With two judges and a two-point rating scale, the test statistic for Kappa is the same as Pearson's chi-square statistic applied to the 2 × 2 table of paired observations. This equivalence allows a quick test of the null hypothesis of no agreement, as Pearson's chisquare statistic is much less cumbersome to compute than the Kappa statistic and its variance. A simple formula for the null hypothesis variance is also derived.
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