THE DISTRIBUTION OF AN ACTUAL SAMPLE-SIZE INCREMENT IN STRATIFIED RANDOM SAMPLING

In stratified random sampling, the determinations of total sample size n and sample size in each stratum n(h) are generally based on cost of survey and precision of estimate, and three kinds of allocation are generally used: Optimal Allocation, Neyman Allocation and Proportional Allocation. But whatever allocation is used, n(h)' = [n(h)] + 1, h = 1, 2, ... L, are usually assumed in practical applications. That is, the allocated sample size n(h) is truncated to its integer part and increased by one. Therefore, the actual sample size exceeds the optimal by an increment. This article investigates the probability distribution, expected value and variance of this increment.