How to Choose the Right Statistical Test

The Selection Framework

Choosing a statistical test depends on three factors: your research question (comparing groups, testing relationships, predicting outcomes), the type of data (continuous, categorical, ordinal), and the number of groups or variables involved.

Comparing Two Groups

For continuous data with normal distribution: independent samples t-test (different subjects in each group) or paired t-test (same subjects measured twice). For non-normal data or ordinal data: Mann-Whitney U test (independent) or Wilcoxon signed-rank test (paired). For categorical data: chi-squared test or Fisher's exact test (small samples).

Comparing Three or More Groups

For continuous normally distributed data: one-way ANOVA (one factor) or two-way ANOVA (two factors). For non-normal or ordinal data: Kruskal-Wallis test. If the ANOVA is significant, follow up with post-hoc tests (Tukey HSD, Bonferroni) to identify which specific groups differ.

Testing Relationships

Pearson correlation measures linear relationships between two continuous variables. Spearman rank correlation measures monotonic relationships and works with ordinal data. Simple linear regression predicts one continuous variable from another. Multiple regression predicts from several variables simultaneously.

Sample Size Considerations

Small samples (n < 30) often violate normality assumptions, favoring non-parametric tests. Power analysis before data collection determines how many observations you need to detect a meaningful effect. A study with too few participants may miss real effects (Type II error); too many wastes resources.

Common Mistakes

Using a t-test to compare more than two groups inflates the false positive rate. Treating ordinal data (1-5 ratings) as continuous is technically incorrect but often produces reasonable results for large samples. Ignoring assumptions (normality, equal variance, independence) without checking can invalidate your conclusions.