Analysis of Variance (ANOVA)

Statistics Tutorial: Analysis of Variance

ANOVA is used to compare averages between three or more groups.

ANOVA is conceptually an extension of the two-sample t-test. The main difference is ANOVA can compare three or more groups whereas the two-sample t-test is designed to compare only two groups.

Continuing with the weight loss example in my Probability and Two-Sample t-test tutorials, imagine you have two new diets plus the standard diet and you want to see if there is a difference in the amount of weight loss “among” the three groups.

As with the two-sample t-test, the Independent variable is “Group”, only this time there are three categories (standard diet, new diet 1, and new diet 2). The dependent variable is the same as the two-sample t-test example, “Weight Loss”, measured in pounds.

Like with the t-test we have variation in weight loss from one participant to the next both within and between groups. So, the logical approach is to compare the average weight loss among the three groups.

As with the two-sample t-test, the complex mathematical calculations are performed by software like SPSS. The software will produce a p-value (probability value). By convention, if p is < 0.05, the sample results provide strong evidence that the averages are different among the three groups. Further testing would be needed to determine which groups were different than which.