KR-20 calculator (Kuder-Richardson)
Reliability of a test scored as correct or incorrect.
Calculator inputs
Results
Enter your values and press “Calculate” to see the result.
In short
- What it calculates
- Reliability of a test scored as correct or incorrect.
- Formula used
KR-20 = (k / (k − 1)) × (1 − Σ p·q / s²ₜ)- Example
- Matrix of 5 respondents and 4 dichotomous items:
KR-20 calculator
KR-20 is the equivalent of Cronbach's alpha for tests where each item is scored right or wrong.
It is the standard reliability figure for multiple choice exams and knowledge tests.
How it works
For each item the proportion of correct answers p and its complement q are computed. The sum of the p·q products is compared with the variance of total scores.
Formula
KR-20 = (k / (k − 1)) × (1 − Σ p·q / s²ₜ)
p = proportion answering the item correctly
q = 1 − p
s²ₜ = variance of total scores
Worked example
Matrix of 5 respondents and 4 dichotomous items:
Σ p·q = 0.96
s²ₜ = 1.7
KR-20 = 0.58 → questionable reliability, the items need review
Explanation
It is Cronbach's alpha for dichotomous responses
When each item allows only right or wrong, KR-20 and Cronbach's alpha give exactly the same result: the former is a special case of the latter. That is why KR-20 is used for multiple choice exams marked correct or incorrect, and alpha for Likert-type scales with several response levels.
It depends on the number of items
Adding questions raises the coefficient even without improving the instrument. A fifty-item mediocre questionnaire can exceed 0.90 while an excellent ten-item one sits at 0.70. The value should therefore always be read alongside the number of questions.
A low value has several causes
It may indicate the test measures several different things at once, that items are ambiguous or badly worded, or that the sample is too homogeneous. If all candidates are at a similar level, variance falls and the coefficient collapses without the exam being poor.
Reliability is not validity
An instrument can be highly consistent while measuring something other than intended. KR-20 says the questions behave coherently with each other, not that they assess what the exam title claims.
Frequently asked questions
How does it differ from Cronbach’s alpha?
KR-20 is a special case of alpha for dichotomous items. With 0/1 data both give exactly the same result.
What if the value is low?
Look at items that almost everyone gets right or wrong: they carry little information and usually drag reliability down.
What is the difference from Cronbach's alpha?
None in result when items are dichotomous: KR-20 is a special case of alpha for right or wrong responses.
What if the coefficient comes out low?
Check whether the test measures several dimensions, whether items are ambiguous, or whether the sample is so homogeneous it generates too little variance.
Need to calculate something else?
These tools are often used alongside this calculator.
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Aiken’s V
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Precision and recall
Classification metrics from a confusion matrix.
Chi-square
Chi-square test for contingency tables and goodness of fit, with Cramér’s V, residuals, Yates’ correction…
Sample size
How many responses you need to estimate a percentage or a mean, with finite population, design effect and…
Pearson correlation
Pearson’s r between two variables, with p value, confidence interval, regression line and scatter plot.