KMO Sampling Adequacy Calculator

KMO observed matched unordered off diagonal correlation squares versus partial correlation squares. Matrices/partial correlation estimation independently performed; not infer sample adequacy solely by universal cutoff. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.

Description

KMO compares squared correlations with squared partial correlations.

KMO compares squared correlations with squared partial correlations.^[1]

The matched pair inventory and prior matrix calculations determine its scope. The calculation and input requirements are explained below.

When to use KMO Sampling Adequacy Calculator

Enter nonempty aligned nonnegative squared-correlation and squared-partial-correlation lists with positive combined sum.

How to use KMO Sampling Adequacy 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 KMO Sampling Adequacy 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
actualOffDiagonalCorrelationSquares	Actual Off Diagonal Correlation Squares. Use the units and matching context stated in the calculation below.	array of number	Required; other constraints below
actualOffDiagonalPartialCorrelationSquares	Actual Off Diagonal Partial Correlation Squares. Use the units and matching context stated in the calculation below.	array of number	Required; other constraints below

Enter nonempty aligned nonnegative squared-correlation and squared-partial-correlation lists with positive combined sum. Return correlation-square sum divided by combined sum. These fields are not capped at one by the implementation; independently verify that they actually represent the stated squares.

KMO=sum(correlationSquares)/(sum(correlationSquares)+sum(partialCorrelationSquares))

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

json

{
  "input": {
    "actualOffDiagonalCorrelationSquares": [
      0.4,
      0.4
    ],
    "actualOffDiagonalPartialCorrelationSquares": [
      0.1,
      0.1
    ]
  },
  "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 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

KMO Sampling Adequacy 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.