Test for symmetry of a joint distribution.

This procedure tests the null hypothesis that the joint distribution is symmetric around the main diagonal, that is


p_{i, j} = p_{j, i} for all i, j

  • A bunch with attributes
  • statistic (float) – chisquare test statistic
  • p-value (float) – p-value of the test statistic based on chisquare distribution
  • df (int) – degrees of freedom of the chisquare distribution


The implementation is based on the SAS documentation. R includes it in mcnemar.test if the table is not 2 by 2. However a more direct generalization of the McNemar test to larger tables is provided by the homogeneity test (TableSymmetry.homogeneity).

The p-value is based on the chi-square distribution which requires that the sample size is not very small to be a good approximation of the true distribution. For 2x2 contingency tables the exact distribution can be obtained with mcnemar

See also

mcnemar, homogeneity

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© 2006 Jonathan E. Taylor
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