Calculating P-values for anova with unequal variances

Abstract

We develop a procedure for calculating P-values associated with the F_u statistic for an ANOVA with unequal variances. The computational procedure is based on the fact that can be expressed as a weighted average P-value from chi square tests , with weights equalling the likelihood of the true population variances given their sample estimates. The procedure to obtain the weighted average is calculation intensive and is best implemented by computer. Software to carry out the procedure is available from the authors.

Keywords:

• Analysis of variance
• F_u test
• unequal variance
• Hermite approximation