Which Statistical Test Should I Use for My Dissertation?

Picking the wrong statistical test is one of the quickest ways to weaken a quantitative dissertation. The good news is that the choice follows a few simple questions. This guide shows you how to match your research question and data to the right test, with a decision table, the non-parametric alternatives and the mistakes to avoid.

3 Questions to Ask First

1. What does my research question ask?

Are you comparing groups, looking for a relationship between variables, or predicting an outcome? This narrows the choice immediately.

2. What type of variables do I have?

Categorical (such as gender or course) or numerical (such as test score or hours worked)? Your outcome variable matters most.

3. Who is in each group?

Are the groups made of different people (independent), or are the same people measured more than once, for example before and after an intervention (related)?

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Know Your Variable Types

Categorical (nominal): labels with no order, such as department or yes/no.
Ordinal: ordered categories, such as satisfaction ranked from low to high.
Numerical (scale): measured numbers, such as age, income or exam score.

Likert-scale data sits between ordinal and numerical. Researchers handle it differently, so check what is accepted in your field and explain your choice in your methodology.

Decision Table

Find the row that matches your question. The last column gives the usual alternative if your data do not meet the assumptions of the first test.

Your question	Typical test	Non-parametric alternative
Compare two independent groups (numerical outcome)	Independent-samples t-test	Mann-Whitney U
Compare the same people twice (before and after)	Paired-samples t-test	Wilcoxon signed-rank
Compare three or more independent groups	One-way ANOVA	Kruskal-Wallis
Compare the same people three or more times	Repeated-measures ANOVA	Friedman test
Relationship between two numerical variables	Pearson correlation	Spearman correlation
Association between two categorical variables	Chi-square test of independence	Fisher's exact test (small counts)
Predict a numerical outcome	Linear regression (simple or multiple). See how to interpret the output	Depends on the problem; ask your supervisor
Predict a yes/no outcome	Logistic regression	—
Check a questionnaire scale is consistent	Cronbach's alpha (reliability)	—

💡 Tip: use the test that matches your research question, and name it in your methodology before you collect data. Choosing a test after seeing the results to get a significant p-value is poor practice.

Check Your Assumptions

Every test rests on assumptions. Common ones include:

Normality: the outcome is roughly normally distributed (important for t-tests and ANOVA, especially in small samples)
Equal variances: the groups have similar spread
Independence: each observation does not influence another
Linearity: for correlation and regression, the relationship is roughly a straight line
Sufficient expected counts: for chi-square, no very small expected frequencies

Report briefly which assumptions you tested and what you did if one failed, such as switching to the non-parametric alternative. Our guide to writing a dissertation results chapter shows how to report the results once you have them, and the discussion chapter guide explains how to interpret them.

Worked Example

Research question (fictional): do students who attend weekly tutorials score higher in the final exam than students who do not?

Outcome: final exam score (numerical)
Groups: attended tutorials vs did not attend (two independent groups)
Test: independent-samples t-test
If the scores are strongly skewed with a small sample: Mann-Whitney U
Report: group means and standard deviations, the test statistic with degrees of freedom, the exact p-value and an effect size

Now suppose you also ask whether study hours predict the exam score. That is a relationship between two numerical variables, so you would use correlation, or regression if you want to predict the score.

Common Mistakes

⚠️ Running many tests until something is significant. The more tests you run, the greater the chance of a false positive. Decide your tests in advance, and ask your supervisor about corrections if you run several.

Using several t-tests instead of ANOVA when comparing three or more groups
Ignoring assumptions or not mentioning them at all
Reporting only p-values without descriptive statistics or an effect size
Treating correlation as causation
Using a test that does not match the variable types, such as a t-test on a categorical outcome
Not explaining the choice of test in the methodology

Checklist

✅ Each research question is linked to a specific test
✅ Variable types are identified
✅ Independent or related groups are identified
✅ Assumptions are checked and reported
✅ A non-parametric backup is named where needed
✅ Effect sizes are reported along with p-values
✅ The choice of test is justified in the methodology

Frequently Asked Questions

How do I choose the right statistical test?

Start with your research question and ask three things: what type of variables you have (categorical or numerical), how many groups or variables you are comparing, and whether the groups are independent or the same people measured more than once. The decision table in this guide matches those answers to a test.

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

Parametric tests, such as the t-test and ANOVA, assume your data meet conditions such as being roughly normally distributed. Non-parametric tests, such as Mann-Whitney U and Kruskal-Wallis, make fewer assumptions and are often used when those conditions are not met, with small samples or with ordinal data.

When should I use a t-test and when should I use ANOVA?

Use a t-test to compare the means of two groups, and ANOVA to compare the means of three or more groups. Running several t-tests instead of one ANOVA increases the chance of a false positive.

When should I use chi-square?

Use a chi-square test of independence when both variables are categorical, for example gender and preferred study mode. If some expected counts are very small, Fisher's exact test is often recommended instead.

What is the difference between correlation and regression?

Correlation measures the strength and direction of a relationship between two variables. Regression goes further: it models how one or more predictor variables explain or predict an outcome.

Can I use a Likert scale with parametric tests?

Practice varies. Some researchers treat summed or averaged Likert scale scores as numerical and use parametric tests, while others treat single Likert items as ordinal and use non-parametric tests. Check what is accepted in your field and justify your choice in your methodology.

How big does my sample need to be?

It depends on the test and the effect size you want to detect. A power analysis, for example with free software such as G*Power, gives an estimate for your design. Ask your supervisor what your department expects.

Do I need to check assumptions before running a test?

Yes. Each test has assumptions, such as normality or equal variances. Say briefly which ones you checked and what you did if they were not met, for example using a non-parametric alternative.

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