Percentage Coefficient (bp) -- Effect Size Analysis (Theory Paper 1)

TL;DR

This paper revisits the theory of the percentage coefficient (bp), an effect size estimator in regression analysis, emphasizing its interpretability and comparability on 0-1 percentage scales, and clarifying its role in measuring specific effect components.

Contribution

It provides a theoretical foundation for the percentage coefficient (bp), highlighting its advantages over other effect size indicators in terms of interpretability and comparison.

Findings

bp is interpretable on 0-1 percentage scales

bp effectively compares different estimands

bp measures the efficiency component of effect

Abstract

Percentage coefficient (bp) has emerged in recent publications as an additional and alternative estimator of effect size for regression analysis. This paper retraces the theory behind the estimator. It's posited that an estimator must first serve the fundamental function of enabling researchers and readers to comprehend an estimand, the target of estimation. It may then serve the instrumental function of enabling researchers and readers to compare two or more estimands. Defined as the regression coefficient when dependent variable (DV) and independent variable (IV) are both on conceptual 0-1 percentage scales, percentage coefficients (bp) feature 1) clearly comprehendible interpretation and 2) equitable scales for comparison. The coefficient (bp) serves the two functions effectively and efficiently. It thus serves needs unserved by other indicators, such as raw coefficient (bw) and standardized beta. Another premise of the functionalist theory is that "effect" is not a monolithic concept. Rather, it is a collection of concepts, each of which measures a component of the conglomerate called "effect", thereby serving a subfunction. Regression coefficient (b), for example, indicates the unit change in DV associated with a one-unit increase in IV, thereby measuring one aspect called unit effect, aka efficiency. Percentage coefficient (bp) indicates the percentage change in DV associated with a whole scale increase in IV. It is not meant to be an all-encompassing indicator of an all-encompassing concept, but rather a comprehendible and comparable indicator of efficiency, a key aspect of effect.