Lesson 3 of 6 · All lessons in this module
- Parametric vs non-parametric tests, and correlation hypotheses
- The t-test for a Pearson correlation
- Sample size, p-values and many correlations at once
- The Spearman rank correlation testVideo lesson
- Contingency tables and the chi-square test of independenceVideo lesson
- Interpreting the result: standardized residuals and mosaics
Lesson 3 of 6 · 13 min
Sample size, p-values and many correlations at once
Whether a correlation counts as significant depends heavily on how many observations you have; with enough data even a tiny correlation passes the test.
In short
- For a fixed r, more data raises the chance of rejecting in two ways: grows, and the critical value shrinks as df rise.
- So the smallest |r| that is significant falls as n grows; a larger sample gives the test more power.
- In very large datasets almost every correlation is significant, so significance alone says little about how strong or useful a relationship is.
- A p-value is the smallest significance level at which can be rejected: reject when p < .
- With k variables there are distinct correlations, and each is tested separately.
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