ABSTRACT
This chapter considers experimental design models that involve random factors. A random effects model is one in which all of the factors are random. The presence of a random effects factor may alter the distribution of a sum of squares. If so, the form of the expected mean squares, and as a consequence, the form of the f–test may change. The distributional assumptions of mixed and random effects models do not change the observed data; therefore, the sums of squares are unchanged. A mixed effects model is one in which at least one factor is fixed and at least one is random. Satterthwaite proposed a procedure for obtaining a test statistic that has an approximate f–distribution. In the procedure the numerator of the f is the mean square of the term associated with the null hypothesis.
