<P> In the illustrations to the right, groups are identified as X, X, etc . In the first illustration, the dogs are divided according to the product (interaction) of two binary groupings: young vs old, and short - haired vs long - haired (e.g., group 1 is young, short - haired dogs, group 2 is young, long - haired dogs, etc .). Since the distributions of dog weight within each of the groups (shown in blue) has a relatively large variance, and since the means are very similar across groups, grouping dogs by these characteristics does not produce an effective way to explain the variation in dog weights: knowing which group a dog is in doesn't allow us to predict its weight much better than simply knowing the dog is in a dog show . Thus, this grouping fails to explain the variation in the overall distribution (yellow - orange). </P> <P> An attempt to explain the weight distribution by grouping dogs as pet vs working breed and less athletic vs more athletic would probably be somewhat more successful (fair fit). The heaviest show dogs are likely to be big strong working breeds, while breeds kept as pets tend to be smaller and thus lighter . As shown by the second illustration, the distributions have variances that are considerably smaller than in the first case, and the means are more distinguishable . However, the significant overlap of distributions, for example, means that we cannot distinguish X and X reliably . Grouping dogs according to a coin flip might produce distributions that look similar . </P> <P> An attempt to explain weight by breed is likely to produce a very good fit . All Chihuahuas are light and all St Bernards are heavy . The difference in weights between Setters and Pointers does not justify separate breeds . The analysis of variance provides the formal tools to justify these intuitive judgments . A common use of the method is the analysis of experimental data or the development of models . The method has some advantages over correlation: not all of the data must be numeric and one result of the method is a judgment in the confidence in an explanatory relationship . </P> <P> ANOVA is a form of statistical hypothesis testing heavily used in the analysis of experimental data . A test result (calculated from the null hypothesis and the sample) is called statistically significant if it is deemed unlikely to have occurred by chance, assuming the truth of the null hypothesis . A statistically significant result, when a probability (p - value) is less than a pre-specified threshold (significance level), justifies the rejection of the null hypothesis, but only if the a priori probability of the null hypothesis is not high . </P>

Repeated-measures anova is considered a generalization of regression and factor analysis