Cronbach's Alpha Calculator
Raw-score Cronbach alpha from actual complete person×item matrix, sample covariance convention. Negative alpha retained; does not imply unidimensionality, validity or diagnosis.
Description
Cronbach's alpha compares summed item variances with variance of the total score.
Cronbach's alpha compares summed item variances with variance of the total score.1
It describes internal consistency under a scoring convention without proving a single construct or validity. The calculation and input requirements are explained below.
When to use Cronbach's Alpha Calculator
Enter a rectangular person-by-item matrix with at least two people and two items.
How to use Cronbach's Alpha Calculator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Cronbach's Alpha Calculator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualPersonByItemScores | Actual Person By Item Scores. Use the units and matching context stated in the calculation below. | array of array of number | Required; other constraints below |
Enter a rectangular person-by-item matrix with at least two people and two items. Compute each item sample variance and sample variance of person total scores using denominator n-1. Require positive total-score variance and apply raw-score alpha. Negative alpha is retained; zero total variance is an error.
alpha=k/(k-1)*(1-sum(itemSampleVariances)/totalScoreSampleVariance) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.cronbachAlpha | Cronbach Alpha. Interpret its unit, sign, order or availability flag as explained above. | number |
{
"input": {
"actualPersonByItemScores": [
[
0,
0
],
[
1,
1
],
[
2,
2
]
]
},
"output": {
"result": {
"cronbachAlpha": 1
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Standard Error of Measurement Calculator for a complementary operation: Classical measurement error combines score variability and applicable reliability.
Use Spearman-Brown Split-Half Reliability Calculator for a complementary operation: The Spearman–Brown equal-half correction transforms a split-half correlation.
References
-
Cronbach's Alpha Calculator — tool.io
Similar or alternative tools
- Standard Error of Measurement Calculator
Classical measurement error combines score variability and applicable reliability.
- Spearman-Brown Split-Half Reliability Calculator
The Spearman–Brown equal-half correction transforms a split-half correlation.