To choose a statistical test, match it to your research question, the type of your outcome variable and how your groups are set up. Which test you personally like more doesn’t come into it. Note down what your question is really asking, what kind of data the outcome variable holds, and how the groups or measurements are arranged. Once these are clear, mostly you are left with one test and its non-parametric alternative.
Further down is a decision table of the tests PhD scholars use most, then the assumptions to check and the common mistakes. These are the mistakes examiners and reviewers keep seeing in Indian theses, like a chi-square test done on every single questionnaire item. The tests covered are the standard ones you would run in SPSS, R, jamovi or JASP. Structural equation modelling, multilevel models and time series are not covered in detail.
Go slow here, because paired data run as independent is enough to give a wrong result. Your design also decides the test, so if the design is not fixed yet, first read types of research design. Pick your test with the help of this guide, and then confirm it with your supervisor or a statistician before writing the results chapter. Last reviewed September 2026.
The three questions that decide the test
1. What are you trying to find out?
Nearly every analysis done in a thesis comes under one of three kinds.
- A difference: are the groups different on the outcome? (Is job stress different for private and government school teachers?)
- A relationship: do the two variables go up and down together? (Is screen time related with sleep duration?)
- A prediction: which factors explain the outcome, and how much do they explain? (What predicts whether a farmer adopts drip irrigation?)
Before you open the software, put your research question or hypothesis in one of these forms. If you are not able to write it like that, the trouble is with the question itself, and no statistics will fix it.
2. What type is your outcome variable?
- Continuous: a gap of 10 means the same 10 anywhere on the scale. Marks, income, yield, blood pressure, or the total score of several Likert items all come under this.
- Categorical: groups without any order, like district, religion or type of school. A binary variable (yes/no, adopted/not adopted) is one special case of this.
- Ordinal: categories that have an order, like a single Likert item or level of education. For these, go with rank-based (non-parametric) tests, unless you have a good reason to do otherwise.
3. How are your groups arranged?
First count the groups. Then see whether each group has different people (independent), or the same people measured more than one time (paired or repeated). If you give a pre-test and a post-test to the same 40 students, the data is paired. Forty students in a control class and another forty in an experimental class are independent. Several tests look nearly the same, and this point tells you which one to pick.
Which statistical test to use: decision table
Look for the row that fits your question. If the assumptions of the parametric test are more or less met, use that test. If they are clearly not met, or your outcome is ordinal, use the non-parametric alternative.
| 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, so 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, as 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 only says that at least one group is different, and which group it is, ANOVA will not say. So follow it with a post hoc test. Tukey’s HSD is used when the variances are similar, and Games-Howell when they are not. If the Kruskal-Wallis test is significant, do pairwise comparisons (Dunn’s test) with some adjustment like Bonferroni.
Running many t-tests instead of one ANOVA
Suppose you compare four groups by doing six separate t-tests, each at the 0.05 level. Then the chance of getting at least one false positive goes far above 5%. ANOVA with post hoc tests takes care of this, so use that, or else adjust the p-values.
Checking the assumptions of parametric tests
Some assumptions of parametric tests are serious, and a few others get more weight in thesis templates than they really deserve.
- Independence. Each observation has to come from a separate person or unit, unless you are running a paired or repeated measures test. Students sitting in the same class, or plots lying in one field, are not fully independent of each other.
- Normality of the right thing. For t-tests and ANOVA, the outcome inside each group (or the residuals) should be roughly normal. The whole dataset need not be normal. Along with the Shapiro-Wilk p-value, look at a histogram or a Q-Q plot also.
- Equal variances. For ANOVA, check Levene’s test. When you have two groups, use Welch’s t-test, because it does not assume equal variances. In the SPSS output it comes on the second row.
- Expected counts for chi-square. Most of the expected cell counts should be 5 or more. When too many cells are under 5, club some categories that naturally go together. Fisher’s exact test is the other way out.
- Linearity and outliers for regression and correlation. Draw the scatter plot and look at it once before you run any number, because just one extreme point is enough to create a correlation, or to hide one.
How much to worry about normality
Many scholars are running a Shapiro-Wilk test on a sample of 400, getting p < 0.05, and then changing every analysis to non-parametric tests. The thing is, with 400 respondents the normality test catches even tiny departures which don’t matter for the result. Also, t-tests and ANOVA handle moderate non-normality fairly well when the groups are of fair size and close to each other in size. In small samples the tests have very little power to catch real problems. Better to look at the plots along with the sample size and then decide with some reasoning. The thesis should then say what was checked and why that test got chosen.
Don’t think of non-parametric tests as a free and safe option. They answer a slightly different question, usually about ranks or medians and not about means. When the parametric assumptions do hold, they also have less power. Keep them for data that actually needs them.
Which statistical test to use for Likert scale data
Most survey-based theses in management, education, commerce and social sciences depend on Likert items. The advice below is the usual one, and most reviewers are fine with it.
