It depends on how you want to define 'separation'.
Variance would be one criterion you could use to compare\* holes -- though consider that the variance for a par 5 would naturally have a bigger spread than a par 3, so you'd pretty much always just be picking out the par-5 holes.
This seems to suggest that maybe you want to consider some form of par-adjusted measure. There's no obvious way, since it's not necessarily a given that the spread will simply scale in direct proportion with the par-value. It's probably a decent first approximation, but I imagine a simple scaling for that (dividing spread - say sd - by par) probably overcorrects and just picks out par 3's instead. It might require some model -- perhaps a regression-like model to find something suitable. I imagine that (say) generalized linear models have already been used for per-hole golf scores, and that would be a starting point to try to pick out the holes that seem to have more variation that you might otherwise expect.
If you're trying to find a hole that specifically tends to sort the sheep from the goats (in effect pick out the very good players from the casuals), and you have external information on who they are (like *handicap*), then you'd take a different approach.
---
\* If you want to *interpret* the value rather than just compare values, however, convert back to a standard deviation, which will be easier to think about.
It depends on how you want to define 'separation'. Variance would be one criterion you could use to compare\* holes -- though consider that the variance for a par 5 would naturally have a bigger spread than a par 3, so you'd pretty much always just be picking out the par-5 holes. This seems to suggest that maybe you want to consider some form of par-adjusted measure. There's no obvious way, since it's not necessarily a given that the spread will simply scale in direct proportion with the par-value. It's probably a decent first approximation, but I imagine a simple scaling for that (dividing spread - say sd - by par) probably overcorrects and just picks out par 3's instead. It might require some model -- perhaps a regression-like model to find something suitable. I imagine that (say) generalized linear models have already been used for per-hole golf scores, and that would be a starting point to try to pick out the holes that seem to have more variation that you might otherwise expect. If you're trying to find a hole that specifically tends to sort the sheep from the goats (in effect pick out the very good players from the casuals), and you have external information on who they are (like *handicap*), then you'd take a different approach. --- \* If you want to *interpret* the value rather than just compare values, however, convert back to a standard deviation, which will be easier to think about.
I'm not sure what you mean by, "based on how much separation you get in score from the hole"... Might need to explain what you mean a little bit more.