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Using Monte Carlo simulation, we investigate the accuracy of the chi2 approximation used in statistical equipment comparison based on the Kruskal-Wallis H statistic. We show that this approximation is conservative and gives an incorrect false-positive rate on individual steps as well as on the full process flow statistical equipment comparison. Alternative approximations of Wallace are investigated and these are shown to perform significantly better in analysis of datasets typical of semiconductor manufacturing. Wallace approximations also improve the ranking of signals.