ANALYSIS OF VARIANCE I. Introduction. A. In independent measures t-tests, the means of two independent samples (groups) on some interval variable were compared with the t-test indicating whether the means of the groups were different. This is fine when you only have two groups, such as with gender. However, when you have more than two groups, a different type of test is required. B. Analysis of variance (ANOVA) is a statistical test in which the means of 3 or more groups on some interval level variable can be compared simultaneously. It indicates whether at least one of the group means is significantly different from the others. C. In analysis of variance, the total variance in the combined sample (all groups taken together) is partitioned (divided) into two parts. 1. The first part represents the amount of variation that exists within each of the the groups being compared. 2. The second part represents the amount of variation between the groups being compared. 3. The ratio of the variation between the groups to the variation within the groups is called an F-ratio. The F-ratio is used in Anova to determine if the means of the groups being compared can be considered equal. II. Doing analysis of variance. A. State the null hypothesis. B. Choose a statistical test. C. Check assumptions. 1. Three or more independent random probability samples. 2. Interval-ratio variable being compared across three or more categories defined by a categorical variable. 3. Populations are normally distributed. 4. Population variances are equal. a. Sample size of each group is relatively large (30 or more). b. Sample sizes of the groups approximately equal. D. Select an alpha level. E. Calculating the F-ratio and making a decision about the null hypothesis. 1. Calculate the statistic. 2. Determine the probability associated with the statistic. 3. Compare probability to alpha level. 4. Decide about the null. III. Limitations and extensions of the one-way analysis of variance. A. The analysis of variance test just performed is called a one-way analysis of variance because means are being compared across a single set of groups or categories. Extensions anova also allow for comparisons across several different sets of groups or categories, called multiple analysis of variance or MANOVA, and for the effects of interval variables (besides the dependent variable) to be controlled, called analysis of covariance or ANCOVA. B. Analysis variance only tells you if at least one of the groups being compared differs from the others. It does not tell you which groups differ from each other. However, there are additional tests that can be performed that do indicate such differences. These are called multiple comparison tests.