If an ANOVA results in a significant F-statistic, which indicates that there is some difference in means, it’s common to investigate which pairs of groups have significantly different means. If the normality and/or equal variance assumption is violated, the non-parametric Kruskal-Wallis test can be run instead of ANOVA. The population variances of all groups are equal.The population of each group is normally distributed.The test statistic, F, where MS group is the mean squared error of between-group variance and MS error is the mean squared error of within-group variance: Where k is the number of groups and N is the overall sample size.ĪNOVA, which stands for analysis of variance, separates the overall variance in the outcome into variance explained by the group differences and variance that is within each group (which is the variance unexplained by group). The test statistic, F, is the ratio of the variation in the outcome that is between groups divided by the amount within groups. H A: At least one population mean is different, or μ i ≠ μ j for some i, jĭegrees of freedom: Group: k – 1 Error: N – k. H o: The population means of all groups are equal, or μ 1 = μ 2 = … = μ k Note that we could not run a two-sample independent t-test because there are more than two groups. For example, suppose we wanted to know if the mean GPA of college students majoring in biology, chemistry, and physics differ. A one-way (or single-factor) ANOVA can be run on sample data to determine if the mean of a numeric outcome differs across two or more independent groups.