Regression and Correlation

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Edexcel IAL Statistics 3 (WST03)

Regression and Correlation

The big idea: Spearman's coefficient measures agreement in rank order; a hypothesis test decides whether a correlation is more than chance.

Summary — What This Chapter Covers

r_s = 1 − 6Σd²/(n(n² − 1)).
Ties: give tied values the mean of their ranks.
Test H₀: ρ = 0 (or ρ_s = 0) using the critical value tables.

1. Spearman's Rank Correlation

Spearman

Ranks, differences, Σd²

Rank each variable, find each difference d, square and sum.

Worked Example

For n = 5 pairs, Σd² = 4. Find r_s.

2. Testing Correlation Coefficients

Tests

Comparing with critical values

Use the PMCC table for r (bivariate normal data) and the Spearman table for r_s. For n = 5 at 5% one-tailed the Spearman critical value is 0.9000, so r_s = 0.8 is not significant.

Memorise

Spearman

1 − 6Σd²/(n(n² − 1))

Ties

Average the ranks

PMCC test

Conclusion

In context

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Regression and Correlation