Which Statistical Test Should You Use? A Decision Guide

The right test follows almost mechanically from three questions about your data. Answer them and you rarely go wrong. Here is the decision path.

Three questions that pick your test

Before reaching for a test, answer these:

• What kind of outcome do you have? Continuous (a score), categorical (a group), or a count?
• How many groups or predictors? One sample, two groups, three or more, or several continuous predictors?
• Are the observations independent or paired/repeated? Different people, or the same people measured twice?

Those three answers point to the test almost every time.

Comparing means

• One group vs a known value → one-sample t-test.
• Two independent groups → independent-samples t-test (Mann–Whitney U if the data are skewed or ordinal).
• Same group, two time points → paired-samples t-test (Wilcoxon signed-rank as the non-parametric option).
• Three or more groups → one-way ANOVA, followed by post-hoc tests (Tukey) to find which groups differ.
• Two factors at once → two-way ANOVA, which also tests their interaction.

Relationships between variables

• Two continuous variables → Pearson correlation (Spearman if non-normal or ordinal).
• Predicting one continuous outcome from one or more predictors → linear regression.
• Predicting a yes/no outcome → logistic regression.
• Association between two categorical variables → chi-square test of independence.

For latent constructs measured by multiple items and several inter-related paths, move up to structural equation modelling.

Check the assumptions — this is where papers fail

A test run on data that violate its assumptions produces a confident wrong answer. The common checks:

• Normality of the outcome (or residuals in regression) — inspect a histogram and Q–Q plot, not just a significance test.
• Homogeneity of variance across groups (Levene's test) for t-tests and ANOVA.
• Independence of observations — violated by clustered or repeated data, which need mixed models.
• Linearity and no severe multicollinearity (VIF) in regression.

When assumptions fail, you usually have a remedy: a non-parametric equivalent, a transformation, or robust standard errors.

Read the result correctly

A p-value is the probability of data this extreme if the null were true — not the probability your hypothesis is correct, and not a measure of effect size. Always report an effect size (Cohen's d, η², r, or an odds ratio) alongside significance, and a confidence interval where you can. A statistically significant result with a trivial effect size is rarely interesting; a non-significant result in an under-powered study is not evidence of no effect.

Report it in APA style

Reviewers expect a standard format: the test statistic, degrees of freedom, exact p-value, and effect size. For example: t(98) = 2.41, p = .018, d = 0.48. Consistency here signals competence and saves a revision round.

Final thought

Good statistics is mostly good matching — the right test for the design — followed by honest reporting of assumptions, effect sizes, and uncertainty. Dr.AIStat handles the computation and the assumption checks and explains the output, so the judgement calls are the only thing left to you.