arXiv subjects

Xinshu Zhao

Publications and source records attributed to Xinshu Zhao.

4 recordsLinked to original sources

arXiv2025

Intellectual Up-streams of Percentage Scale ($ps$) and Percentage Coefficient ($b_p$) -- Effect Size Analysis (Theory Paper 2)

Percentage thinking, i.e., assessing quantities as parts per hundred, spread from Roman tax ledgers to modern algorithms. Building on Simon Stevin's La Thiende (1585) and the 19th-century metrication that institutionalized base-10 measurement (Cajori, 1925), this article traces how base-10 normalization, especially the 0-1 percentage scale, became a shared language for human and machine understanding. We retrace 1980s efforts at UW-Madison and UNC Chapel Hill to "percentize" variables to make regression coefficients interpretable, and relate these experiments to established indices, notably the Pearson (1895) correlation r (range -1 to 1) and the coefficient of determination r-squared (Wright, 1920). We also revisit Cohen et al.'s (1999) percent of maximum possible (POMP) metric. The lineage of 0-100 and 0-1 scales includes Roman fiscal practice, early American grading at Yale and Harvard, and recurring analyses of percent (0-100) and percentage (0-1, or -1 to 1) scales that repeatedly reinvent the same indices (Durm, 1993; Schneider and Hutt, 2014). In data mining and machine learning, min-max normalization maps any feature to [0, 1] (i.e., 0-100%), equalizing scale ranges and implied units across percentized variables, which improves comparability of predictors. Under the percentage theory of measurement indices, equality of units is the necessary and sufficient condition for comparing indices (Cohen et al., 1999; Zhao et al., 2024; Zhao and Zhang, 2014). Seen this way, the successes of machine learning and artificial intelligence over the past half century constitute large-scale evidence for the comparability of percentage-based indices, foremost the percentage coefficient (bp).

stat.ME↗

arXiv2024

Liberal-Conservative Hierarchies of Intercoder Reliability Estimators

While numerous indices of inter-coder reliability exist, Krippendorff's α and Cohen's \{kappa} have long dominated in communication studies and other fields, respectively. The near consensus, however, may be near the end. Recent theoretical and mathematical analyses reveal that these indices assume intentional and maximal random coding, leading to paradoxes and inaccuracies. A controlled experiment with one-way golden standard and Monte Carlo simulations supports these findings, showing that \{kappa} and α are poor predictors and approximators of true intercoder reliability. As consensus on a perfect index remains elusive, more authors recommend selecting the best available index for specific situations (BAFS). To make informed choices, researchers, reviewers, and educators need to understand the liberal-conservative hierarchy of indices, i.e., which indices produce higher or lower scores. This study extends previous efforts by expanding the math-based hierarchies to include 23 indices and constructing six additional hierarchies using Monte Carlo simulations. These simulations account for factors like the number of categories and distribution skew. The resulting eight hierarchies display a consistent pattern and reveal a previously undetected paradox in the Ir index.

physics.soc-ph↗

arXiv2024

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

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.

stat.AP↗

arXiv2023

Total-effect Test May Erroneously Reject So-called "Full" or "Complete" Mediation

The procedure for establishing mediation, i.e., determining that an independent variable X affects a dependent variable Y through some mediator M, has been under debate. The classic causal steps require that a "total effect" be significant, now also known as statistically acknowledged. It has been shown that the total-effect test can erroneously reject competitive mediation and is superfluous for establishing complementary mediation. Little is known about the last type, indirect-only mediation, aka "full" or "complete" mediation, in which the indirect (ab) path passes the statistical partition test while the direct-and-remainder (d) path fails. This study 1) provides proof that the total-effect test can erroneously reject indirect-only mediation, including both sub-types, assuming least square estimation (LSE) F-test or Sobel test; 2) provides a simulation to duplicate the mathematical proofs and extend the conclusion to LAD-Z test; 3) provides two real-data examples, one for each sub-type, to illustrate the mathematical conclusion; 4) in view of the mathematical findings, proposes to revisit concepts, theories, and techniques of mediation analysis and other causal dissection analyses, and showcase a more comprehensive alternative, process-and-product analysis (PAPA).

econ.EM↗