Error of Measurement and Statistical Inference: Some Anomalies.
This paper was designed to examine some relations between the reliability of a dependent variable and the magnitude of the associated test statistic, and to point out some anomalies that arise when the usual reliability formulas are applied. These anomalies suggest that error of measurement, as investigated in classical test theory, cannot be routinely incorporated into the “error term” in statistical tests, and that the reliability of test scores, as traditionally defined, does not have the simple relationship to statistical inference that one might expect.