Which Statistical Test to Use for Your Thesis: A Complete Decision Guide
4 min read
Choosing the wrong statistical test is the #1 reason supervisors send thesis drafts back for revision. It is not about memorising formulas - it is about answering four questions in the right order. Get them right and your test choice becomes obvious. This guide gives you a step-by-step decision framework, a comparison table covering every common thesis test, and copy-paste methods section text you can use immediately.
Key takeaways
- 4 questions decide your test: research question type β data scale β number of groups β assumption checks - answer them in order.
- Shapiro-Wilk + Levene's test: run both before any parametric test and report the results in your methods section.
- Non-normal data: switch t-test β Mann-Whitney U, ANOVA β Kruskal-Wallis - never force parametric tests on violated assumptions.
- Effect size is mandatory: always report Cohen's d (t-test), Ξ·Β² (ANOVA), or r (correlation) alongside every p-value.
- Methods section: document your test selection logic with test name, data type, group count, and assumption check results.
The 4 Questions That Decide Your Statistical Test
Every statistical test follows from four questions. Answer them in order and your test choice becomes straightforward.
- Question 1 - What does your research question ask?
- Difference: Do groups differ? β t-test, ANOVA, Mann-Whitney, Kruskal-Wallis
- Relationship: Do variables move together? β Pearson, Spearman, Regression
- Frequency: How are observations distributed? β Chi-square
- Question 2 - What scale level is your data?
- Metric (interval/ratio): Height, weight, exam score β parametric tests
- Ordinal (ranked/Likert): Satisfaction 1β5 β non-parametric tests
- Nominal (categories): Gender, country, yes/no β Chi-square
- Question 3 - How many groups are you comparing?
- 2 groups β t-test or Mann-Whitney
- 3+ groups β ANOVA or Kruskal-Wallis
- Same subjects twice β Paired t-test or Wilcoxon
- 1 group vs. known value β One-sample t-test
- Question 4 - Are parametric assumptions met?
- Normality: Shapiro-Wilk p > .05 β parametric OK
- Equal variances: Levene's p > .05 β standard t-test / ANOVA
- Either fails β use non-parametric alternative
Complete Test Comparison Table
Use this reference table to find the right test based on your research question, data type, and group structure.
| Research Question | Data Type | Groups | Assumption | Test |
|---|---|---|---|---|
| Difference | Metric | 2 independent | Normal, equal var. | Independent t-test |
| Difference | Metric | 2 independent | Non-normal | Mann-Whitney U |
| Difference | Metric | 2 paired | Normal | Paired t-test |
| Difference | Metric | 2 paired | Non-normal | Wilcoxon signed-rank |
| Difference | Metric | 3+ | Normal, equal var. | One-way ANOVA |
| Difference | Metric | 3+ | Non-normal | Kruskal-Wallis |
| Difference | Ordinal | 2 | Any | Mann-Whitney U |
| Difference | Ordinal | 3+ | Any | Kruskal-Wallis |
| Relationship | Metric | - | Both normal | Pearson correlation |
| Relationship | Ordinal | - | Any | Spearman correlation |
| Relationship | Metric | - | Normal | Linear regression |
| Frequency | Nominal | - | Any | Chi-square test |
| 1 group vs. value | Metric | 1 | Normal | One-sample t-test |
Step-by-Step Decision Walkthrough
Example scenario: "I want to compare exam scores between male and female students."
- Step 1: Question type = Difference (comparing two groups)
- Step 2: Data type = Metric (exam scores are continuous)
- Step 3: Groups = 2 independent groups (male vs. female)
- Step 4: Check assumptions - run Shapiro-Wilk on both groups
- If Shapiro-Wilk p > .05 for BOTH groups AND Levene's p > .05 β Use independent samples t-test
- If Shapiro-Wilk p < .05 for EITHER group β Use Mann-Whitney U test
- If Levene's p < .05 but normality OK β Use Welch's t-test
Copy-Paste Methods Section Template
For your thesis methods chapter, copy and adapt this paragraph:
"The appropriate statistical test was selected based on the research question, data type, number of groups, and parametric assumptions. [Difference/Relationship/Frequency] was assessed using [test name]. Data were checked for normality using the Shapiro-Wilk test and for homogeneity of variances using Levene's test. All analyses were conducted using [SPSS / Jamovi / JASP version X]. Effect size was reported as [Cohen's d / eta-squared / r] alongside p-values."
Common Test Selection Mistakes
These are the most frequent wrong choices supervisors flag during thesis reviews.
| Mistake | Why It Is Wrong | Correct Choice |
|---|---|---|
| Multiple t-tests with 3+ groups | Inflates Type I error (family-wise error) | One-way ANOVA |
| t-test on single Likert items | Violates interval scale assumption | Mann-Whitney U |
| ANOVA with only 2 groups | Overly complex; t-test is simpler and sufficient | Independent t-test |
| Skipping assumption checks | Results may be statistically invalid | Always run Shapiro-Wilk + Levene's |
| Pearson on ordinal data | Violates linearity assumption | Spearman correlation |
Frequently asked questions
What if my data violates normality?
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How do I know if my groups are independent or paired?
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Can I use a t-test with small sample sizes?
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Further reading
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Statoria Team
Statistics educators & software developers
We build Statoria to help bachelor and master students get through their thesis data analysis without stress. Our guides are written by researchers with experience in social science statistics and student supervision.