The Effects of Correlated Data and Correction Procedures for F-Test in Unbalanced Two Way Model

Independence of observations is one of the standard assumption in analysis of Variance (ANOVA) table. Where the error terms in the model are independent, identically distributed normal variables with null means and homogeneous variances. In this paper investigate the effect of dependence of observations in ANOVA for unbalanced 2-way nested fixed model and developing a method for adjusting it. When the error terms are correlated and focus on the effects of departures from independence assumptions on hypothesis testing by determining the expect mean squares for errors as well as treatments for this model and correcting the F statistics for testing the factor effect. The model considered is one in which all measurements have same variance, and the covariance matrix enjoy a structure defined as follows: every pair of measurements comes from:
i) The same experimental observation and the same experimental unit;
ii) Different experimental observation, but in the same experimental unit;
ii) Different experimental unit;
has covariance and respectively.