# Analysis of Variance (ANOVA)

The tests we have learned up to this point allow us to test hypotheses that examine the difference between only two means. Analysis of Variance or ANOVA will allow us to test the difference between 2 or more means. ANOVA does this be examining the ratio of variability between two conditions and variability within each condition. For example, say we give a drug that we believe will improve memory to a group of people and give a placebo to another group of people. We might measure memory performance by the number of words recalled from a list we ask everyone to memorize. A t-test would compare the likely-hood of observing the difference in the mean number of words recalled for each group. An ANOVA test, on the other hand, would compare the variability that we observe between the two conditions to the variability observed within each condition. The following animation demonstrates the difference in between group variability and within group variability. Recall that we measure variability as the sum of the difference of each score from the mean. When we actually calculate an ANOVA we will use a short-cut formula

Thus, when the variability that we predict (between the two groups) is much greater than the variability we don't predict (within each group) then we will conclude that our treatments produce different results.