Bartlett Sphericity Statistic Calculator
Bartlett sphericity chi²approximation−(n−1−(2p+5)/6) ln(detR), dfp(p−1)/2external; valid correlation determinant0<d≤1and positive correction. No automatic pvalue. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
Bartlett's sphericity approximation uses sample size, variable count and a correlation determinant.
Bartlett's sphericity approximation uses sample size, variable count and a correlation determinant.1
The determinant and asymptotic correction must meet the formula's branch conditions. The calculation and input requirements are explained below.
When to use Bartlett Sphericity Statistic Calculator
Enter integer sample size and variable count 1–1000000, with at least two variables, determinant greater than zero and at most one, and positive n-1-(2p+5)/6.
How to use Bartlett Sphericity Statistic 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 Bartlett Sphericity Statistic 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 |
|---|---|---|---|
| actualCompleteSampleSize | Actual Complete Sample Size. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
| actualVariableCount | Actual Variable Count. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
| actualCorrelationMatrixDeterminant | Actual Correlation Matrix Determinant. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
Enter integer sample size and variable count 1–1000000, with at least two variables, determinant greater than zero and at most one, and positive n-1-(2p+5)/6. Return the asymptotic chi-square statistic. The tool does not calculate the determinant, df or p-value.
chiSquared=-(n-1-(2*p+5)/6)*ln(detR) 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": {
"actualCompleteSampleSize": 100,
"actualVariableCount": 3,
"actualCorrelationMatrixDeterminant": 0.5
},
"output": {
"result": {
"value": 67.35080104440802
}
}
}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 SRMR Fit Band Lookup for a complementary operation: SRMR summarizes standardized residual discrepancies in a fitted model.
Use RMSEA Cutoff Band Lookup for a complementary operation: RMSEA interpretation depends on fitted-model and sampling context.
References
-
Bartlett Sphericity Statistic Calculator — tool.io
Similar or alternative tools
- SRMR Fit Band Lookup
SRMR summarizes standardized residual discrepancies in a fitted model.
- RMSEA Cutoff Band Lookup
RMSEA interpretation depends on fitted-model and sampling context.