Modified testing procedures and multiple comparison methods for ANOVA with AR(1) correlated errors.

In many experiments, several observations are taken over time or with several treatments applied to each subject. These observations tend to be highly correlated, particularly those observed adjacent to each other with respect to time. In this paper, we investigate the effect of the correlations among observations in one-way and two-way ANOVA. A modification of the standard tests suitable for AR(1) correlation structure is proposed and its properties are investigated. We also apply the approximations to the distribution of F tests as suggested by some authors in the past and carry out the analysis. The modified procedure allows us to have a better control of the nominal significance level alpha. Consequently, the multiple comparisons and multiple tests based on this modified procedure will lead to conclusions with better accuracy.