test. If the research question examines relationships, and the X and Y variable are categorical, then chi-square is the appropriate test. The main point is that both the phasing of the research question and the level of measurement of the variables dictate the selection of the test. This video on decision trees may be useful.

Statistical Assumptions in Data Analysis Plan

Part of the data analysis plan is to document the assumptions of a particular statistical test. Most assumptions fall into the normality, homogeneity of variance, and outlier bucket of assumptions. Other tests have additional assumptions. For example, in a linear regression with several predictors, the variance inflation factor needs to be assessed to determine that the predictors are not too highly correlated. This data analysis plan video may be helpful.

Composite Scores and Data Cleaning

Data analysis plans should discuss any reverse coding of the variables and the creation of composite or subscale scores. Before creating composite scores, alpha reliability should be planned to be examined. Data cleaning procedure should be documented.  For example, the removal of outliers, transforming variables to meet normality assumption, etc. 

Sample Size and Power Analysis

After selecting the appropriate statistical tests, data analysis plans should follow-up with a power analysis. The power analysis determines the sample size for a statistical test, given an alpha of .05, a given effect size (small, medium, or large) at a power of .80 (that is, an 80% chance of detecting differences or relationships if in fact difference are present in the data. This power analysis video may be helpful.