Note on the radical inflation in the estimates of error variance in measurement models

Abstract

<p>This note discusses a radical technical inflation in error variance and related standard error related to the test score from the conceptual and empirical viewpoint. The technical inflation is a strict consequent of technical underestimation of item-score correlation by product-moment coefficient of correlation (PMC) embedded in the traditional estimators of reliability such as coefficients alpha, theta, omega, or rho (maximal reliability). Specifically, in the educational settings where the compilation usually embeds both easy and difficult items, the estimate by PMC may be far off the true association between an item and the score. Then, by using the traditional estimators of reliability in the process, the estimates of standard errors are technically inflated because the error variance related to the traditional measurement models is radically inflated and, consequently, the estimates of reliability are radically deflated. Within the educational testing settings, deflation-corrected standard errors using deflation-corrected estimators of reliability in the process would draw us nearer the true accuracy of the test score.</p>