Probability Density Plots of the Non-Central χ 2 and Non-Central F Distributions

Abstract

Summary Largely for pedagogical purposes, the authors have plotted four sets of curves which permit one to observe how the non-centrality parameters affect the shape of the non-central X2 and non-central F distributions. The non-central F distribution is most frequently encountered in an applied setting when one is interested in testing the equality of several treatment means via the usual analysis of variance. When the hypothesis of equal treatment effects is assumed false, the test statistic, F, no longer has a central F distribution as under the null hypothesis; rather, the test statistic has a non-central F distribution arising as the ratio of a non-central X2 to an independent central x2. Consequently, the non-central F distribution can be utilized in computing power functions of the usual analysis of variance.