Analysis of Variance , otherwise known as ANOVA, is the study of variance among  and between the groups. When you have three groups who react different to an outcome variable it is not enough to compare mean estimates and call it a night. You also have to take into account the variability around the sample mean for each subgroup. Let me back up for a second. You are not interested mainly in the  group classifications. Rather your focus should be on how your outcome variable reacts in each group. You want to know if you are dealing with groups that come from different populations. What is the real deal with this population talk? Why do we care if something comes from the same population or not? Well trust me you care. If its the same population all the members of that group share the same variance. They behave similarly in terms of the mean, for instance. So your objective with an ANOVA is to show a statistically significant difference among the groups.

Now the ANOVA will not tell you specifics about the difference. Group 1 could be different from the other groups. You just know there is a difference.

If you enjoyed this short blog there are more to follow. -Amy