Parametric and Non-Parametric Tests of Independence

How to test whether two variables are related: the parametric t-test on a Pearson correlation, the non-parametric Spearman rank correlation when normality is doubtful or the data are ranks, and the chi-square test of independence for categorical data in a contingency table, including how to read standardized residuals.

1. 1. Parametric vs non-parametric tests, and correlation hypothesesBefore testing whether two variables are related, decide what kind of data you have, which assumptions you can defend, and which direction the alternative hypothesis points.Free12 min
2. 2. The t-test for a Pearson correlationA sample correlation is never exactly zero, so convert it into a t-statistic with n − 2 degrees of freedom and ask whether it is too large to be sampling noise.13 min
3. 3. Sample size, p-values and many correlations at onceWhether a correlation counts as significant depends heavily on how many observations you have; with enough data even a tiny correlation passes the test.13 min
4. 4. The Spearman rank correlation testWhen the data are not normal, contain outliers or are already ranks, replace each value by its rank and correlate the ranks instead.Video · 7 min14 min
5. 5. Contingency tables and the chi-square test of independenceFor categorical data, compare the count in each cell with the count you would expect if the two classifications had nothing to do with each other.Video · 6 min14 min
6. 6. Interpreting the result: standardized residuals and mosaicsRejecting independence tells you the classifications are related; standardized residuals tell you which cells are responsible and in which direction.12 min