Lexis Variation
A closely related concept is the Lexis variation. Let k samples each of size n be drawn at random. Let the probability of success (p) be constant and let the actual probability of success in the kth sample be p1, p2, ..., pk.
The average probability of success (p) is
The variance in the number of successes is
where var( pi ) is the variance of the pi.
If all the pi are equal the sampling is said to be Bernoullian; where the pi differ the sampling is said to be Lexian and the dispersion is said to be supranormal.
Lexian sampling occurs in sampling from non homogenous strata.
Read more about this topic: Lexis Ratio