  # Kaiser-Meyer-Olkin (KMO) Test for Sampling Adequacy

Factor Analysis > Kaiser-Meyer-Olkin (KMO) Test

## What is the Kaiser-Meyer-Olkin (KMO) Test?

Kaiser-Meyer-Olkin (KMO) Test is a measure of how suited your data is for Factor Analysis. The test measures sampling adequacy for each variable in the model and for the complete model. The statistic is a measure of the proportion of variance among variables that might be common variance. The lower the proportion, the more suited your data is to Factor Analysis.

KMO returns values between 0 and 1. A rule of thumb for interpreting the statistic:

• KMO values between 0.8 and 1 indicate the sampling is adequate.
• KMO values less than 0.6 indicate the sampling is not adequate and that remedial action should be taken. Some authors put this value at 0.5, so use your own judgment for values between 0.5 and 0.6.
• KMO Values close to zero means that there are large partial correlations compared to the sum of correlations. In other words, there are widespread correlations which are a large problem for factor analysis.

For reference, Kaiser put the following values on the results:

• 0.00 to 0.49 unacceptable.
• 0.50 to 0.59 miserable.
• 0.60 to 0.69 mediocre.
• 0.70 to 0.79 middling.
• 0.80 to 0.89 meritorious.
• 0.90 to 1.00 marvelous.

## Running the Kaiser-Meyer-Olkin (KMO) Test

The formula for the KMO test is: where:
R = [rij] is the correlation matrix and
U = [uij] is the partial covariance matrix.

This test is not usually calculated by hand, because of the complexity.

Reference:
Cerny, C.A., & Kaiser, H.F. (1977). A study of a measure of sampling adequacy for factor-analytic correlation matrices. Multivariate Behavioral Research, 12(1), 43-47.
Kaiser, H. 1974. An index of factor simplicity. Psychometrika 39: 31–36.

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