Research Statistical Tests: A Primer


Understanding research statistical tests is crucial for analyzing data effectively. These tools can help us summarize data, make educated guesses about larger groups from smaller samples, and support our findings with solid evidence. Here’s a quick overview:

  • Descriptive statistics offer a snapshot of your data, focusing on averages, ranges, and visuals.

  • Inferential statistics allow for predictions about larger groups based on sample data, including hypothesis testing and understanding p-values.

  • Common tests include t-tests (comparing two groups), ANOVA (multiple groups), chi-square tests (categorical data), and regression analysis (predicting relationships).

  • Choosing the right test depends on your data type, variables, and research questions. Tools like can simplify this process.

  • Hypothesis testing involves null and alternative hypotheses, with the significance of results often determined by p-values.

Whether you’re comparing average reactions, predicting outcomes, or exploring categories, picking the appropriate statistical test is a foundational step in research.

Defining Statistical Tests

Statistical tests are like tools that help scientists make sense of their study results. They use these tools to figure out if what they observed in their experiment can tell us something true about the world, or if it just happened by chance.

There are two main kinds of these tools:

  • Descriptive statistics are all about giving a summary of your data. Think of it as the highlight reel of your data set, showing stuff like the average score, the range of scores, and visuals like charts.

  • Inferential statistics are a bit like detectives. They help you take a small bit of information (like a survey from a few people) and guess what a much larger group might think or do. This includes figuring out if two things are connected, if one thing affects another, or how likely something is to happen.

Some tools you might have heard of include t-tests, ANOVA (which helps compare groups), regression analysis (looking at relationships), and more. While computer programs do the heavy math lifting, it's important for researchers to pick the right tool for their question.

The Scientific Method and Statistics

Statistical tests and the scientific method are best buddies. The scientific method is a step-by-step way to explore questions and get answers. Statistical tests are what you use to make sure those answers make sense.

Here's how they work together:

  • Research design - Before you start, statistics help you figure out things like how many people to include in your study to get reliable results.

  • Objectivity - These tests use numbers to help make sure we're not letting our personal feelings sway the results.

  • Drawing conclusions - The numbers from these tests tell us if what we found in our study is likely true or just happened by chance.

  • Generalizing - Inferential statistics help us be more sure that what we found in a small group can apply to a larger one.

Together, they make sure that when we say something is true based on our study, it's backed up by solid math. This way, we can trust our findings and so can everyone else.

Types of Data and Variables

Scale of Measurement

Think of data like different kinds of measuring sticks. Depending on what you're measuring, you'll need a different kind:

  • Nominal - This is when you're just naming things without worrying about order. Like if you're sorting people by their hair color or where they're from. You can count how many are in each group, but that's about it. For this kind of data, you might use tests like chi-square or binomial tests.

  • Ordinal - Here, things have a specific order, but you can't measure the gaps between them. It's like rating pain from 1 to 10. You know 10 hurts more than 1, but not by how much. Tests for ordinal data include Mann-Whitney U or Spearman correlation.

  • Interval - Now, you can measure the distance between points, like temperature. But there's no starting point of zero. You can do more math here, like averages, and use tests like ANOVA or t-tests.

  • Ratio - This is the full package. You've got order, measurable gaps, and a true zero point. Think height or weight. You can do all sorts of calculations and use complex analyses.

Understanding Variables

When we talk about variables, we're talking about the things we're studying or measuring:

  • Independent variable - This is what you change or control to see what happens. It's your starting point.

  • Dependent variable - This is what you're measuring to see if it changes because of the independent variable.

  • Categorical variable - This puts things into groups, like types of fruit or book genres. It's about sorting.

  • Continuous variable - This is when your measurements can be super precise, like measuring height or the temperature of a cup of coffee.

Knowing what kind of data and variables you have helps you pick the right tools (tests) to understand your research better.

Descriptive vs. Inferential Statistics

Describing the Data

Descriptive statistics are all about summarizing your data. Think of them as giving you a quick snapshot of what your data looks like without making any big assumptions or predictions. Here’s what they help you figure out:

  • Measures of central tendency: This fancy term just means finding the average (mean), the middle value (median), and the most common value (mode) in your data. It’s like figuring out the most typical or expected outcome.

  • Measures of variability: This tells you how spread out your data is. If the range, variance, or standard deviation is high, your data points are more scattered. It’s about understanding how much your data varies.

