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Definition and Measurement of Selection Bias: From Constant Ratio to Constant Difference
Author(s) -
Cahan Sorel,
Gamliel Eyal
Publication year - 2006
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/j.1745-3984.2006.00009.x
Subject(s) - constant (computer programming) , selection (genetic algorithm) , converse , statistics , mathematics , selection bias , conceptualization , econometrics , computer science , artificial intelligence , geometry , programming language
Despite its intuitive appeal and popularity, Thorndike's constant ratio (CR) model for unbiased selection is inherently inconsistent in n ‐free selection. Satisfaction of the condition for unbiased selection, when formulated in terms of success/acceptance probabilities, usually precludes satisfaction by the converse probabilities of rejection/failure, and vice versa. This paper suggests that this inconsistency is unavoidable due to the (negative) linear relation between “percent accepted” ( P ) and “percent rejected” (1 – P ), which does not preserve ratios and, thus, invalidates the conceptualization and measurement of selection bias in ratio terms. Therefore, we propose to substitute the CR model with a constant difference (CD) model for the definition and measurement of selection bias, and show the latter's underlying rationale and its applicability in both n ‐free and fixed‐ n selection.