Cohen's weighted Kappa and weighted Chi square techniques are extended to n-way tables. Formulas are provided for calculating the covariance of two weighted Kappas defined for the same table. This allows a joint Chi square test of several sets of weights. The relationship of this joint test to Cochran's test for a linear trend and to Lancaster's partition of Chi square is shown. Some examples of the use of the joint test in evaluating hypotheses about contingency tables are given.
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