KR-20 Test Reliability Calculator
Estimate the internal-consistency reliability of a dichotomous test with the Kuder–Richardson KR-20 formula.
How it works
KR-20 = [k ÷ (k − 1)] × [1 − (Σ p·q) ÷ σ²]
KR-20 measures how consistently the items on a test with right/wrong (dichotomous) scoring measure the same underlying trait. It compares the sum of the individual item variances (Σp·q, where p is the fraction answering correctly) against the variance of the total scores: the more the total-score variance exceeds the item variances, the more the items agree, and the higher the coefficient. Values run up to 1.0; 0.70 is a common minimum for classroom tests and 0.80–0.90 is expected of high-stakes exams. KR-20 is the special case of Cronbach’s alpha for binary items.
Worked example
For a 20-item test with total-score variance 25 and Σp·q = 4: KR-20 = (20 ÷ 19) × (1 − 4 ÷ 25) = 1.0526 × 0.84 = 0.884 — good reliability.
Frequently asked questions
What is a good KR-20 value?
As a rule of thumb, 0.70 is acceptable for a classroom quiz, 0.80 is good, and 0.90+ is expected for standardized or high-stakes tests. Below 0.50 the test is not measuring consistently.
How is KR-20 different from Cronbach’s alpha?
They are the same idea. KR-20 is the version used when every item is scored right or wrong (0/1). Cronbach’s alpha generalizes it to items with more than two possible scores, such as rating scales.
What is Σp·q?
For each item, p is the proportion of test-takers who got it right and q = 1 − p; p·q is that item’s variance. Summing p·q over all items gives the total item variance the formula needs.
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This calculator is for educational purposes. Double-check important results before acting on them.