How to choose a statistical test: a quick guide for your paper or thesis
Two questions decide which test fits: what kind of variable you're measuring, and how many groups or variables you're comparing. One table sums it all up.
Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide
Choosing a test isn't a matter of taste. It follows directly from your research question and the type of data you have. Answer two questions correctly and most of the choice is already made.
Question 1: What type is the dependent variable?
The dependent variable is what you measure and want to explain.
- Continuous (quantitative): a score, age, income, a questionnaire mean. A mean of it makes sense.
- Categorical: yes/no, group, type. You count frequencies.
- Ordinal: a ranking, a single Likert item. There's an order, but the gaps aren't necessarily equal.
Question 2: What are you comparing or testing?
- A difference between two groups or three or more?
- Are the groups independent (different people) or dependent (the same people measured twice)?
- Or are you testing a relationship between variables, or predicting one variable from several?
The table that sums up the choice
| What you test | Continuous dependent variable | Non-parametric alternative |
|---|---|---|
| Difference between 2 independent groups | Independent-samples t-test | Mann–Whitney |
| Difference between 2 measurements of the same people | Paired-samples t-test | Wilcoxon |
| Difference between 3+ groups | One-way ANOVA | Kruskal–Wallis |
| 3+ measurements of the same people | Repeated-measures ANOVA | Friedman |
| Effect of two independent variables | Two-way ANOVA | |
| Relationship between two continuous variables | Pearson correlation | Spearman correlation |
| Predicting a continuous variable from several | Multiple linear regression |
When the dependent variable is categorical:
- Relationship between two categorical variables: chi-square (and if expected frequencies are below 5, Fisher's exact test).
- Predicting a yes/no outcome from several variables: logistic regression.
When do you switch to the non-parametric alternative?
Parametric tests (t, ANOVA, Pearson) mainly assume a roughly normal distribution and similar variances across groups. They're fairly robust to violations when the sample is large. Switch to the non-parametric alternative mainly when the variable is ordinal, or when the sample is small and the distribution is far from normal, for example with extreme outliers.
Common mistakes
- Running several t-tests instead of ANOVA. Every extra test raises the chance of a significant result by accident. With three or more groups, start with ANOVA and only then check pairwise comparisons.
- Ignoring dependence. If the same people were measured twice, a test for independent groups gives a wrong result.
- Choosing the test by what came out significant. You choose the test before you look at the results, based on the research question.
If your question doesn't fit the table, for example there's a mediator or moderator, or nested data (students within classes), you probably need a more complex model. That's exactly the point to get advice.
Next steps
The test follows from the hypothesis - if you haven't worded it yet, start with how to write research hypotheses. Once you've chosen, there's a guide for each test: t-tests, ANOVA and post-hoc comparisons, correlation and regression, chi-square, and non-parametric tests when assumptions fail. For models with variables in a chain - mediation and moderation with PROCESS or SEM and path analysis. And if you're checking your choice with ChatGPT, read what AI gets right, and wrong, in statistical analysis first.
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