6.8.5.2.34. statsmodels.sandbox.stats.multicomp.varcorrection_unequal¶

statsmodels.sandbox.stats.multicomp.varcorrection_unequal(var_all, nobs_all, df_all)[source]¶

return joint variance from samples with unequal variances and unequal sample sizes

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Parameters:

var_all : array_like

The variance for each sample

nobs_all : array_like

The number of observations for each sample

df_all : array_like

degrees of freedom for each sample

Returns:

varjoint : float

joint variance.

dfjoint : float

joint Satterthwait’s degrees of freedom

Notes

(copy, paste not correct) variance 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/n.

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.

This is for variance of mean difference not of studentized range.