Choosing the Right Statistical Tool
The Pearson correlation coefficient (r) quantifies the strength and direction of a linear relationship between two continuous variables. It ranges from (perfect negative) to (perfect positive), with indicating no linear relationship.
| Test | Used for |
|---|---|
| Pearson correlation | Linear relationship between two continuous variables |
| T-test | Comparing means of exactly TWO groups |
| ANOVA | Comparing means of THREE OR MORE groups |
| Chi-square test | Relationships between CATEGORICAL variables |
A scatterplot is essential here because only captures linear patterns and can badly understate a strong, curved non-linear relationship.
Avoiding Type I Errors with ANOVA
ANOVA (Analysis of Variance) tests all groups simultaneously in a single analysis. This controls the Type I error (false positive) rate, which would otherwise balloon if you ran multiple separate t-tests.
If ANOVA is significant, researchers use targeted post-hoc tests to pinpoint exactly which specific group pairs differ from one another.
Common pitfall: Running multiple separate t-tests across group pairs instead of ANOVA. Each extra test compounds your overall Type I error rate across the full set of comparisons, which is the exact problem ANOVA solves.