1. One-way nonparametric ANOVA with trigonometric scores by Kravchuk, O.Y. School of Land and Food Sciences, University of Queensland
The trigonometric scores one-way analysis of variance is developed. Numerical simulations are performed on normal hyperbolic secant and Cauchy distributions. The test is compared to the ANOVA and Kruskal-Wallis tests.
S1=1.17
S2=2.58
S3=-3.75
The trigonometric ANOVA on log-transformed Cauchy (n1=n2=n3=8)
One-way ANOVA
F = 5.78, p = 0.01
Kruskal-Wallis
KW = 11.26, p = 0.004
Trigonometric ANOVA
Q=11.33, p = 0.003
The test allows one to work with data which is heavier tailed than the normal. This type of non-normality is common in biometrical applications and also describes the distribution of the log-transformed Cauchy data. The distribution of the test statistic corresponds to the distribution of the first component of the Cramer-von Mises test statistic.
Olena Kravchuk, LAFS, UQ, , (07)