The modified Mood test for the scale alternative and its numerical comparisons

On statistical hypotheses testing in two-sample problems, the Mood test is popular as one of the most efficient nonparametric tests for dispersion differences. In this paper, we show that a modification of the Mood test proposed by Tamura (1963) can gain even more efficiency and power under various distributional assumptions. The accuracy of the proposed approximations to the tail probabilities and critical values of the modified Mood test, namely MpMp, were investigated. Our results showed that the Edgeworth expansion was more accurate than the other approximations. Asymptotic efficiencies and the optimal value pp of the modified Mood test under various distributional assumptions were examined, with the results revealing that the large (small) value of pp was useful for light (heavy) tail distributions. Additionally, the power of the modified Mood test for the one-sided alternative with various population distributions for small sample sizes was investigated via Monte Carlo simulations. Finally, the proposed method was demonstrated using real data.