Neyman n_h = n·N_h·σ_h/Σ

This calculator determines the optimal sample size for each stratum in a stratified sampling study using Neyman allocation. The method distributes the sample proportionally to the size and variability of each stratum, minimizing the variance of the total estimate. The formula used is n_h = (n × N_h × σ_h) / Σ(N_h × σ_h), where n_h is the sample size for stratum h, N_h is the population size of the stratum, and σ_h is the standard deviation of the variable of interest in that stratum.

The tool is ideal for heterogeneous populations that can be divided into distinct subgroups (strata) with varying levels of variability. For instance, in market research or epidemiological studies, where representative samples must be collected from the most dispersed groups. This enhances the accuracy of final estimates, especially in resource-constrained scenarios.

Ensure that N_h and σ_h values for each stratum are known beforehand. Neyman allocation requires a clear understanding of population structures and variability patterns. If a stratum has a standard deviation of zero, it will not contribute to the allocation since there is no variability to capture.

This approach is preferable to methods like equal allocation (same number of samples per stratum) when strata differ significantly. However, if all strata have the same variability or size, the result will resemble proportional allocation. Always round final values to whole numbers, adjusting as needed.