Stratifiedtwo

Stratifiedtwo is a term used in statistics and data analysis to describe a two-stratum stratification framework intended to improve estimation precision by dividing a population into two homogeneous blocks with respect to the variable of interest. In this approach, the population is partitioned along a stratification variable (or set of variables) into Stratum 1 and Stratum 2. After partitioning, samples are drawn within each stratum, often with different sampling fractions to reflect relative size or variability.

The key idea of stratifiedtwo is that estimators computed within each stratum, when combined, can yield lower overall variance than a simple random sample. The usual estimator for a population mean is a weighted average of the stratum means: ȳ = (N1/N) ȳ1 + (N2/N) ȳ2, where N1 and N2 are stratum sizes and N = N1 + N2. The variance of this estimator depends on the within-stratum variances and the allocation of samples between strata. Under fixed costs, Neyman allocation suggests choosing n1 and n2 proportionally to N1 S1 and N2 S2, where Sh is the standard deviation within each stratum, to minimize variance.

Applications of stratifiedtwo include survey sampling, public health studies, and market research where a two-way or two-level structure exists. In machine learning and data preprocessing, a two-stratum stratification can be used to preserve balanced representation across a key category (such as class labels) when creating training and evaluation folds.

Limitations include the need for reliable prior information about within-stratum variability and the potential for reduced effectiveness if the two strata do not capture the major sources of heterogeneity.