Testing the Normal Approximation and Minimal Sample Size Requirements of Weighted Kappa When the Number of Categories is Large

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Abstract
The results of this computer simulation study in dicate that the weighted kappa statistic, employing a standard error developed by Fleiss, Cohen, and Everitt (1969), holds for a large number of k cate gories of classification (e.g., 8 < k ≤ 10). These data are entirely consistent with an earlier study (Cicchetti & Fleiss, 1977), which showed the same results for 3 ≤ k ≤ 7. The two studies also indicate that the minimal N required for the valid ap plication of weighted kappa can be easily approxi mated by the simple formula 2 k2. This produces sample sizes that vary between a low of about 20 (when k = 3) to a high of about 200 (when k = 10). Finally, the range 3 ≤ k ≤ 10 should encompass most extant clinical scales of classification.