Measuring Associations in Data#

Stage 2 · 🔗 Associations & Correlation · Lesson 10 of 56 · beginner

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Important

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One idea, many measures#

To move from “these two variables seem related” to a number, you need an association measure — a single value capturing how strongly, and often in which direction, two variables move together. There is no one measure for all cases; the right choice depends on what kind of variables you have.

It depends on the types#

Variables come in two broad flavours — continuous (numbers on a scale, like fare or distance) and categorical (labels, like payment type or company). The pairing decides the tool: comparing two numbers is a different problem from comparing two labels, or a number against a label.

The taxonomy#

The map for this stage:

continuous ↔ continuous — correlation (Pearson, Spearman, Kendall);
categorical ↔ categorical — the chi-square test and Cramér’s V;
continuous ↔ categorical — ANOVA and its effect size eta-squared (\(\eta^2\)).

The lessons ahead take these in turn.

Strength and direction#

Two properties matter. Strength — how tightly the variables track, usually scaled so that 0 means “no association” and 1 (or \(\pm 1\)) means “perfect”; and direction — whether they rise together or move oppositely, which only makes sense for ordered variables. A good measure reports strength on a comparable scale, so associations across different variable pairs can be ranked.

Hint