Tate and Hyer [9] indicated in a recent article that the χ2test of goodness of fit is markedly in error when expected frequencies are small, and that, moreover, errors of substance remain even with large expected frequencies. This result appears to arise from the application of an improper statistical model. When the multinomial test proposed here is substituted, it is found that errors of the χ2test are smaller than Tate and Hyer would suggest for small expected frequencies, and negligible for large expected frequencies. These empirical results support the logical arguments presented here in favor of the proposed “Exact χ2Test.”