ABSTRACT
This chapter considers the nature of the assumptions commonly made for analysis of designed experiments. There are four basic assumptions commonly employed in the comparison of group means, or more generally in the analysis of variance: the model is correct, responses are uncorrected, variances are equal and responses have a normal distribution. Many problems with the basic assumptions can be examined in the regression setting by plotting residuals against predicted values or against other factors. It can be very valuable to augment residual plots with identifying symbols for factor levels. Evidence from residual plots may suggest removing outliers, employing suitable transformations, using weighted analysis, or redefining the model relationship between factors and response. If responses are uncorrelated, then group variances summarize the most relevant information about variability in the data. Residual plots of group mean against response or of group mean against residual can show evidence of unequal variance.
