McDonald's Omega Total Reliability
Restricted unidimensional McDonaldomegatotal(sum loadings)²/[(sum loadings)²+Σresidual], unit factor variance and uncorrelatedresiduals. Not hierarchical omega, multi factor fit or norm. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
Unidimensional omega total compares common-factor variance with total variance.
Unidimensional omega total compares common-factor variance with total variance.1
This restricted form assumes unit factor variance and uncorrelated item residuals. The calculation and input requirements are explained below.
When to use McDonald's Omega Total Reliability
Enter nonempty aligned finite factor loadings and nonnegative residual variances.
How to use McDonald's Omega Total Reliability 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 McDonald's Omega Total Reliability.
- 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 |
|---|---|---|---|
| actualGeneralFactorLoadings | Actual General Factor Loadings. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
| actualUncorrelatedResidualVariances | Actual Uncorrelated Residual Variances. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
Enter nonempty aligned finite factor loadings and nonnegative residual variances. Require the squared loading sum plus residual sum positive. Divide squared loading sum by that total under unit factor variance and uncorrelated residuals.
omegaTotal=(sum(loadings))^2/((sum(loadings))^2+sum(residualVariances)) 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.value | Numeric result under the formula and output units explained above. | number |
{
"input": {
"actualGeneralFactorLoadings": [
1,
1
],
"actualUncorrelatedResidualVariances": [
0.5,
0.5
]
},
"output": {
"result": {
"value": 0.8
}
}
}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
-
McDonald's Omega Total Reliability — 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.