ABSTRACT
The analysis of variance has certain underlying assumptions to make the analysis valid. This includes that the data were obtained from a random sample of the population; that the error terms occur randomly, are normally distributed, and are not correlated. The sample populations have equal or homogeneous variances. This is often referred to as homoscedastic variances. This can be a little confusing. If this is an analysis of variance, how can the variances be the same? The assumption is that the variance within one group is the same as the variance in other groups. The means of the groups, however, may differ. In ANOVA (analysis of variance), the F-tests are based on a ratio-the variation between the group means divided by the variation within the groups (pooled across groups). It is when there is a disparity between these variances that a significant difference is detected. The variances and treatment means should not be correlated. Finally, the factor levels are assumed to be additive. That is, the model parameters, treatments, replications, error, etc. are added together to create the model. This is often referred to as a linear model or it has linearity.
