Picking the wrong statistical test is one of the most common reasons a thesis committee sends an analysis chapter back for revisions. Here's a quick decision framework.
Step 1 — What's your outcome variable?
- Continuous (scores, measurements) → Step 2a
- Categorical (yes/no, groups) → Step 2b
Step 2a — Comparing continuous outcomes
- 2 independent groups, normal distribution → independent-samples t-test
- 2 independent groups, non-normal/ordinal → Mann-Whitney U
- 3+ independent groups, normal → one-way ANOVA (+ Tukey HSD post-hoc)
- 3+ independent groups, non-normal → Kruskal-Wallis (+ Dunn's post-hoc)
- Repeated measures, 2 timepoints → paired t-test
- Repeated measures, 3+ timepoints → repeated-measures ANOVA or Friedman test
- Relationship between two continuous variables → Pearson (linear, normal) or Spearman (monotonic, non-normal)
Step 2b — Categorical outcomes
- 2 categorical variables, independence → chi-square test of independence (check expected cell counts ≥5, otherwise Fisher's exact)
- Predicting a binary outcome from multiple predictors → logistic regression
Step 3 — Check assumptions before trusting the result
Normality (Shapiro-Wilk), homogeneity of variance (Levene's), and for repeated designs, sphericity (Mauchly's) should be checked, not assumed. If normality fails on a 2-group comparison, that's the cue to switch from t-test to Mann-Whitney.
Step 4 — Report in APA format
APA 7th edition wants the test statistic, degrees of freedom, exact p-value (or p < .001), and an effect size. Example: t(48) = 2.14, p = .038, d = 0.61.
Getting the test right is half the work; writing it up the way your committee expects is the other half. If you'd rather skip the manual assumption-checking and APA formatting, statmate.org runs the test selection and formats the write-up for you — but the framework above works fine by hand, in R, or in SPSS too.
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