How would you explain the logic of ANOVA to smeone with no e

How would you explain the logic of ANOVA to smeone with no experience?

Solution

ANOVA tests if there is significant difference between at least 2 group means.

It basically tests if the difference between the means is simply due to the variation in each group or if they really are different.

To do that, they compute the ratio of the variation between the groups and within the group.

Then, we check how rare this ratio is if the means are all the same.