Sampling Fluctuations Resulting from the Sampling of Test Items

Sampling fluctuations resulting from the sampling of test items rather than of examinees are discussed. It is shown that the Kuder-Richardson reliability coefficients actually are measures of this type of sampling fluctuation. Formulas for certain standard errors are derived; in particular, a simple formula is given for the standard error of measurement of an individual examinee's score. A common misapplication of the Wilks-Votaw criterion for parallel tests is pointed out. It is shown that the Kuder-Richardson formula-21 reliability coefficient should be used instead of the formula-20 coefficient in certain common practical situations.