KaiserMeyerOlkin

Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is a statistic that indicates the suitability of data for factor analysis. Named for Henry F. Kaiser and extended by Meyer and Olkin, the KMO evaluates whether the partial correlations among variables are small enough to produce reliable factors. In addition to the global measure, there are also individual measures of sampling adequacy (MSA) for each variable, which help determine if a specific variable should be retained in a factor analysis.

The KMO statistic is derived from the correlation matrix by comparing the magnitudes of observed correlations to the magnitudes of partial correlations. The global KMO is calculated as the sum of squared correlations divided by the sum of squared correlations plus the sum of squared partial correlations. Each variable’s MSA is computed in a similar way, using only its relationships with other variables. Values for both global KMO and MSA fall between 0 and 1; higher values indicate that the data are more suitable for factor analysis.

Common interpretation guidelines suggest: values around 0.9 or higher are superb, 0.8–0.9 meritorious, 0.7–0.8 middling, 0.6–0.7 mediocre, and below 0.6 unacceptable. KMO is typically reported alongside Bartlett’s test of sphericity, which assesses whether the correlation matrix differs from an identity matrix. While helpful, KMO is only an indicator of sampling adequacy and is influenced by sample size and data structure; it does not guarantee successful factor extraction. Software such as SPSS, R, and SAS can compute KMO and MSA values.