Estimation of Reliability Coefficients Using the Test Information Function and Its Modifications

The reliability coefficient and the standard error of measurement in classical test theory are not properties of a specific test, but are attributed to both a specific test and a specific trait distribution. In latent trait mod els, or item response theory, the test information func tion (TIF) provides more precise local measures of accuracy in trait estimation than are available from the reliability coefficient. The reliability coefficient is still widely used, however, and is popular because of its simplicity. Thus, it is worthwhile to relate it to the TIF. In this paper, the reliability coefficient is predicted from the TIF, or two modified TIF formulas, and a spe cific trait distribution. Examples demonstrate the vari ability of the reliability coefficient across different trait distributions, and the results are compared with empiri cal reliability coefficients. Practical suggestions are given as to how to make better use of the reliability coefficient. Index terms: adaptive testing, bias, clas sical test theory, item information function, latent trait models, maximum likelihood estimation, reliability co efficieno, standard error of measurement, test informa tion function, trait estimation.