Reliability Tests
KR-20 Calculator
KR-20 Calculator calculate reliability for dichotomous items.
Reliability Tests
KR-20 Calculator
Calculate reliability for dichotomous items.
Formula
KR-20 = k/(k-1) * (1 - sum p*q / population variance of total scores). Using population variance consistently makes KR-20 exactly equal to raw Cronbach alpha for dichotomous 0/1 items.
About the KR-20 Calculator
Calculate reliability for dichotomous items. Reliability calculators quantify internal consistency, dichotomous-item consistency, split-half agreement, item-rest association, or congeneric construct reliability.
How the KR-20 Calculator Works
KR-20 = k/(k-1) * (1 - sum p*q / population variance of total scores). Using population variance consistently makes KR-20 exactly equal to raw Cronbach alpha for dichotomous 0/1 items.
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Dichotomous item matrix (0/1) (required)
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
methodrespondentsitemsitem_proportionsitem_q_valuessum_pqtotal_score_variancekr20decision
KR-20 Calculator Example
Use the example data button to load a known sample, then calculate and review the statistic, p-value or estimate, and interpretation.
| Input | Example value |
|---|---|
| Dichotomous item matrix (0/1) | 0,1,1,1,1
0,1,1,0,1
0,1,1,0,0
0,0,0,0,0
1,1,0,1,1
0,0,0,0,0
0,0,1,0,0
0,1,0,0,0 |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
A high coefficient does not prove unidimensionality, validity, good item wording, or freedom from redundant items.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the KR-20 Calculator calculate?
Calculate reliability for dichotomous items.
Which formula does the KR-20 Calculator use?
KR-20 = k/(k-1) * (1 - sum p*q / population variance of total scores). Using population variance consistently makes KR-20 exactly equal to raw Cronbach alpha for dichotomous 0/1 items.
What input does this calculator need?
The calculator form shows the required values and validates them before calculating.
Are the formulas visible?
Yes. Each calculator displays its method, assumptions, and interpretation unless disabled by the site administrator.