You choose a statistical test by matching it to your research question, the type of your outcome variable and the arrangement of your groups, not by taste. The right test follows from three things: the question you are asking, the type of data your outcome variable is, and how your groups or measurements are arranged. Get those three straight and the choice usually narrows to one test and its non-parametric alternative.
This guide gives you a decision table for the tests PhD scholars use most, explains the three questions behind it, covers the assumptions worth checking, and lists the mistakes examiners and reviewers see most often in Indian theses, such as a chi-square test run on every questionnaire item. It covers the standard tests you would run in SPSS, R, jamovi or JASP. It does not cover structural equation modelling, multilevel models or time series in detail.
Statistics is a field where the details matter. The test also depends on your design, so if that is still open, start with types of research design. Use this guide to choose, then confirm the choice with your supervisor or a statistician before you write the results chapter. Last reviewed September 2026.
The three questions that decide the test
1. What are you trying to find out?
Almost every analysis in a thesis is one of three kinds:
- A difference: do groups differ on the outcome? (Do private and government school teachers differ in job stress?)
- A relationship: do two variables move together? (Is screen time related to sleep duration?)
- A prediction: which factors explain the outcome, and by how much? (Which factors predict a farmer’s adoption of drip irrigation?)
Write your research question or hypothesis in one of these forms before you open the software. If you can’t, the problem is the question, not the statistics.
2. What type is your outcome variable?
- Continuous: measured on a scale with meaningful distances, such as marks, income, yield, blood pressure, or a total score from several Likert items.
- Categorical: groups with no order, such as district, religion or type of school. A binary variable (yes/no, adopted/not adopted) is a special case.
- Ordinal: ordered categories, such as a single Likert item or an education level. Treat these with rank-based (non-parametric) tests unless you have a good reason not to.
3. How are your groups arranged?
Count the groups, and ask whether they contain different people (independent) or the same people measured more than once (paired or repeated). A pre-test and post-test on the same 40 students is paired. Forty students in a control class and forty in an experimental class are independent. This one distinction decides between tests that look similar but give different answers.
Which statistical test to use: decision table
Find the row that matches your question. Use the parametric test when its assumptions are reasonably met; use the alternative when they clearly are not, or when the outcome is ordinal.
| Your question | Outcome variable | Groups or predictors | Parametric test | Non-parametric alternative |
|---|---|---|---|---|
| Do two independent groups differ? | Continuous | 2 separate groups (e.g. rural vs urban) | Independent samples t-test (Welch’s version) | Mann-Whitney U test |
| Did the same people change? | Continuous | 2 measurements on the same people (pre/post) | Paired t-test | Wilcoxon signed-rank test |
| Do three or more groups differ? | Continuous | 3+ separate groups | One-way ANOVA, then post hoc tests | Kruskal-Wallis test |
| Did the same people change over three or more times? | Continuous | 3+ measurements on the same people | Repeated measures ANOVA | Friedman test |
| Do two factors, and their interaction, affect the outcome? | Continuous | 2 categorical factors (e.g. gender and district) | Two-way ANOVA | No simple equivalent; consider regression or a transformation |
| Are two categorical variables associated? | Categorical | Another categorical variable | Chi-square test of independence | Fisher’s exact test when expected counts are small |
| Are two continuous variables related? | Continuous | One continuous variable | Pearson correlation | Spearman rank correlation |
| Can I predict a continuous outcome? | Continuous | One or more predictors of any type | Linear regression (simple or multiple) | Quantile regression, or bootstrapped confidence intervals |
| Can I predict a yes/no outcome? | Binary | One or more predictors of any type | Binary logistic regression | Not needed: logistic regression makes no normality assumption |
| Does one group differ from a known value? | Continuous | One group vs a standard or benchmark | One-sample t-test | One-sample Wilcoxon signed-rank test |
After ANOVA: post hoc tests
A significant ANOVA tells you that at least one group differs, not which one. Follow it with a post hoc test: Tukey’s HSD when variances are similar, Games-Howell when they are not. After a significant Kruskal-Wallis test, use pairwise comparisons (Dunn’s test) with an adjustment such as Bonferroni.
Running many t-tests instead of one ANOVA
If you compare four groups with six separate t-tests at the 0.05 level, the chance of at least one false positive is far higher than 5%. Use ANOVA and post hoc tests, which control for this, or adjust the p-values.
Checking the assumptions of parametric tests
Parametric tests make assumptions about your data. Some matter a great deal; others matter less than thesis templates suggest.
- Independence. Each observation comes from a different person or unit, unless you are using a paired or repeated measures test. Students in the same class, or plots in the same field, are not fully independent.
- Normality of the right thing. For t-tests and ANOVA, it is the outcome within each group (or the residuals) that should be roughly normal, not the whole dataset. Look at a histogram or Q-Q plot as well as the Shapiro-Wilk p-value.
- Equal variances. For ANOVA, check Levene’s test. For two groups, use Welch’s t-test, which does not assume equal variances. SPSS shows it on the second row of the output.
- Expected counts for chi-square. Most expected cell counts should be 5 or more. If not, merge sensible categories or use Fisher’s exact test.
