Lesson 6 of 6 · 12 min

Interpreting the result: standardized residuals and mosaics

Rejecting independence tells you the classifications are related; standardized residuals tell you which cells are responsible and in which direction.

In short

Standardized residual (also Pearson residual) = $(O_{ij}-E_{ij})/\sqrt{E_{ij}}$ .
Positive: more observations than independence predicts; negative: fewer.
Each squared residual is that cell’s contribution to $\chi^2$ , so the squared residuals sum to $\chi^2$ .
A mosaic pictures the table: rectangle widths and heights show proportions, and shading shows the size and sign of the residuals.
Choosing the test: Pearson t (continuous, normal), Spearman (non-normal, outliers or ranks), chi-square (categories).

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