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The Estimation of Mean Achievement Scores for Schools by the Item-Sampling Technique

Cahen, Leonard S.; Romberg, Thomas A.; Zwirner, Walter
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Achievement Tests, Cooperative Arithmetic Test, Longitudinal Studies, Mathematics Tests, Prediction, Sampling


An application of the item-sampling technique is described. The technique was used by the National Longitudinal Study of Mathematical Abilities (NLSMA) to estimate school means on mathematics achievement tests. The study reports a comparison of school means on Forms A and B of the Cooperative Arithmetic Test. The mean for each school on Form A was estimated by conventional procedures where each student tested in the school took all of the 50 items on the form. The mean on the other form was estimated by the item- sampling technique where each student took a randomly selected set of five items from the complete set of 50 items. Means obtained by the item-sampling administration were systematically greater than the means obtained by the conventional administration. Hypotheses are formulated to account for the bias favoring the item-sampling administration. The data from the study indicated that the relative order of school means was preserved by the item-sampling administration and the precision of estimating school means by item sampling is monotonically related to the number of students tested in the sampling units (schools).

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