Reliability Tests
KR-20 Statistical Calculator
KR-20 Calculator calculate reliability for dichotomous items. Use KR-20 Calculator to validate dichotomous item matrix (0/1) and report method, respondents, items, item_proportions, item_q_values, sum_pq with method-specific calculations, diagnostics, and interpretation. Use the tabbed test workspace below for data, variables, analysis, visualizations, results, interpretation and reporting.
Quick method summary
The KR-20 Statistical Calculator calculates the named method using calculator-specific formulas and reports auditable results, warnings, and interpretation. It uses the calculator-specific formula and reports the intermediate values, final result, warnings, and interpretation.
Reliability Tests
KR-20 Calculator
Calculate reliability for dichotomous items. Use KR-20 Calculator to validate dichotomous item matrix (0/1) and report method, respondents, items, item_proportions, item_q_values, sum_pq with method-specific calculations, diagnostics, and interpretation.
Calculated result
Calculation method
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.
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.
Assumptions and limits
Items must be coded in the same direction and intended to measure the same scale or construct. Rows should represent independent respondents or targets and columns should represent the selected items or raters. A high coefficient does not establish unidimensionality, validity, or freedom from redundant items.
Formula review
Formula and independent control cases reviewed 2026-08-02; variable assumptions remain visible inputs.
KR-20 Calculator method, assumptions and reporting guideComplete selected-test explanation, assumptions, formula and reporting details
Data Import and Variable Requirements
For the KR-20 Statistical Calculator, upload item-level XLSX, CSV, or TSV data, review cleaning and coding, then select the item columns required by KR-20 Calculator. For KR-20 Calculator, map Dichotomous item matrix (0/1) from the cleaned browser-local table; every mapped variable remains editable before calculation, and the active dataset remains available while you work with this selected test and when you return to the Test Finder.
Uploaded files are processed locally in the browser. The cleaning report appears before variable selection, and the selected cleaned columns are mapped to this exact calculator rather than a generic fallback.
KR-20 Calculator Workspace Features
- Dedicated KR-20 Calculator variable mapping, calculation contract, result explanation, and diagnostics
- Manual inputs plus browser-local XLSX, CSV, or TSV analysis for this exact statistical method
- Auditable cleaning report before method-valid variable dropdowns are created
- Calculator-specific formulas, intermediate quantities, assumptions, warnings, and interpretation
- Responsive method-specific charts generated from the selected cleaned data
- Copy, result CSV, cleaned-data CSV, chart PNG, and result-only print controls
- Protected canonical URL, focused FAQs, and a dedicated selected-test workspace
About the KR-20 Calculator
Calculate reliability for dichotomous items. Use KR-20 Calculator to validate dichotomous item matrix (0/1) and report method, respondents, items, item_proportions, item_q_values, sum_pq with method-specific calculations, diagnostics, and interpretation. Reliability calculators quantify internal consistency, dichotomous-item consistency, split-half agreement, item-rest association, or congeneric construct reliability.
When to Use the KR-20 Calculator
Use the KR-20 Statistical Calculator when your research question, variable types, and sampling or experimental design require kr-20. Do not select it only because the data produce a convenient p-value or familiar output.
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 the browser. Submitted values are validated for required numeric ranges, data shape, units and method-specific restrictions before results are shown.
Assumptions and Checks
- Items must be coded in the same direction and intended to measure the same scale or construct.
- Rows should represent independent respondents or targets and columns should represent the selected items or raters.
- A high coefficient does not establish unidimensionality, validity, or freedom from redundant items.
Required Inputs
- Dichotomous item matrix (0/1) (required)
Results Reported
The result workspace shows the final answer and intermediate quantities needed to audit the calculation. Depending on the method, reported values include:
- Method
method - Respondents
respondents - Items
items - Item Proportions
item_proportions - Item Q Values
item_q_values - Sum Pq
sum_pq - Total Score Variance
total_score_variance - Kr20
kr20 - Decision
decision
KR-20 Calculator Worked 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 |
Verified Worked Result
The packaged automated fixture produces the following checked values from the example inputs. Display rounding can differ from the full-precision browser result.
| Result | Verified value |
|---|---|
| Respondents | 8 |
| Items | 5 |
| Item Proportions 0 | 0.125 |
| Item Proportions 1 | 0.625 |
| Item Proportions 2 | 0.5 |
| Item Q Values 0 | 0.875 |
| Item Q Values 1 | 0.375 |
| Item Q Values 2 | 0.5 |
| Item Pq Values 0 | 0.109375 |
| Item Pq Values 1 | 0.234375 |
| Item Pq Values 2 | 0.25 |
| Sum Pq | 1.015625 |
How to Use This Workspace
- Confirm that the method matches the quantity, hypothesis, model or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date or option format.
- Use Example Data to inspect a valid input layout, or enter your own values and run the calculation.
- Review the result table, formula, substitutions, warnings and interpretation rather than relying only on the headline number.
- Copy, download or print the result when you need a reusable analysis record.
Understanding and Reporting the Result
Review Method, Respondents, Items, Item Proportions, Item Q Values, Sum Pq, Total Score Variance, Kr20, and Decision. Use the displayed assumptions, warnings, and interpretation before reporting the result. In the KR-20 Calculator result workspace, interpret method, respondents, items, item_proportions, item_q_values, sum_pq together with the method assumptions, warning messages, confidence information, effect magnitude, and diagnostic plots shown for the selected variables.
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.
How to Report the Result
When reporting results from the KR-20 Statistical Calculator, identify the design and software, state the valid sample size and exclusions, then report Method, Respondents, Items, Item Proportions, Item Q Values, Sum Pq, Total Score Variance, Kr20. Include the selected alpha level, tail, coding, and assumption decisions when they apply. A reproducible KR-20 Calculator report should identify the mapped variables, valid observations, exclusions or missing-data handling, selected options, principal outputs, uncertainty, diagnostics, and the practical conclusion supported by the analysis.
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. Use KR-20 Calculator to validate dichotomous item matrix (0/1) and report method, respondents, items, item_proportions, item_q_values, sum_pq with method-specific calculations, diagnostics, and interpretation.
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.
When should I use the KR-20 Statistical Calculator?
Use the KR-20 Statistical Calculator when your research question, variable types, and sampling or experimental design require kr-20. Do not select it only because the data produce a convenient p-value or familiar output.
What inputs does the KR-20 Statistical Calculator require?
Upload item-level XLSX, CSV, or TSV data, review cleaning and coding, then select the item columns required by KR-20 Calculator.
What does the KR-20 Statistical Calculator report?
Review Method, Respondents, Items, Item Proportions, Item Q Values, Sum Pq, Total Score Variance, Kr20, and Decision. Use the displayed assumptions, warnings, and interpretation before reporting the result.
Can the KR-20 Statistical Calculator analyze Excel or CSV data?
Yes. The file is cleaned locally in the browser, then method-valid variable dropdowns place the selected data into this exact calculator.