A New View of Statistics
Root Mean-Square Error (RMSE)
The RMSE is a kind of generalized standard deviation. It pops up whenever you look for differences between subgroups or for other effects or relationships between variables. It's the spread left over when you have accounted for any such relationships in your data, or (same thing) when you have fitted a statistical model to the data. Hence its other name, residual variation. I'll say more about residuals for models, about fitting models in general, and about fitting them to data like these much later.
Here's an example.
Suppose you have heights for a group of females and males. If you
analyze the data without regard to the sex of the subjects, the
measure of spread you get will be the total variation. But
stats programs can take into account the sex of each subject, work
out the means for the boys and the girls, then derive a single
SD that will do for the boys and the girls. That single SD is the
RMSE. Yes, you can also work out the SDs for the boys and girls
separately, but you may need a single one to calculate
effect sizes. You can't simply average the
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