<P> The weights, W h (\ displaystyle W_ (h)), frequently, but not always, represent the proportions of the population elements in the strata, and W h = N h / N (\ displaystyle W_ (h) = N_ (h) / N). For a fixed sample size, that is n = ∑ n h (\ displaystyle n = \ sum (n_ (h))), </P> <Dl> <Dd> Var ⁡ (x _̄ w) = ∑ h = 1 H W h 2 V a r h (1 n h − 1 N h), (\ displaystyle \ operatorname (Var) ((\ bar (x)) _ (w)) = \ sum _ (h = 1) ^ (H) W_ (h) ^ (2) \, Var_ (h) \ left ((\ frac (1) (n_ (h))) - (\ frac (1) (N_ (h))) \ right),) </Dd> </Dl> <Dd> Var ⁡ (x _̄ w) = ∑ h = 1 H W h 2 V a r h (1 n h − 1 N h), (\ displaystyle \ operatorname (Var) ((\ bar (x)) _ (w)) = \ sum _ (h = 1) ^ (H) W_ (h) ^ (2) \, Var_ (h) \ left ((\ frac (1) (n_ (h))) - (\ frac (1) (N_ (h))) \ right),) </Dd> <P> which can be made a minimum if the sampling rate within each stratum is made proportional to the standard deviation within each stratum: n h / N h = k S h (\ displaystyle n_ (h) / N_ (h) = kS_ (h)), where S h = V a r h (\ displaystyle S_ (h) = (\ sqrt (Var_ (h)))) and k (\ displaystyle k) is a constant such that ∑ n h = n (\ displaystyle \ sum (n_ (h)) = n). </P>

How large does a sample size need to be to be statistically significant