ABSTRACT
Despite the name, analysis of variance is used to draw inferences about means, not variances. It is particularly useful as a way of determining if there are differences among the means of more than two populations: The null hypothesis is that the means of all populations are equal, and the alternative hypothesis is that at least one population mean differs. The term “analysis of variance” is commonly abbreviated “ANOVA.” The basic idea of analysis of variance is to partition (i.e., divide up) the variability observed in the data into two parts: variability that can be accounted for by group membership, and variability that cannot. The null hypothesis tested in a one-way ANOVA is that the means of several populations are equal. The alternative hypothesis is that at least one mean differs from the others.
