9. Correlation and Association

Quantifying Relationships Without Imposing a Response Model

NoteIn This Chapter

• Correlation as a measure of association
• Pearson, Spearman, and Kendall correlation
• Correlation versus regression
• Interpreting strength, sign, and uncertainty

1 Introduction

Correlation measures the strength and direction of association between variables. Unlike regression, it does not assign one variable the formal role of response and the other the role of predictor.

That distinction matters. Correlation is useful when we want to describe association. Regression is more appropriate when we want to model a response as a function of one or more predictors.

2 Key Concepts

This chapter depends on a small number of core distinctions.

• Correlation quantifies the strength and direction of association between variables.
• Association is not directionality because correlation does not define a response and predictor.
• Pearson, Spearman, and Kendall answer related but not identical questions.
• Strength, sign, and uncertainty all matter when interpreting a correlation coefficient.
• Regression should be preferred when the goal is explicit modelling rather than association alone.

3 Main Forms of Correlation

• Pearson correlation for approximately linear relationships among continuous variables.
• Spearman correlation for monotonic relationships or ordinal data.
• Kendall correlation as a rank-based alternative that can be useful in smaller datasets or where tied ranks are common.

4 Practical Rule

Use correlation when the question is about association. Use regression when the question is about modelling a response.

5 Link

This chapter replaces the earlier standalone chapter:

• 10-correlations.qmd