Last month, I described a simple problem to determine which gear material resulted in longer wear. We reviewed the extremely powerful technique called Analysis of Variance (ANOVA) and found a statistically significant and important effect on the average wear due to gear material. I also promised to tell you about an infrequently used next step that would make you a lot of money.

(In the event that you missed last month’s column, due to being hit by a meteor or some other equally valid excuse, click here for the research description and data.)

We showed with our initial ANOVA that there was a significant difference in wear for the five different materials, and using the statistic ω², we showed that the differences were large enough to be considered important as compared to the total variation. But the ANOVA only tells us that there’s a difference somewhere, it doesn’t tell us where the differences are.

 …