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…

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.…

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.…

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)

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)

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…

Considers the degree of bias in testlet-based alpha (internal consistency reliability) through hypothetical examples and real test data from four tests of the Iowa Tests of Basic Skills. Presents a simple formula for computing a testlet-based congeneric coefficient. (SLD)

Two relatively simple methods for estimating the condition standard error of measurement (SEM) for nonlinearly derived score scales are proposed. Applications indicate that these two procedures produce fairly consistent estimates that tend to peak near the high end of the scale and reach a minimum in the middle of the raw score scale. (SLD)

It has often been asserted that the reliability of a measure places an upper limit on its validity. This article demonstrates in theory that validity can rise when reliability declines, even when validity evidence is a correlation with an acceptable criterion. Whether empirical examples can actually be found is an open question. (SLD)

Considers the situation in which content or administrative considerations limit the way in which a test can be partitioned to estimate the internal consistency reliability of the total test score. Demonstrates that a single-valued estimate of the total score reliability is possible only if an assumption is made about the comparative size of the…

Examined the stability of the standard error of measurement and the relationship between the reliability coefficient and the variance of both true scores and error scores for 170 school districts in a state. As expected, reliability coefficients varied as a function of group variability, but the variation in split-half coefficients from school to…