Item analysis with small samples

Abstract

Traditional item analysis centers on the characteristics of individual items, typically on the item’s level of difficulty and discrimination power. In constructing new tests, attempts are therefore made to obtain large samples of subjects in order to decrease the standard error of measurement of the item’s characteristics. However, there are common test situations in which the exact parameters of individual items are not of much importance. Rather, the focus of interest is on the position of the items in relation to one another or in relation to some critical statistical value. Five such test situations are described. Quasi-simulations of item analyses were performed to determine the optimal sample sizes required in such test situations. These simulations consisted of analyzing responses of 5,200 university applicants, each of whom completed three different multiple-choice tests. Sample sizes of 16, 32, 64, 128, 256, 512, and 1,024 were chosen; and for each size, eight samples were randomly drawn from the population of applicants. For three of five different indices of accuracy that were employed, the results showed that the sample size needed for the pretest stage in test construction is considerably smaller than the traditionally recommended size.