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Lesson 21 of 22 · 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) = (Oij−Eij)/Eij (O_{ij}-E_{ij})/\sqrt{E_{ij}} .
  • Positive: more observations than independence predicts; negative: fewer.
  • Each squared residual is that cell’s contribution to χ2 \chi^2 , so the squared residuals sum to χ2 \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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Interpreting the result: standardized residuals and mosaics · Estimation and Hypothesis Testing