6.8.5.2.31. statsmodels.sandbox.stats.multicomp.varcorrection_pairs_unbalanced¶

statsmodels.sandbox.stats.multicomp.varcorrection_pairs_unbalanced(nobs_all, srange=False)[source]¶

correction factor for variance with unequal sample sizes for all pairs

this is just a harmonic mean

Parameters:

nobs_all : array_like

The number of observations for each sample

srange : bool

if true, then the correction is divided by 2 for the variance of the studentized range statistic

Returns:

correction : array

Correction factor for variance.

Notes

variance correction factor is

1/k * sum_i 1/n_i

where k is the number of samples and summation is over i=0,...,k-1. If all n_i are the same, then the correction factor is 1.

This needs to be multiplies by the joint variance estimate, means square error, MSE. To obtain the correction factor for the standard deviation, square root needs to be taken.

For the studentized range statistic, the resulting factor has to be divided by 2.