Editing Stratified sampling (section)

== Mean and standard error ==
The mean and variance of stratified random sampling are given by:<ref name=":0" />

:<math>\bar{x} = \frac{1}{N} \sum_{h=1}^L N_h \bar{x}_h</math>

:<math>s_\bar{x}^2 = \sum_{h=1}^L \left(\frac{N_h}{N}\right)^2 \left(\frac{N_h - n_h}{N_h - 1}\right)\frac{s_h^2}{n_h}</math>

where

:<math>L ={}</math>number of strata

:<math>N ={}</math>the sum of all stratum sizes

:<math>N_h ={}</math>size of stratum <math>h</math>

:<math>\bar{x}_h ={}</math>sample mean of stratum <math>h</math>

:<math>n_h ={}</math>number of observations in stratum <math>h</math>

:<math>s_h ={}</math>sample standard deviation of stratum <math>h</math>

Note that the term <math>(N_h-n_h) / (N_h-1)</math>, which equals <math>1-\frac{n_h - 1}{N_h - 1}</math>, is a [[Standard error#Correction for finite population|finite population correction]] and <math>N_h</math> must be expressed in "sample units". Forgoing the finite population correction gives:

:<math>s_\bar{x}^2 = \sum_{h=1}^L \left(\frac{N_h}{N}\right)^2 \frac{s_h^2}{n_h}</math>

where the <math>w_h = N_h/N</math> is the population weight of stratum <math>h</math>.