INDAL: A Computer Program for Comparing Multiple Independent Coefficient Alphas

There are times when one might want to compare the coefficient alphas of three or more tests measuring the same construct. The computer program, INDAL, is introduced which compares multiple coefficient alphas using the omnibus Fisher-Bonett approach followed by subsequent pairwise comparisons using F tests


Review Article
Suppose an industrial psychologist, striving to be economically practical, compared the coefficient alphas of three tests measuring the same construct given varying numbers of items. Second, suppose a test is translated into several languages. In this case, some items may be eliminated or modified based upon incomparable meanings across languages. Finally, suppose different types of participants (e.g., different classes of high school students) complete a particular test (e.g., self-esteem). In all three cases, a test of multiple independent coefficient alphas might be of interest.
Comparing multiple independent coefficient alphas has been addressed by Feldt et al. [1] among others. Kim and Feldt [2] simulated the Hakstian and Whalen TE [3] and the Fisher-Bonett statistics, which they modified from Bonett [4] to test the difference among more than two coefficient alphas, and found that both were similar in terms of Type I error, power, and their robustness to heteroscedasticity. Moreover, Feldt et al. [1] and Charter [5] explained that subsequent F tests could be used to compare pairwise alphas. However, because these comparisons are not independent, a Bonferroni correction would be appropriate. Therefore, the purpose of the program was to compute the Fisher-Bonett statistic and subsequent F tests for comparing multiple independent coefficient alphas.

Description
The user is queried interactively for the number of coefficient alphas, the magnitude of each, sample size, and number of items. The output consists of a restatement of the input, the Fisher-Bonett value, its degrees of freedom, and probability using the algorithm by Dunlap and Duffy [6]. Next, the user provides the number of subsequent pairwise F tests and is queried for the two coefficient alphas and sample sizes. The program responds with the values of the coefficient alphas, the degrees of freedom, F ratio, and probability for each subsequent comparison as explained by Charter and Feldt [7]. Moreover, the Bonferroni correction is provided at the .05 and .01 levels for comparing probability levels. The program is written in FORTRAN 90 and runs on an IBM-PC or compatible. The output is contained in INDAL.OUT.

Example
The Eating Attitudes Test [8] has gone through a couple of iterations. Initially, the scale consisted of 40 items (EAT40). However, a few years later, a shorter 26-item scale was developed [9]. Garner et al. [9] provided the coefficient alphas for EAT26 and EAT40 for both anorexia nervosa and female comparison participants. Because one is comparing independent coefficient alphas, only the EAT26 data will be used. Likewise, in a separate study, Lane et al. [10] computed the coefficient alpha of the EAT26 with athletes. Finally, Mukai et al. [11] developed the Japanese version of the EAT26 and administered it to Japanese females along with the English version of the scale to American females [11]. The coefficient alphas and sample sizes for these studies are presented in Table 1.

Psychology and Behavioral Science International Journal
As shown in the output from Table 2, the Fisher-Bonett statistic (which distributes out as a chi-square on k-1 df) was 45.91 with a p<.0001 indicating that there was a statistically significant difference among the coefficient alphas. Suppose one is subsequently interested in determining if there was a statistically significant difference between the coefficient alphas of athletes and anorexia nervosa participants on the EAT26. Moreover, suppose a second question concerned testing the difference between the coefficient alphas of the Japanese and American females in the Mukai et al.
[12] study. A third comparison examined the difference between the coefficient alphas of the anorexia nervosa and female comparison groups of the Garner et al. [9] study. Because these are non-independent comparisons, a Bonferroni approach would be more viable. As indicated from the output, there was a significantly higher coefficient alpha on the EAT26 for anorexia nervosa participants than for athletes and the female comparison group, ps <.01. However, there was no statistically significantly significant difference between coefficient alphas on the EAT26 for the American and Japanese females, p >.05.