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Test Norms and Sampling Theory

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Norms, Sampling, Statistical Bias, Statistics, Test Norms


Three different ways of drawing two-stage samples are described. In each case, the question of the choice of the sample statistic to be used for estimating the mean score in the norms population is discussed, with particular reference to the bias and sampling error of each estimate. Standard error formulas are derived for three of these estimates. Some numerical examples are given showing the economies achieved by using two-stage sampling instead of simple cluster sampling. A simple method is given by means of which the same formulas can be used to provide standard errors for each percentile rank in the norms table as well as for the mean of the norms distribution. A numerical example indicates that the advantage of two-stage sampling over cluster sampling holds for estimating percentile ranks as well as for estimating the arithmetic mean. Methods of obtaining school-mean norms from two-stage-sampling data are briefly discussed.

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