This thesis considers the effect of nonnormality, in terms of skewness and kurtosis, on the power of the analysis of variance test for a two-way classification, fixed effects model (with two replicates and no interaction). Most of the populations considered were only moderately non-normal, that is, only slightly peaked or skewed. We first considered the effect of a change in skewness for a fixed kurtosis. We then considered the effect of a change in kurtosis for a fixed skewness. In both cases, there was no significant deviation in power, as compared with the power in the normal case. The effect of non-normality on the power for an increase in both skewness and kurtosis for a particular Pearson Curve was then considered. A significant deviation in the power was found. The results indicate that for moderate departures from normality, the two-way classification, fixed effects model, is robust. / M.S.