Estimating Total-Test Scores From Partial Scores in a Matrix Sampling Design

Abstract

In establishing national test norms, sampling both examinees and items serves to reduce the amount of testing time required. It is often desired to obtain a total-test score for an individual who was administered only a subset of the total test. The present study compared six methods, two of which utilize the content structure of items, to estimate total-test scores using 450 students and 60 items of the 110-item Stanford Mental Arithmetic Test. The items were sampled in such a way as to make comparisons between overlapping subtest designs and nonoverlapping subtest designs feasible. Three methods yielded fairly good estimates of the total-test score, namely regression with perfectly correlated nonoverlapping item samples, regression with correlation between item samples on overlapping subtests, and perfectly parallel overlapping or nonoverlapping item samples. The second method is suggested to be more robust than the other two and is, therefore, recommended.