Problems in Mental Test Theory Arising from Errors of Measurement

Several unsolved basic problems of mental test theory, arising from the presence of errors of measurement in the test scores, are discussed. The inadequacies of the classical model, with its normally and independently distributed errors, are pointed out. Two newer stochastic models, available for dealing with these problems, are described. It is observed that the proportion of test questions answered correctly by the examinee is by itself usually not a satisfactory estimate of the corresponding population proportion. Methods for estimating such population proportions are considered. Such methods are required in order (i) to determine whether or not two tests measure the same dimension, (ii) to measure changes in the characteristics of the examinees.