How strong is a predictor?

Step 1 Warm-up recall

From Module 1: how is Cohen’s d calculated, and what do the labels 0.2, 0.5 and 0.8 mean?

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Step 2 Learning goal

By the end of this lesson you can:

• read the direction and strength of a correlation coefficient (Foundation);
• convert r into the share of variation accounted for, and say what that does and does not mean (Core);
• explain why predictors overlap and why strength depends on sample and measure (Core).

Step 3 A familiar example

Height predicts weight, but not perfectly: some tall people are light and some short people are heavy. A well-being predictor works the same way. It shifts the odds without fixing the outcome for any one person.

Step 4 Clear explanation

The correlation coefficient, r, runs from −1 to +1. The sign gives the direction (positive: both rise together; negative: one rises as the other falls). The distance from zero gives the strength. Cohen (1988) offered rough anchors: about 0.1 small, 0.3 medium, 0.5 large. They are conventions, not verdicts.

Squaring r gives r², the share of the variation in one measure that is statistically accounted for by the other. r = 0.30 gives 0.09, or 9%. That does not make the predictor “only 9% important”: it says that, across a group, most of the differences between people remain unexplained by this one factor.

Three cautions. Predictors overlap (income, health and relationships are related), so their shares cannot simply be added. Strength depends on the sample and measure: a narrow range of incomes weakens a correlation. And correlation describes a group, not a person.

Step 5 Worked example (4 marks)

Predictor A correlates 0.50 with life satisfaction and predictor B correlates 0.25.

1. A: 0.50 × 0.50 = 0.25, so 25% of the variation. (1 mark)
2. B: 0.25 × 0.25 = 0.0625, so about 6%. (1 mark)
3. A’s r is twice B’s, but its share of variation is four times B’s (25 ÷ 6.25 = 4). (1 mark)
4. If A and B overlap, together they account for less than 31%, because the shares are not additive. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• r runs from −1 to +1: sign is direction, distance from zero is strength.
• r² is the share of variation accounted for. Strong-looking r values give modest shares.
• Predictors overlap, so shares are not additive.
• Strength depends on sample and measure.

Step 8 Exit ticket (ungraded)

Pick a claim you have heard (for example, “exercise makes you happier”). What r would make it worth acting on, and what else would you need to know?

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Step 9 Go further (Extension)

Find a published correlation between a lifestyle factor and life satisfaction. Record the sample, the r, the r², and whether the authors claim cause.