Conditional Subscore Reporting Using Iterated Discrete Convolutions

Abstract

The literature showing that subscores fail to add value is vast; yet despite their typical redundancy and the frequent presence of substantial statistical errors, many stakeholders remain convinced of their necessity. This article describes a method for identifying and reporting unexpectedly high or low subscores by comparing each examinee’s observed subscore with a discrete probability distribution of subscores conditional on the examinee’s overall ability. The proposed approach turns out to be somewhat conservative due to the nature of subscores as finite sums of item scores associated with a subdomain. Thus, the method may be a compromise that satisfies score users by reporting subscore information as well as psychometricians by limiting misinterpretation, at most, to the rates of Type I and Type II error.