meanA

MeanA is the average value of a variable computed over a specified subset A of a dataset. If x1, x2, ..., xn are the observed values and A denotes the indices i for which observation i satisfies a given condition, then meanA = (1 / n_A) sum_{i in A} x_i, where n_A is the number of observations in A. For example, meanA could denote the average outcome among users who received treatment A in an experiment, or among observations with a feature threshold met.

Notationally, meanA is often written as E[x | A] or μ_A to emphasize its interpretation as the conditional mean given the event A. In practice, meanA_hat denotes the sample analog computed from data. If A is a fixed subset, meanA_hat is an unbiased estimator of μ_A under standard sampling assumptions; if A is determined from the data, care is needed to avoid selection bias.

Properties: meanA is a linear functional of the data restricted to A. The value of meanA changes with the composition of A and can differ substantially from the overall mean μ = (1/n) sum x_i. The standard error of meanA depends on the variance of x within A and on n_A; smaller A yields larger uncertainty. When A partitions the data into subgroups, comparing meanA across groups highlights potential heterogeneity.

Applications and considerations: meanA is widely used in subgroup analysis, stratified statistics, and causal inference to assess heterogeneity of outcomes. It is helpful for comparing group performance in A/B tests, medicine, and social sciences. Report the size of A and the associated uncertainty alongside the estimate to ensure clear interpretation.