- Linearity and outliers for regression and correlation. Draw the scatter plot first. One extreme point can create or hide a correlation.
How much to worry about normality
Many scholars run a Shapiro-Wilk test on a sample of 400, find p < 0.05, and switch every analysis to non-parametric tests. With large samples, normality tests flag tiny departures that make no practical difference, and t-tests and ANOVA are fairly tolerant of moderate non-normality when groups are of reasonable and similar size. With small samples, the tests have little power to detect real problems. So look at the plots, consider the sample size, and make a reasoned choice. Report what you checked and why you chose the test.
Non-parametric tests are not a free safe option. They answer a slightly different question (usually about ranks or medians rather than means) and have less power when the parametric assumptions hold. Choose them because the data call for it, not by default.
Which statistical test to use for Likert scale data
Most survey-based theses in management, education, commerce and social sciences rest on Likert items. The usual advice, which most reviewers accept:
- A single Likert item (strongly disagree to strongly agree) is ordinal. Describe it with frequencies, percentages and the median. Compare groups with Mann-Whitney U or Kruskal-Wallis, or with chi-square if you treat the categories as groups.
- A scale score, the sum or mean of several items measuring one construct, is usually treated as continuous. Check the scale’s reliability (Cronbach’s alpha or, better, omega) first. Then t-tests, ANOVA, correlation and regression are commonly used.
What reviewers object to is item-by-item testing: fifty chi-square tests, one per questionnaire item, each reported with a p-value. That produces false positives, buries the real findings, and says nothing about your constructs. Build scale scores for each construct in your conceptual model and test the hypotheses on those.
Percentage analysis is description, not testing
Many theses present “percentage analysis” as a statistical technique. It is useful for describing respondents, but it tests nothing. A finding that 62% of respondents agree does not tell you whether men and women differ, or whether agreement relates to anything else. Use percentages to describe, and tests to answer your research questions.
How to report a statistical test result
A p-value tells you whether a result is unlikely under the null hypothesis. It does not tell you how large or important the effect is. With a big enough sample, trivial differences become significant. Examiners and reviewers increasingly expect three things with every test:
- The test statistic and degrees of freedom: for example, t(78) = 2.41, p = 0.018.
- An effect size: Cohen’s d for t-tests, eta squared or partial eta squared for ANOVA, Cramér’s V for chi-square, r or R² for correlation and regression (see interpreting regression output), odds ratios for logistic regression.
- A confidence interval for the difference, coefficient or effect, where the software provides one.
Report exact p-values (p = 0.032) rather than only “p < 0.05”, and report non-significant results too. A hypothesis that is not supported is a finding, not a failure.
Effect sizes also connect your analysis to your sample size. If you planned the study with a power analysis, you assumed an effect size; our sample size guide explains how. Your methodology chapter should name each test and say why it fits, as our methodology chapter guide describes.
Common mistakes in thesis analysis
- Choosing the test after seeing the results. Trying several tests until one gives p < 0.05 is a form of p-hacking. Decide the analysis from your hypotheses, ideally before collecting data.
- Treating paired data as independent. Pre-test and post-test scores analysed with an independent samples t-test lose the pairing and usually the power.
- Correlation read as cause. A correlation between training hours and productivity does not show that training caused the productivity. Say “associated with”.
- Regression with too many predictors for the sample. Fifteen predictors and 90 respondents produce unstable coefficients.
- Ignoring missing data. Report how many responses were incomplete and how you handled them.
- Copying the SPSS output tables into the thesis. Build clean tables in your style guide’s format and interpret each one in words.
If your analysis is already done and you are unsure whether it holds up, it is far better to find out before the pre-submission seminar than at the viva. Our statistical analysis support can review a plan or a finished analysis with you, and you run and defend the analysis yourself.
Sources
FAQ
Questions scholars ask
Should I use a t-test or ANOVA?
Use a t-test for two groups and ANOVA for three or more. With exactly two groups they give the same answer. For two groups, prefer Welch’s t-test, which does not need equal variances.
My data are not normal. Do I have to use non-parametric tests?
Not automatically. With reasonably large and similar-sized groups, t-tests and ANOVA tolerate moderate non-normality. Look at the plots, consider outliers and sample size, and justify your choice. Use non-parametric tests when the data are clearly skewed, the samples are small, or the outcome is ordinal.
When do I use chi-square?
When both variables are categorical and you want to know whether they are associated, for example gender and choice of bank. Check that expected cell counts are mostly 5 or more; if not, use Fisher’s exact test or combine categories.
Is SPSS required, or can I use R or jamovi?
Any standard software is acceptable if you use the right test and report it properly. SPSS is common in Indian universities; R, jamovi and JASP are free. Name the software and version in your methodology chapter.
My hypothesis was not supported. What does that mean for my thesis?
A well-designed study that finds no effect is still a result, provided the sample was adequate and the analysis was right. Report it clearly and discuss possible reasons in the discussion chapter.
Do I need structural equation modelling (SEM)?
Only if your research model has latent constructs measured by several items and paths between them that you need to test together. Many theses use SEM because it looks advanced when regression would answer the question. Choose it because the model needs it.
