sharedstat: diagnose and correct statistics built from a shared component

Abstract

An R package for statistics formed from a difference, ratio or residual of two quantities that share a measured component. Four such constructions are covered: a divergence measured against a shared reference arm, a trans term obtained by subtracting a cis term, a count of significant features read as an ordering of effect sizes, and an interaction contrast on compositional counts. The central analytical result is that when one noisy reference is used both as the regression predictor and as a component of the contrast, the naive estimator returns the true gain multiplied by the reliability of the reference arm. An apparent divergence is therefore produced even when the true divergence is exactly zero, and the direction of the inference inverts once the reliability falls below the reciprocal of the gain. The package quantifies this for a given design, applies an instrumental-variable correction where an instrument is available, and includes a known-truth simulator in which compositionality emerges from closed-sum sampling rather than being imposed. The test suite asserts the values the package can compute from its bundled tables, alongside each estimator's input-domain contract. The reliability, gain and mixture-test values of the accompanying paper are re-derived by lock scripts in its analysis deposit. This record archives version 0.1.3, a maintenance release of 0.1.2 that fixes edge cases listed in NEWS.md; it exports the same thirteen functions. The accompanying paper's reliability results were computed with version 0.1.2 (doi:10.5281/zenodo.22946335). Version 0.1.0 (doi:10.5281/zenodo.22693748) exports eleven functions and does not contain reliability_from_blocks() or reliability_from_replicates().