  • Visual representations: Things like charts and graphs can show you at a glance what your data looks like. They can help spot trends, outliers, or how your data is grouped.

Descriptive statistics are great for getting to know your data, but they don’t make any guesses about what that data might say about the bigger picture.

Making Inferences

Inferential statistics are where you start making some educated guesses based on your data. You use what you’ve learned from a smaller group (your sample) to make predictions or decisions about a larger group (the population). Here’s how it works:

  • Hypothesis testing: This is when you test out an idea to see if it holds up against your data. You start with a null hypothesis, which is a fancy way of saying you assume there’s no effect or difference until proven otherwise.

  • Confidence intervals: These give you a range that your true result likely falls within. A wider range means you’re less sure about the exact number.

  • Statistical significance: This tells you if your results are probably just by chance or if they’re something worth noting. A small p-value (a way of measuring this) means your findings are likely not just a fluke.

  • Correlation and regression: These tools help you see if and how things are related. Correlation tells you if two things move together, but not why. Regression tries to predict one thing based on another.

Inferential statistics take the details from your sample and help you make broader conclusions. It’s about using what you know to make smart guesses about what you don’t know.

Common Statistical Tests


Imagine you want to see if two groups of people feel differently about a new chocolate bar. A t-test helps you figure this out by comparing their average reactions. It's especially handy when you don't have a lot of people in your study.

Things to remember about t-tests:

  • They compare average reactions from two different groups or situations

  • Help find out if the differences in reactions are just by chance or if they're real

  • Good for studies with fewer people

  • Assumes everyone's reaction follows a common pattern (normally distributed)

  • Two flavors:

    • Independent - when the two groups don't overlap

    • Paired - when the same people are in both groups, like before and after trying the chocolate

  • The end result tells you if the groups truly felt differently

In short, t-tests are great for figuring out if two groups have different opinions or reactions in an experiment.


What if you have more than two chocolate bars and want to compare how much people like each one? ANOVA is your go-to test. It's like doing several t-tests at once but better because it keeps the math in check.

Key points about ANOVA:

  • Compares average likes or dislikes across three or more groups

  • It's like a supercharged t-test for multiple groups

  • Checks if any differences in likes are too big to be just by chance

  • Different types for different situations:

    • One-way - when you're looking at one feature, like flavor

    • Two-way - when considering two features, like flavor and packaging

    • Repeated measures - when the same people try all the bars

  • Tells you if there's a big difference in how the groups feel

ANOVA helps when you're comparing several things at once in your research.

Chi-Square Tests

Now, let's say you're curious if there's a link between people's favorite chocolate bar and their age group. Chi-square tests are perfect for this. They work with categories (like age groups) instead of numbers.

What to know about chi-square tests:

  • Great for when you're dealing with types or categories

  • Helps see if two categories are connected

  • Compares what you observe with what you'd expect

  • Often used in surveys

  • Needs:

    • Data to be in groups

    • Each observation to be independent

    • Enough people in the study

  • Shows if there's a real link between categories

Chi-square tests are useful for finding out if there's a relationship between different kinds of categories, like age and chocolate preferences.

Regression Analysis

Imagine you want to predict how much someone will like a chocolate bar based on its sweetness and how much they like sweet things in general. Regression analysis is the tool for this job. It helps you understand and predict relationships between things.

Key points about regression analysis:

  • Helps predict one thing based on others

  • Lots of types, but here are a few:

    • Linear - predicts using a straight line

    • Multiple - uses more than one factor to predict

    • Logistic - for yes/no predictions

  • The strength of the prediction is shown by regression coefficients

  • Assumes:

    • A straight-line relationship

    • Each person's response is independent

    • A normal pattern in the predictions

  • Tells you how well your prediction matches real life

Overall, regression analysis is a powerful way to predict how factors like sweetness affect someone's chocolate bar preference.

Choosing the Right Test

Factors to Consider

When you're trying to figure out which statistical test to use, think about these things:

  • Types of variables - Are you working with categories (like types of fruit) or numbers (like weights)? This choice impacts which tests are suitable.

  • Number of groups/conditions - Are you comparing two things or several? Some tests only work for two.

  • Paired vs independent groups - If comparing, are your groups completely separate or somehow connected? There are specific tests for each scenario.

