The Theoretical and Empirical Equivalence of Cronbach Alpha and Kuder-Richardson Formular-20 Reliability Coefficients

Abstract

Reliability as one the psychometric properties of a research and measurement instrument is very desirable in research, under the classical test theory(CTT). One group of such reliability measures is that of internal consistency of a scale. Cronbach Alpha and KuderRichardson formula 20 are measures of internal consistencies. In many texts, authorities specify that Kuder-Richardson formula 20 should be applied when test items are dichotomously scored while Cronbach Alpha should be applied when test items are not scored dichotomously. These guide lines are religiously adhered to by both researchers and measurement practitioners. Both reliability estimates are recognized as valid measures of internal constituency. In research, an informed choice has to be made about which one to apply, particularly, when only one of them has to be applied. These guidelines are seen as conditions that validate the use of each of them. These specifications are erroneously interpreted. A score is a score whether dichotomous or not. This paper examined both the theoretical and empirical equivalence of these two estimates, for tests of the same length and for varying test lengths. To demonstrate the empirical equivalence of Cronbach Alpha and KR-20, 65 biology achievement tests of the same length (40 items), were administered on 65 samples of senior secondary two students, consisting of 60 students selected from 36 public secondary schools, in Calabar Education zone of Cross River State, Nigeria. Both the Cronbach Alpha and KR-20 were estimated for each test and for the 65 samples. Another test of 100 items adapted from the 2018 and 2019 WAEC-SSCE English Language objective test, was administered on a sample of 300 students. Both reliability measures were estimated for varied lengths of the test, by randomly removing five(5)items at a time. This resulted in 19 sub-tests. The resulting reliability coefficients were compared using the related sample t-test while repeated measures ANOVA was used to compare the reliability coefficients under the influence test length, measured in terms of number of items. The results showed that there is significant difference between Cronbach Alpha and KR-20(t=4.022, p=.000). The correlation between KR-20 and Cronbach alpha is positive and highly significant(r=.944& .999, p=.000). Test length has significant influence on the difference between KR-20 and Cronbach alpha reliability estimates (F=1372.074, p=.000). The implications of these results for tests developers and users are discussed.