Definition and measurement of selection bias: From constant ratio to constant difference

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.