Test selection

Which Statistical Test to Use for Your Thesis: A Complete Decision Guide

Q: Can I use a t-test if my data is not normally distributed?

No - if Shapiro-Wilk p < .05, your data significantly deviates from normality. Switch to Mann-Whitney U for two independent groups, or Wilcoxon signed-rank for paired data.

Q: What is the difference between parametric and non-parametric tests?

Parametric tests assume normal distribution and equal variances and work on raw values. Non-parametric tests make fewer assumptions and work on ranks. Non-parametric tests are less statistically powerful but valid when assumptions fail.

Q: Do I need to check assumptions before every statistical test?

Yes. Report Shapiro-Wilk and Levene's results in your methods section alongside your main analysis. Skipping this is one of the most common reasons supervisors request revisions.

Q: Which statistical test is most common in psychology theses?

The independent samples t-test and one-way ANOVA are the most common. Most thesis designs compare group means - two conditions, two genders, or multiple treatment groups - which maps directly onto these tests.

Q: How do I document my test choice in the methods section?

State: (1) which test you used, (2) why it fits your design (data type, number of groups, research question), (3) which software was used, and (4) the results of assumption checks. Example: "An independent samples t-test was used to compare exam scores between groups. Normality was confirmed using Shapiro-Wilk (p > .05) and equal variances using Levene's test (p = .312). Analysis was conducted in SPSS version 28."

February 20264 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.

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Key takeaways

4 questions decide your test: research question type → data scale → number of groups → 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 → Mann-Whitney U, ANOVA → Kruskal-Wallis - never force parametric tests on violated assumptions.
Effect size is mandatory: always report Cohen's d (t-test), η² (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.

How to Choose the Right Statistical Test for Your ThesisWatch on YouTube

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? → t-test, ANOVA, Mann-Whitney, Kruskal-Wallis
Relationship: Do variables move together? → Pearson, Spearman, Regression
Frequency: How are observations distributed? → Chi-square

Question 2 - What scale level is your data?
Metric (interval/ratio): Height, weight, exam score → parametric tests
Ordinal (ranked/Likert): Satisfaction 1–5 → non-parametric tests
Nominal (categories): Gender, country, yes/no → Chi-square

Question 3 - How many groups are you comparing?
2 groups → t-test or Mann-Whitney
3+ groups → ANOVA or Kruskal-Wallis
Same subjects twice → Paired t-test or Wilcoxon
1 group vs. known value → One-sample t-test

Question 4 - Are parametric assumptions met?
Normality: Shapiro-Wilk p > .05 → parametric OK
Equal variances: Levene's p > .05 → standard t-test / ANOVA
Either fails → 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 → Use independent samples t-test
If Shapiro-Wilk p < .05 for EITHER group → Use Mann-Whitney U test
If Levene's p < .05 but normality OK → 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

Can I use a t-test if my data is not normally distributed?

▾

No - if Shapiro-Wilk p < .05, your data significantly deviates from normality. Switch to Mann-Whitney U for two independent groups, or Wilcoxon signed-rank for paired data.

What is the difference between parametric and non-parametric tests?

▾

Parametric tests assume normal distribution and equal variances and work on raw values. Non-parametric tests make fewer assumptions and work on ranks. Non-parametric tests are less statistically powerful but valid when assumptions fail.

Do I need to check assumptions before every statistical test?

▾

Yes. Report Shapiro-Wilk and Levene's results in your methods section alongside your main analysis. Skipping this is one of the most common reasons supervisors request revisions.

Which statistical test is most common in psychology theses?

▾

The independent samples t-test and one-way ANOVA are the most common. Most thesis designs compare group means - two conditions, two genders, or multiple treatment groups - which maps directly onto these tests.

How do I document my test choice in the methods section?

▾

State: (1) which test you used, (2) why it fits your design (data type, number of groups, research question), (3) which software was used, and (4) the results of assumption checks. Example: "An independent samples t-test was used to compare exam scores between groups. Normality was confirmed using Shapiro-Wilk (p > .05) and equal variances using Levene's test (p = .312). Analysis was conducted in SPSS version 28."

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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.