Correlation coefficients

A single number from −1 to +1 captures how two variables move together — and examiners love to see whether you can read its sign and its strength separately. Nail that split and correlation questions become quick points.

A correlation coefficient (r) ranges from −1.00 to +1.00. It has two independent parts. The sign = direction: a positive r means variables move together (both up or both down); a negative r means they move oppositely (one up, the other down). The absolute value = magnitude / strength: the closer to 1 (either end), the stronger; 0 = no linear relationship. So −.85 is stronger than +.40 — the minus sign is only direction, never weakness.

Rough strength benchmarks: near ±.10 weak, ±.30 moderate, ±.50+ strong (Cohen's convention). The most common index is Pearson's r for two continuous variables; Spearman's rho handles ranked/ordinal data.

Two classic testable pitfalls. First, restriction of range: when the spread of scores is narrowed — e.g., studying GRE-vs-grades only among already-admitted students — the correlation is artificially reduced (attenuated), because you've cut off the variability the coefficient needs to detect. Second, r² (coefficient of determination) gives the proportion of variance shared/explained — r = .40 means only 16% (.40²) of variance is shared.

One boundary line: this topic owns the correlation coefficient as a statistic (direction, magnitude, restriction of range). The correlational research design — the 'correlation is not causation' methodology — lives in a separate topic; just remember correlation alone cannot establish causation (third variables, directionality).

Clinical Pearl: Sign = direction, absolute value = strength — so −.80 is a stronger relationship than +.30. And restriction of range shrinks r: narrowing the sample's variability artificially weakens the correlation.