Final answer:
Discriminant analysis predicts categories using independent variables, while simple ANOVA tests if group means differ for a single categorical variable. ANOVA uses the F ratio from the F distribution, while discriminant analysis is used for classification.
Step-by-step explanation:
Discriminant analysis differs from simple ANOVA in that discriminant analysis is used for predicting a categorical dependent variable by one or more continuous or binary independent variables. In contrast, simple ANOVA compares the means of a response variable for several groups to determine if at least one group mean is statistically different from the others.
Simple ANOVA utilizes the F distribution and the F ratio to test the null hypothesis of equal means. It requires that samples be drawn from normally distributed populations with equal variances, and it can only handle a single categorical independent variable affecting a continuous dependent variable. In ANOVA, within and between group variations are compared, and the F statistic is computed from these variations with specific numerator and denominator degrees of freedom. This forms the basis of the ANOVA table.
Contrarily, discriminant analysis can handle multiple independent variables and is often used in situations like market research, where the aim is to classify observations into predefined categories based on various predictors.