Which Statistical Test Should I Use?
The right statistical test is determined by three questions: (1) What type is your dependent variable — continuous or categorical? (2) How many groups or measurements are you comparing, and are they independent or paired? (3) Are parametric assumptions (especially normality) met? Answer these three and the test practically selects itself — the decision tables below walk you through it.
This guide covers the most common scenarios. If you're still unsure which test fits your data, send us your research question and data structure — we'll name the right method, with justification, in a free assessment.
Who is this guide for?
Thesis students at the analysis stage, unsure which test to choose
Researchers whose advisor asked for test justification in the methods section
Anyone holding SPSS output but unsure the right test was used
Authors told by reviewers that “the choice of test must be justified”
The three steps of test selection
- 01
Identify variable types
Is the dependent variable continuous (age, score, scale total) or categorical (yes/no, groups)? How many levels does the independent variable have?
- 02
Pin down the design
Are the groups independent (treatment vs. control) or paired (pre-post, matched)? How many groups or measurements?
- 03
Test the assumptions
Normality (Shapiro-Wilk; Kolmogorov-Smirnov for n>50), homogeneity of variance (Levene). Met → parametric; violated → nonparametric.
Decision table: group comparisons
When the dependent variable is continuous (scores, measurements, scale totals):
| Scenario | Parametric test | Nonparametric counterpart |
|---|---|---|
| 2 independent groups (treatment-control) | Independent-samples t-test | Mann-Whitney U |
| 2 paired measurements (pre-post) | Paired t-test | Wilcoxon signed-rank |
| 3+ independent groups | One-way ANOVA | Kruskal-Wallis H |
| 3+ repeated measurements | Repeated-measures ANOVA | Friedman test |
| Joint effect of 2+ factors | Factorial (two-way) ANOVA | — |
| Group difference with covariate control | ANCOVA | — |
Decision table: association and prediction
| Scenario | Appropriate method |
|---|---|
| Association between two continuous variables (normal) | Pearson correlation |
| Two continuous/ordinal variables (non-normal) | Spearman correlation |
| Association between two categorical variables | Chi-square test (Fisher's exact if expected counts <5) |
| Predicting a continuous outcome from several variables | Multiple linear regression |
| Predicting a binary (yes/no) outcome | Logistic regression |
| Examining a scale's factor structure | Exploratory / confirmatory factor analysis |
| A scale's internal consistency | Cronbach's alpha |
The 5 most common test-selection mistakes
Running t-tests/ANOVA without ever testing normality — the first thing committees and reviewers check
Using an independent test on a paired design (e.g. independent t-test on pre-post data)
Comparing 3+ groups with pairwise t-tests — Type I error inflates; use ANOVA + post-hoc
Treating a single Likert item as continuous (scale totals are accepted as continuous; single items are contested)
Interpreting correlation as causation — even regression alone doesn't establish causality
What if assumptions are violated?
When normality fails, the first option is switching to the nonparametric counterpart (the pairings in the table). With large enough samples (~30+ per group), parametric tests are relatively robust to deviations thanks to the central limit theorem — the parametric test can then be reported, but the justification must be written. For heavily skewed distributions, a log transformation is an alternative. Which route is defensible for your data depends on the shape of the distribution and your field's conventions — our reports always state this decision with its reasoning.
Frequently asked questions
Shapiro-Wilk or Kolmogorov-Smirnov for normality?
Shapiro-Wilk is more powerful for small and medium samples (n<50); Kolmogorov-Smirnov (with Lilliefors correction) is common for large ones. Since these tests flag even trivial deviations in large samples, it's healthiest to also examine skewness-kurtosis values (±1 or ±2 criteria) and the histogram.
Can Likert-scale data be analyzed with parametric tests?
A multi-item scale's total or mean score is widely accepted as continuous, so parametric tests apply if normality holds. A single Likert item is ordinal data — a nonparametric test is more defensible.
My ANOVA is significant — which groups differ?
ANOVA only says “at least one group differs.” Post-hoc tests show which: Tukey HSD or Bonferroni when variances are homogeneous, Games-Howell when they're not.
What is the chi-square test's assumption?
Adequate expected frequencies: if more than 20% of cells have expected counts below 5, chi-square becomes unreliable. Fisher's exact test solves it for 2x2 tables; merging categories helps in larger ones.
I still can't pick the test — what should I do?
Send us your research question, variables and data. In a free assessment we'll tell you which test fits and why — and if you like, complete the analysis in 15 minutes and deliver the publication-ready report the same day, often within hours or even minutes.
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Last updated: July 8, 2026