  • Normality of data distribution - Some tests need your data to fit a 'normal' pattern. It's like checking if your data plays by certain rules.

  • Hypotheses and research questions - Think about what you're trying to find out. Do you want to see if two things are related, or if one thing affects another? Choose a test that helps answer your question.

  • Assumptions of statistical tests - Every test has its own set of rules about the data. Make sure your data fits these rules.

Keeping these points in mind will help you choose the right test for your data.

A Step-by-Step Guide

Here's how to pick a statistical test, step by step:

  1. First, figure out what kind of data you have (like categories or numbers) and how you're grouping it.

  2. Decide if you're comparing different groups or looking at changes in the same group over time. Count how many groups you have.

  3. Think about your main question. What do you want to learn from your data?

  4. Check if your data fits the 'normal' pattern. If not, you might need to adjust it.

  5. Use a guide or a chart that helps pick tests based on your data type and what you're trying to find out. Narrow it down to a few options.

  6. Learn more about these options to understand how they work and what they assume about your data.

  7. Choose the one test that fits your needs the best. If you have different questions, you might need more than one test.

  8. Make sure your findings are solid by looking at things like how big the effect is, how certain you are (confidence intervals), and how likely your test was to catch a real effect (statistical power).

Following these steps will guide you to the right statistical test for your research. Double-check your choice before you dive into the analysis.

Hypothesis Testing Concepts

Null and Alternative Hypotheses

When we do statistical tests, we start with two main ideas: the null hypothesis and the alternative hypothesis.

The null hypothesis is a fancy way of saying we don’t think anything special is happening. For instance, if we’re looking at study times and test scores, the null hypothesis would say that studying 1 hour per day or 3 hours per day makes no difference in scores.

The alternative hypothesis is what we suspect might be true instead. In our study time example, this would mean we think that studying 3 hours a day actually leads to better test scores than studying just 1 hour.

The alternative hypothesis can come in a few flavors:

  • Directional - This is when we’re pretty specific, saying one group will do better or worse than the other.

  • Non-directional - Here, we just think there’s a difference, but we’re not saying who’s better or worse.

  • Greater/less than - This is saying specifically that one group’s scores will be higher or lower than the other’s.

Choosing between these depends on what we’re curious about and how we’ve set up our study.

p-values and Significance Levels

A p-value is a number that tells us how likely our results are if the null hypothesis was actually true. A really small p-value means it’s pretty unlikely our results happened by accident, which makes us doubt the null hypothesis.

Significance levels are like the goalposts for deciding if our p-value is small enough to matter. Common goals are 0.05, 0.01, and 0.001. If our p-value is smaller than our goal, we say our results are "statistically significant".

So, if we get a p-value of 0.03 and our goal was 0.05, our results are significant. This means there’s only a 3% chance we’d see this big of a difference by chance, which is pretty good evidence against the null hypothesis.

But, if our p-value is 0.06 and our goal was 0.05, it’s not significant. Now, there’s a 6% chance our results could just be a fluke, which isn’t convincing enough to say the null hypothesis is wrong.

P-values and significance levels help us figure out if we should believe our alternative hypothesis over the null hypothesis, based on how unlikely our results are under the null hypothesis.

Advanced Topics

Non-Parametric Tests

Non-parametric tests are a go-to when your data doesn't play nice and fit into neat, normal patterns. These tests don't make as many assumptions about your data, which means they're more versatile.

Here's the lowdown:

  • Perfect for when your data is a bit all over the place or doesn't follow the usual rules

  • They focus more on the order or ranking of your data, not the exact numbers

  • Some common ones you might come across include:

    • Wilcoxon signed-rank test

    • Mann-Whitney U test

    • Kruskal-Wallis H test

  • They might not be as strong (statistically powerful) as other tests, but they're great when you're working with smaller groups or when your data is ranked

  • Super useful when you can't use the more common tests because your data isn't typical

Non-parametric tests give you options when your data isn't perfect, trading some power for flexibility.

Bayesian Statistics

Bayesian statistics is like adding your own experience or what you already believe into your research. It mixes what you think before you start with what you find out.

Here's the gist:

  • You begin with what you believe (prior probability) and mix it with new data to update your beliefs

  • This mix gives you a new probability (posterior) that tells you what you believe now, after seeing the new data

  • It's like saying, "Based on what I knew and what I've just learned, there's a 95% chance this is true."

