<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> <P> In the typical application of ANOVA, the null hypothesis is that all groups are random samples from the same population . For example, when studying the effect of different treatments on similar samples of patients, the null hypothesis would be that all treatments have the same effect (perhaps none). Rejecting the null hypothesis is taken to mean that the differences in observed effects between treatment groups are unlikely to be due to random chance . </P> <P> By construction, hypothesis testing limits the rate of Type I errors (false positives) to a significance level . Experimenters also wish to limit Type II errors (false negatives). The rate of Type II errors depends largely on sample size (the rate is larger for smaller samples), significance level (when the standard of proof is high, the chances of overlooking a discovery are also high) and effect size (a smaller effect size is more prone to Type II error). </P>

When do we typically use anova to test a hypothesis
find me the text answering this question