When two categorical variables have the same levels, use the Agreement Statistic option in the Contingency platform to compute the Kappa statistic (Agresti 1990). This option also computes the Kappa statistic standard error, confidence interval, hypothesis test, and Bowker’s test of symmetry. See Example of the Agreement Statistic Option.
The Kappa statistic and associated p-value in this report are approximate. See Statistical Details for the Agreement Statistic. An exact version of the agreement statistic is available. See Fisher’s Exact Test Report.
The Kappa Coefficient report contains the following statistics:
Kappa
The Kappa statistic.
Std Err
The standard error of the Kappa statistic.
Lower 95%
The lower endpoint of the confidence interval for Kappa.
Upper 95%
The upper endpoint of the confidence interval for Kappa.
Prob>Z
The significance probability (p-value) for a one-sided asymptotic test for Kappa. The null hypothesis tests if Kappa equals zero.
Prob>|Z|
The significance probability (p-value) for a two-sided asymptotic test for Kappa.
The Bowker’s Test report contains the following statistics:
ChiSquare
The test statistic for Bowker’s test. For Bowker’s test of symmetry, the null hypothesis is that the probabilities in the square table satisfy symmetry, or that pij=pji for all pairs of table cells. When both the Y and X variables have exactly two levels, Bowker’s test is equivalent to McNemar’s test.
Prob>ChiSq
The significance probability (p-value) for the Bowker’s test statistic. The null hypothesis of Bowker’s test is that the probabilities in the square table satisfy symmetry.