  • Great for when you want to keep building on what you know or when you have expert advice guiding your study

  • It makes your results feel more personal and direct, but you need to be careful about how you start (your priors)

  • Needs more computer power but can make your results easier to understand

Bayesian statistics is handy when you're adding new info to what you already know or when you want to use expert knowledge in your study. It makes your findings a bit more relatable but requires a good starting point.

Practical Application with

The Platform is a website that makes it easier for researchers to work with their data. It has features like:

  • A simple way to upload your data and set up tests without needing to know a lot of math or computer coding

  • Guides that help you pick the right test for your data and what you want to find out

  • Automatic calculations for tests like t-tests, ANOVA, and regression analysis

  • Easy-to-understand charts and graphs that help you see what your analysis means

  • Tools for working together so you can share your work and talk about it with others

  • Reports you can download that explain your methods, results, and what they mean in a clear way

With, you can do complex analyses easily, even if you're not a math expert.

Case Study Examples

Here are some real examples of how people have used

Predicting Crop Yields with Regression Analysis

  • A team studying farming uploaded information about weather and crop sizes to

  • They used the site to set up a study that looks at how weather affects crop sizes

  • The site figured out the math for them and showed which weather factors are important

  • They got charts and tables that clearly showed how different weather conditions affect crops

  • This helped them give advice to farmers on the best conditions for growing crops

Comparing Fertilizers with a T-Test

  • A scientist studying plants uploaded data about how different fertilizers affect plant growth

  • She used to easily compare the growth of plants with organic versus chemical fertilizers

  • The site did the math to show if the difference in plant growth was significant

  • She got a report that clearly explained the test, the results, and what they mean, showing which fertilizer works better

These stories show how makes it easier to use advanced statistics to understand research data and make informed decisions. The site's step-by-step guides, automatic math, and tools for sharing make it a great help for researchers.


Statistical tests are super helpful for researchers who need to understand their data and make smart conclusions. Even though it might look complicated with all the different tests and details, knowing just a bit about the basics can really help.

Let's go over the main points again:

  • Descriptive statistics are about summarizing your data. They make it easy to see what's going on in your data set.

  • Inferential statistics let you make guesses about a big group based on a smaller sample. This includes important ideas like testing hypotheses, understanding p-values, figuring out confidence intervals, and knowing when your results are significant.

Some tests you'll probably see a lot include:

  • t-tests, which compare averages between two groups

  • ANOVA, which compares averages across several groups

  • Correlation and regression analyses that look at and predict relationships

  • Chi-square tests for exploring how categories are related

Choosing the right test depends on a few things like:

  • The types of variables you're working with

  • How many groups you're comparing

  • What you're trying to find out with your research

  • What you assume about your data

Following a step-by-step guide can help you pick the right test. And tools like can make the whole process easier by doing the hard math, showing you visuals, and helping you share your findings.

While the world of statistics might seem a bit intimidating at first, just knowing some of the basics can really empower researchers. It opens up new ways to explore and make meaningful contributions to their field.

Appendix: Statistical Tests Cheat Sheet

Here's a handy guide to help you quickly understand some common tests used in research. Think of it as a cheat sheet for when you're not sure which test fits your needs.


What it does

Key assumptions

When to use


Checks if two groups are different on average

Assumes everyone in the groups is different (independent), the data follows a bell curve (normal distribution), and both groups have similar spread (variances)

Use it when you're comparing how two groups react to something


Checks if three or more groups are different on average

Same as t-test, but for more than two groups

Use it when comparing several groups to see if they react differently

Linear regression

Shows how one thing can predict another, and the type of relationship they have

Assumes a straight-line relationship, each person's answer doesn't affect the others, and the predictions are normally spread

Use it to show how one thing affects another or to predict outcomes

Logistic regression

Predicts whether something belongs in one group or another based on different factors

Assumes each person's answer is independent

Use it to predict which group something belongs to

Chi-square test

Checks if there's a pattern or relationship between two kinds of categories

Assumes each observation is independent and you have enough data

Use it to see if two categories are related, like if age affects chocolate preference

Wilcoxon signed-rank test

Compares two sets of scores that are connected in some way, without needing the data to follow a bell curve

Assumes the scores are paired or repeated

Use it when comparing two related groups without assuming a bell curve

Mann-Whitney U test

Compares two separate groups to see if they're different, without needing the data to follow a bell curve

Assumes each group is independent

Use it for comparing two groups without assuming a bell curve

Kruskal-Wallis H test

Compares more than two separate groups to see if they're different, without needing the data to follow a bell curve

Assumes each group is independent

Use it for comparing several groups without assuming a bell curve

This table gives you a quick look at some popular statistical tests, what they're good for, and when you might want to use them. It's sorted by the kind of test, including those for comparing averages, predicting outcomes, dealing with categories, and managing data that doesn't fit the normal curve.


