The Assumptions Behind the Analysis
This chapter looks at three assumptions in turn so as to be able to recognize situations in which they are likely to break down. The assumptions are normality, homogeneity of variance, and additivity. The assumption of normality means that it must be reasonable to suppose that the distribution of the population of observations is approximately normal. The assumption of additivity concerns the construction of the model for the mean values of the measurement. The other two assumptions relate to the random variation or error term. The benefit of separate modelling of the mean and the error term distribution may be perceived by considering again the use of the logarithmic transformation. The chapter also looks at empirical methods for detecting when the assumptions do not hold for a given set of data, and discusses how to modify the analysis when the assumptions are plainly untrue.