This article presents a simple, computer-assisted method of determining the extent to which increases in reliability increase the power of the "F" test of equality of means. The method uses a derived formula that relates the changes in the reliability coefficient to changes in the noncentrality of the relevant "F" distribution. A readily available…

The primary purpose of this study is to investigate the mathematical characteristics of the test reliability coefficient rho[subscript XX'] as a function of item response theory (IRT) parameters and present the lower and upper bounds of the coefficient. Another purpose is to examine relative performances of the IRT reliability statistics and two…

Develops a statistical test for the hypothesis that alpha'(1) =alpha'(2) when alpha'(1) is the Spearman-Brown extrapolated value of Cronbach's alpha reliability for test 1 and alpha'(2) is the unadjusted coefficient for test 2. The test is shown to exercise tight control of Type I error. (Author/SLD)

It is recognized that the typical difference score used by educators is likely to be relatively weak in reliability. Formulas are developed for estimating changes in the reliability of X-Y under the assumption of equal or unequal variances before and after reliabilities are modified. (SLD)

Developed a statistical test for the hypothesis of the equality of extrapolated coefficients when the original values (Cronbach's alpha) are based on the same sample of persons and, therefore, are statistically dependent. Monte Carlo studies show that the test precisely controlled Type I error, even with small numbers of parttest units or raters.…

Two new reliability coefficients have been derived for situations in which a test must be divided into parts of unequal length. This report summarizes a study of the statistical bias and the standard errors of these coefficients and compares them to Guttman's lambda coefficients and Cronbach's alpha coefficient. (Author/JKS)

Developed a graphical method of determining adequate sample size based on the power of L. Feldt's (1969) test of the difference between two values of Cronbach's alpha coefficient. Discusses assumptions on which this approach is based. (SLD)

Developed an approximate statistical test for the hypothesis of equality between the Spearman-Brown extrapolations of two independent values of Cronbach's alpha reliability coefficient. Monte Carlo simulations demonstrate that the procedure effectively controls Type I error. (SLD)

Develops formulas to cope with the situation in which the reliability of test scores must be approximated even though no examinee has taken the complete instrument. Develops different estimators for part tests that are judged to be classically parallel, tau-equivalent, or congeneric. Proposes standards for differentiating among these three models.…

Evaluating a test's reliability often requires dividing it into 3 or more unequal parts, which causes violation of the tau equivalence assumption of Cronbach's alpha. This article presents a criterion for abandoning alpha and an approach for computing a more appropriate estimate of reliability, the Gilmer-Feldt coefficient. (Author)

Sampling theory for the intraclass reliability coefficient, a Spearman-Brown extrapolation of alpha to a single measurement for each examinee, is less recognized and less cited than that of coefficient alpha. Techniques for constructing confidence intervals and testing hypotheses for the intraclass coefficient are presented. (SLD)

Seven approaches to averaging reliability coefficients are presented. Each approach starts with a unique definition of the concept of "average," and no approach is more correct than the others. Six of the approaches are applicable to internal consistency coefficients. The seventh approach is specific to alternate-forms coefficients. Although the…

In some situations where reliability must be estimated it is impossible to divide the measuring instrument into more than two separately scoreable parts. In such a case, neither Cronbach's coefficient alpha nor Kristof's three-part approach are satisfactory. A technique is developed for estimating reliability in such situations. (Author/BJG)

An approximate statistical test of the equality of two intraclass reliability coefficients based on the same sample of people is derived. Such a test is needed when a researcher wishes to compare the reliability of two measurement procedures, and both procedures can be applied to results from the same group. (SLD)

Rigorous comparison of the reliability coefficients of several tests or measurement procedures requires a sampling theory for the coefficients. This paper summarizes the important aspects of the sampling theory for Cronbach's (1951) coefficient alpha--a widely used internal consistency coefficient. This theory enables researchers to test a…