A single-factor ANOVA derives its name from the fact that the test deals with one independent variable; in this case, we discuss the population mean. The question that the ANOVA attempts to ask is this: are the samples really of the same population, or is there enough variance in the sample means to suggest that the samples were taken from independent populations? The type of test we shall consider in a moment deals with the comparison of three or more sample means. The sample sizes themselves need not be equal. This test makes several assumptions:
- The populations must be Normally Distributed.
- The samples must be independent.
- The variances must be equal.
We may now discuss the hypothesis testing procedures for a single-factor ANOVA.