ANOVA

Music and Lyrics © 2016 Monty Harper

Suppose you study 12 different herds of  elephants 
Can the differences in their average weights 
be explained by random error?
Or do any herds have weights that are truly different?
It's a difficult conundrum
Lucky for you there's a test that will help you compare!

The variance of the average weight 
between the different herds 
Is matched against the variance of
weights within each set
The ratio of "between" against
"within" gives your statistic
If the average weights are all equal, how
unlikely is the "between" / "within" ratio you get?

If the variance between your herds 
Dominates that within
You can reject the null hypothesis
And let the real work begin
At least one herd of your elephants features
weights  of a different mean
But ANOVA gives no details -
It's a one trick multiple mean comparing machine.