What is an acceptable alpha level?
Underlying theory should motivate the development of an analysis of variance model whenever possible. Simplified, a relation is thought to exist such that the level of a factor variable is thought to affect the mean of a dependent variable Y. Theories and empirical evidence should suggest which factor levels of the independent variable are important, and how they are thought to affect Y. Figure 1 shows two possible relationships between a response variable Yobs and an independent variable Xi. Figure 1a shows a regression model used when both variables X and Y are continuous. Figure 1b shows the results of an ANOVA when the response variable Y is continuous and the X variable (Factor) is at two levels (in figure 1b the observations are scattered across X so they can be seen, for a true categorical response with two levels the observations would fall on two vertical lines). The X variable may be either qualitative or quantitative.
