Choosing the Right Statistical Tool
The Pearson correlation coefficient (r) quantifies the strength and direction of a LINEAR relationship between two continuous variables, ranging from (a perfect negative relationship) through (no linear relationship) to (a perfect positive relationship). The closer is to 1, the stronger the linear relationship; a scatterplot is the natural visual companion, since only captures LINEAR patterns and can badly understate a strong but curved (non-linear) relationship.
Beyond correlation, different research questions call for different statistical tests, chosen mainly by how many groups are being compared and what kind of data is involved:
| Test | Used for |
|---|---|
| Pearson correlation (r) | Strength/direction of a linear relationship between two continuous variables |
| T-test | Comparing the means of exactly TWO groups |
| ANOVA (Analysis of Variance) | Comparing the means of THREE OR MORE groups |
| Chi-square test | Testing relationships between CATEGORICAL variables (frequencies/counts) |
A key reason ANOVA exists, rather than just running many separate t-tests across multiple group pairs, is that each additional t-test inflates the overall chance of a Type I error (a false positive) somewhere across the whole set of comparisons — ANOVA tests all groups together in one single analysis, controlling this inflated error rate, and (if significant) is typically followed by more targeted "post-hoc" tests to pinpoint exactly which specific groups differ.
Common pitfall: running many separate t-tests across multiple group pairs instead of one ANOVA, assuming this is equivalent and error-free. Each additional t-test compounds the overall Type I error rate across the full set of comparisons — which is exactly the statistical problem ANOVA is designed to solve.