A new formula, expressing relative efficiency solely in terms of the standard errors of measurement and the frequency of distributions of true scores, is developed for the relative efficiency of two tests measuring the same trait. Subtests from the Scholastic Aptitude Test provide a numerical illustration. (Author/RC)

A new formula is developed for the relative efficiency of two tests measuring the same trait. The formula expresses relative efficiency solely in terms of the standard errors of measurement and, surprisingly, the frequency distributions of true scores. Approximate methods for estimating relative efficiency may make this function routinely…

The standard error of an equipercentile equating is derived for four situations. Some numerical results are checked by Monte Carlo methods. Numerical standard errors are computed for two sets of real data. Standard errors of linear and equipercentile equating are compared. (Author)

Formulas are derived for the bias in the maximum likelihood estimators (MLE) of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission. Most typically the bias of an MLE is about one-tenth of its standard error. It is very seldom more…

A possible method is developed for computing the asymptotic sampling variance-covariance matrix of joint maximum likelihood estimates in item response theory when both item parameters and abilities are unknown. For a set of artificial data, results are compared with empirical values and with the variance-covariance matrices found by the usual…

A formula is derived for the asymptotic standard error of a true-score equating by item response theory (IRT). The equating method is applicable when the two tests to be equated are administered to different groups along with an "anchor test." Numerical standard errors are shown for an actual equating 1) comparing the standard errors of…

Transformations or equating of raw test scores on two or more forms of the same test are made interchangeable by empirical procedures deriving the standard error of an equipercentile equating for four different situations. Some numerical results are checked by Monte Carlo methods. Numerical standard errors are computed for two sets of real data.…

A simple, rigorous, small-sample statistical technique is described for testing the hypothesis that two sets of measurements differ only because of errors of measurement and because of differing origins and units of measurement. (Author)

Faced with a nonstandard, complicated practical problem in statistical inference, the applied statistician sometimes must use asymptotic approximations in order to compute standard errors and confidence intervals and to test hypotheses. This usually requires that he derive formulas for one or more asymptotic sampling variances (and covariances)…

Given a loss function, an asymptotic method for optimal test design for a specified target population of examinees is presented. Also, of more practical use, given an existing unidimensional test and target population, a way is presented to find the loss function for which the test is optimal. (NSF)

Given known item parameters for a test, unbiased estimators are derived for an examinee's ability parameter, his or her proportion correct true score for the variances of these parameters and for the parallel forms reliability of the maximum likelihood estimator of the ability parameter. (Author/JKS)

A general Computer program is described that will compute asymptotic standard errors and carry out significance tests for an endless variety of (standard and) nonstandard large-sample statistical problems, without requiring the statistician to derive asymptotic standard error formulas. The program assumes that the observations have a multinormal…

Four methods are outlined for estimating or approximating from a single test administration the standard error of measurement of number-right test score at specified ability levels or cutting scores. The methods are illustrated and compared on one set of real test data. (Author)

A broad-range tailored test of verbal ability, appropriate at any level from fifth grade upwards, is briefly described. The test score places persons at all levels directly on the same score scale. (Author/RC)

If a loss function is available specifying the social cost of an error of measurement in the score on a unidimensional test, an asymptotic method, based on item response theory, is developed for optimal test design for a specified target population of examinees. Since in the real world such loss functions are not available, it is more useful to…