# Psychometrics 101: How do I know if an assessment is reliable? (Part 3)

Posted by Greg Pope

Following up from my posts last week on reliability I thought I would finish up on this theme by explaining the internal consistency reliability measure: Cronbach’s Alpha.

Cronbach’s Alpha produces the same results as the Kuder-Richardson Formula 20 (KR-20) internal consistency reliability for dichotomously scored questions (right/wrong, 1/0), but Cronbach’s Alpha also allows for the analysis of polytomously scored questions (partial credit, 0 to 5). This is why Questionmark products (e.g., Test Analysis Report, RMS) use Cronbach’s Alpha rather than KR-20.

People sometimes ask me about KR-21. This is a quick and dirty reliability estimate formula that almost always produces lower values than KR-20. KR-21 assumes that all questions have equal difficulty (p-value) to make hand calculations easier. This assumption of all questions having the same difficulty is usually not very close to reality where questions on an assessment generally have a range of difficulty. This is why few people in the industry use KR-21 over KR-20 or Cronbach’s Alpha.

My colleagues and I generally recommend that Cronbach’s Alpha values of 0.90 or greater are excellent and acceptable for high-stakes tests, while values of 0.7 to 0.90 are considered to be acceptable/good and appropriate for medium-stakes tests. Generally values below 0.5 are considered unacceptable. With this said, in low stakes testing situations it may not be possible to obtain high internal consistency reliability coefficient values. In this context one might be better off evaluating the performance of an assessment on an item-by-item basis rather than focusing on the overall assessment reliability value.

These are good estimates for norm-referenced tests, but if you have a criterion-referenced test for example, and all succeed–a nice outcome for most trainers–your alpha and KR-20s will go to zero as there would be no variance in the equation and that means dividing by zero–which you can’t do. Thus a good CRT might have a bad alpha–there are more accurate ways of establishing reliability–especially if you have a high stakes test.

Thanks for making this important point Bill. As you and Sharon detail in Chapter 14 of your 3rd edition book (“Criterion-References Test Development”) there are a number of techniques that can be used in CRT situations where you don’t have the variance needed to produce internal consistency reliability coefficients like Cronbach’s Alpha. I suggest people interested in these techniques give this chapter a read as it provides a great review of reliability methods in contexts like you described.

Not sure if you can help but here goes,i am having a problem matching my instrment to a set of objectives. I have looked at bloom’s and i am still a bit lost can you offer any advice.

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