standard error calculation inconsistent between 'stats' and 'mstats'

[bulli92]

The routine sem() in stats and mstats is inconsistent in several ways:

1. arguments are different
   sem(a, axis=0, ddof=1) for stats
   sem(a, axis=0): for mstats
2. normalization is different
   / sqrt(n-1) in mstats
   / sqrt(n) in stats

[rgommers]

The mstats version can get ddof=1 added. The right denominator is sqrt(n), so that's a bug in the mstats version.

[josef-pkt]

I think these two cancel, they should produce the same result,
1/n * 1/(n-1) can be calculated in two ways
(based on the above description not source)

[rgommers]

Ah, because of different ddof. You're right. So not a bug right now, but should still be made consistent.

[shaunagm]

I'd like to resolve this issue. When you say it should be made consistent, should stats be changed to match mstats, or mstats be changed to match stats?

My understanding is that, with stats, the degree of freedom is being passed into the np.std calculation, so you get:

sqrt(sum-of-squared-deviation/n-1)/sqrt(n)

Whereas with mstats, the degree of freedom is not being passed into the np.std calculation, so you get:

sqrt(sum-of-squared-deviation/n)/sqrt(n-1)

My understanding is that the std calculation is more commonly where you want to incorporate degrees of freedom. The stats method also allows the user to override the 1 degree of freedom, whereas mstats hardcodes it in. So I will go ahead and try to change mstats to stats, but let me know if I should do otherwise!