- A single Likert item (strongly disagree to strongly agree) is ordinal. To describe it, give frequencies, percentages and the median. For comparing groups use Mann-Whitney U or Kruskal-Wallis. Chi-square also works if you take the categories as groups.
- A scale score is a different case. You add up or average several items that measure one construct, and that score is usually treated as continuous. First check the reliability of the scale with Cronbach’s alpha or, better, omega. After that, t-tests, ANOVA, correlation and regression are commonly used.
Reviewers object to item-by-item testing. Means fifty chi-square tests, one for each questionnaire item, and fifty separate p-values. This gives false positives, hides the real findings and tells nothing about your constructs. For each construct in your conceptual model, make a scale score, and test your hypotheses on those scores.
Percentage analysis is description, not testing
Many theses show “percentage analysis” as if it were a statistical technique. It is helpful for describing your respondents, but no testing happens in it. Take 62% of respondents agreeing. From that number alone you cannot say whether men and women differ, or whether agreement is linked with anything else. For describing the sample percentages are okay. To answer the research questions you have to run proper tests.
How to report a statistical test result
A p-value shows whether a result is unlikely under the null hypothesis. How big the effect is, or how important, the p-value cannot show. Give a big enough sample and even a tiny, useless difference will come out significant. So examiners and reviewers are more and more expecting three things along with every test.
- The test statistic and degrees of freedom: like t(78) = 2.41, p = 0.018.
- An effect size: Cohen’s d goes with t-tests, and eta squared or partial eta squared with ANOVA. For chi-square give Cramér’s V, and for correlation and regression give r or R² (see interpreting regression output). In logistic regression it is the odds ratios you report.
- A confidence interval for the difference, coefficient or effect, whenever the software gives one.
Give exact p-values (p = 0.032), and not only “p < 0.05”. Report the non-significant results also. When a hypothesis is not supported, that is still a finding of your study.
Effect sizes also link to sample size. Suppose you did a power analysis while planning. Some effect size was assumed there itself, and our sample size guide shows how. Our methodology chapter guide describes how to name every test in the methodology chapter along with why it suits your data.
Common mistakes in thesis analysis
- Choosing the test after seeing the results. Trying one test after another till something gives p < 0.05 is a kind of p-hacking. Fix the analysis from your hypotheses, ideally before the data collection itself.
- Running paired data as if it is independent. If pre-test and post-test scores go into independent samples t-test, the pairing is lost. Mostly you lose power also.
- Correlation read as cause. Say training hours and productivity go up together in your data. From that alone nobody can say the training caused it. Write “associated with” in your findings.
- Regression with too many predictors for the sample. With fifteen predictors and only 90 respondents, the coefficients you get will be unstable.
- Saying nothing about missing data. Mention how many responses were incomplete, and what you did with them.
- Copying the SPSS output tables into the thesis. Make clean tables as per your style guide’s format, and explain every table in words.
Already finished the analysis but having doubts whether it will hold up? Finding out before the pre-submission seminar is much better than finding out at the viva. Our statistical analysis support can go through a plan or a completed analysis along with you. Running the analysis and defending it in the viva stays your own work.
Want a specialist to help with this in your own work? Statistics Training and Analysis Review (SPSS, R, AMOS, SmartPLS): a free first consultation, then a written scope and fixed quote.
Sources
FAQ
Questions scholars ask
Should I use a t-test or ANOVA?
A t-test is enough for two groups. ANOVA is for three groups or more, and if you run both on exactly two groups the answer comes out the same. For two groups I would suggest Welch’s t-test, because equal variances are not needed for it.
My data are not normal. Do I have to use non-parametric tests?
Not automatically. t-tests and ANOVA manage moderate non-normality fairly well when the groups are reasonably large and close in size. First see the plots and check for outliers. Keep the sample size in mind and give the reason for your choice. Go non-parametric when the data is clearly skewed or the samples are small, or when the outcome is ordinal.
When do I use chi-square?
Use it when both variables are categorical and your question is whether they are associated. Gender and choice of bank is one example of two categorical variables. The expected cell counts should mostly be 5 or more. When many cells fall short of that, club some categories together, or Fisher’s exact test can be used in place of chi-square.
Is SPSS required, or can I use R or jamovi?
You can use any standard software. Only thing is, the test has to be correct and reported properly. In Indian universities SPSS is common, while R, jamovi and JASP are free. Mention the software and its version in your methodology chapter.
My hypothesis was not supported. What does that mean for my thesis?
It is still a result, provided the study was well designed, the sample was adequate and the analysis was correct. Report it clearly. Then in the discussion chapter, discuss about the possible reasons.
Do I need structural equation modelling (SEM)?
SEM is needed when your model has latent constructs measured by several items each, and the paths between those constructs have to be tested together. Many scholars are choosing it just because it looks advanced, even when a regression would have answered their question.
