Kuder-Richardson Formulas: A Brief Overview
The Kuder-Richardson (KR) formulas are a set of statistical formulas used for the calculation of internal consistency reliability. Developed in 1937 by George Kuder and Mary Richardson, the KR formulas are widely used in psychological research and are an important part of the field of psychometrics (Vacha-Haase & Mertens, 2010).
The KR formulas consist of three different formulas: KR-20, KR-21, and KR-21. The KR-20 formula is used for the calculation of the internal consistency of a test that includes multiple items of a single-dimension. On the other hand, the KR-21 and KR-21 formulas are used to measure the internal consistency of a test that includes multiple items of multiple dimensions (Vacha-Haase & Mertens, 2010). All of these formulas have been empirically tested and found to be reliable in measuring the internal consistency of a test (Vacha-Haase & Mertens, 2010).
The KR formulas are relatively easy to use, with the KR-20 being the most straightforward. In the case of the KR-20 formula, the equation used is:
KR-20 = 1 – (e/(e + N)),
where e is the sum of the item variances, and N is the number of items in the test (Vacha-Haase & Mertens, 2010). The KR-21 and KR-21 formulas are more complex, and require the calculation of multiple item variances and the sum of those item variances (Vacha-Haase & Mertens, 2010).
In conclusion, the Kuder-Richardson formulas are a set of statistical formulas used to measure the internal consistency of a test. They are widely used in psychological research, and have been empirically tested and found to be reliable. The KR-20 formula is the simplest of the three formulas, while the KR-21 and KR-21 formulas are more complex and require the calculation of multiple item variances.
References
Vacha-Haase, T., & Mertens, D. M. (2010). Kuder-Richardson Reliability Coefficients. In J. C. Norcross (Ed.), Psychometrics and Psychological Assessment (pp. 215-218). Oxford, UK: Wiley.