Here's a simple guide to some important terms you'll come across in statistics and research:

Descriptive Statistics

This part of statistics helps us understand and describe our data better by giving us simple summaries. It tells us things like the average score, how spread out the scores are, and what the data looks like in charts.

Inferential Statistics

This area lets us use a small group of data (like a survey from a few people) to guess what a much larger group might think or how they might act. It involves figuring out if what we see in our sample is likely true for more people.

Statistical Significance

When we find something in our data that's very unlikely to have happened just by chance, we say it's "statistically significant." It's like being pretty sure that what we found isn't just a fluke.

Effect Size

This tells us how big of a deal our finding is. It helps us understand if the difference or relationship we found really matters, without getting tricked by large or small sample sizes.

Confidence Interval

This is a range of numbers that we believe includes the real answer for the whole group we're interested in. If the range is narrow, we're more confident; if it's wide, we're less sure.

Correlation Coefficient

A number that shows how two things are related. If it's close to 1 or -1, they have a strong relationship. If it's near 0, they don't really relate to each other much.

Regression Coefficient

In studies that try to predict one thing based on another, this number tells us how much we expect the thing we're predicting to change when the thing we're using to predict changes a little bit.

Degrees of Freedom

This is about the number of choices we have when figuring out certain statistics. It affects how we do some math in tests like t-tests and chi-square tests.

Statistical Power

This is about how likely our study is to spot a real effect when it exists. A study with high power is good at catching real differences or relationships that are there.

Type I and Type II Errors

A Type I error is when we think we've found something interesting, but we're wrong. A Type II error is when we miss something that's actually there. We try to avoid these errors to make sure our findings are reliable.

This guide should help you get a handle on some of the key concepts in statistics. If you have any questions or need more details, just ask!

Related Questions

What is a statistics primer?

A statistics primer is like a beginner's guide to statistics. It covers the basics, such as:

  • Different types of data (like numbers or categories)

  • Understanding the difference between the whole group you're interested in (population) and the smaller group you actually study (sample)

  • Basic tools of statistics (averages, middle values, how spread out data is)

  • Ways to show data visually (charts and graphs)

  • The basics of probability

  • How to start making guesses about a larger group based on a smaller group's data

  • How to see if two things are related or if one thing affects another

  • An overview of common tests (like t-tests and chi-square)

The main goal is to get you familiar with the language and basic ideas of statistics, so you're ready to dive deeper later.

What are statistical tests used for in research?

Statistical tests are tools researchers use to make sense of their data. They help with things like:

  • Checking theories: These tests can show if the data supports a specific idea or prediction.

  • Comparing groups: They can tell us if there's a real difference between groups in a study, helping us know which conditions are more effective.

  • Finding patterns: Tests help identify and understand how different things are connected in the data.

  • Drawing conclusions about a bigger group: By looking at a small sample, tests help us make educated guesses about a larger group.

What statistical test to use for pre and post data?

When you have data from before and after an event and you want to see if there's a significant change, the paired samples t-test is a good choice. This test looks at the difference in scores from the same group of people before and after something happens to see if the change is big enough to be meaningful. It's based on the idea that the changes should follow a normal pattern and each pair of before-and-after scores is independent from the others.

What are the 5 basic methods of statistical analysis?

Here are five key methods you'll come across in statistics:

  1. Means - This is about finding the average.

  2. Standard deviation - This tells you how much the data varies.

  3. Regression - This method helps us understand and predict how things are related.

  4. Hypothesis testing - This is about using data to test out ideas or theories.

  5. Sample size calculation - This helps figure out how many observations you need for your study.

These methods are the building blocks for more complex analysis, covering the basics of describing data, understanding relationships, and making predictions.