Chapter 4: Two-Way Contingency Tables


The analysis of two-way frequency tables concerns the association between two variables. A variety of specialized graphical displays help us to visualize the pattern of association, using area of some region to represent the frequency in a cell. Some of these methods are focused on visualizing an odds ratio (for 2 x 2 tables), or the general pattern of association, or the agreement between row and column categories in square tables.


4.1. Introduction
4.2. Tests of association for two-way tables
4.3. Stratified analysis
4.4. Fourfold display for 2 x 2 tables
4.5. Sieve diagrams
4.6. Association plots
4.7. Observer agreement
4.8. Trilinear plots
4.9. Chapter summary
4.10. Lab exercises

Selected figures

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  • Figure 4.2

    Spineplot of the Mental data.
  • Figure 4.2

    Fourfold displays for the Berkeley admission data. Left: unstandardized; right: equating the proportions of males and females.
  • Figure 4.9

    Sieve diagrams for the HairEyeColor data. Left: expected frequencies shown in cells as numbers and the number of boxes; right: observed frequencies shown in cells.
  • Figure 4.17

    Association plot for the hair-color eye-color data. Left: marginal table, collapsed over gender; right: full table.
  • Figure 4.18

    Agreement charts for husbands’ and wives’ sexual fun. Left: unweighted chart, showing only exact agreement; right: weighted chart, using weight w1 = 8/9 for a one-step disagreement.
  • Figure 4.20

    Weighted agreement charts for both patient samples in the MSPatients data. Departure of the middle rectangles from the diagonal indicates lack of marginal homogeneity.
  • Figure 4.22

    Lifeboats on the Titanic, showing the composition of each boat. Boats with more than 10% male passengers are labeled.