What's Analysis of Variance?

Question

Simple explanations are preferred.

Answer 1

A simple explanation is that it's a statistical process to test the relationship between two variables, usually with the assumption that one of them has an effect on the other. It involves dividing a bunch of observations into groups and looking at how much variation there is both within the groups and between them. When there's a low level of variation within the groups as compared to the amount of variation between the groups, that suggests that the variables are related in some significant way.

For example, let's say you want to find out if money makes people happy. You could gather a random selection of people and divide them into three groups: a rich group, a poor group, and a middle group. Then you could measure their happiness somehow, with interviews or whatever, and give everyone a happiness score. You could then perform an Analysis of Variance (or ANOVA as it's more often called for short) to measure the relationship between how much money you have and how happy you are. If all the rich people are pretty happy and all the poor people are miserable, that makes it look like money helps make you happy; the variation between the groups (i.e., between the rich in general and the poor in general) is high relative to the variation within them (between the happiest and saddest rich folks, and between the happiest and saddest poor folks). If there are miserable people and happy people in both groups, that indicates that there might not be a relationship.

Answer 2

D.