Predictions of Reliability Coefficients and Standard Errors of Measurement Using the Test Information Function and Its Modifications

There seems to be a concensus that two main measures in classical mental test theory are the reliability and validity coefficients of a test. Although these measures have widely been accepted by psychologists and test users in the past decades, they are actually the attributes of a specified group of examinees as well as of a given test, since the correlation coefficient is used in either case. In addition, representation of these measures by single numbers results in over-simplification and the lack of useful information for both theorists and actual users of tests. The same applies for the standard error of measurement also. In latent trait models, the item and test information functions provide us with abundant information about the local accuracy of estimation, a concept which is totally missing in classical mental test theory. These functions do not depend upon any specific group of examinees as the reliability coefficient does, or we can say that they are population-free. By virtue of this characteristic, adding further information about the MLE bias function of the test and the ability distribution of the examinee group, we can provide the tailored reliability coefficient and standard error of measurement in the classical mental test theorys sense for each and every specified group of examinees who have taken the same test.