A Kaiser-Meyer-Olkin (KMO) value of at least .50 is the minimum for factor analysis, and most researchers prefer .60 or higher; Kaiser (1974) described values in the .90s as marvellous, the .80s meritorious, the .70s middling, the .60s mediocre, the .50s miserable and below .50 unacceptable. Alongside KMO, Bartlett's test of sphericity should be significant (p < .05) and each item's individual measure of sampling adequacy (MSA) should be at least .50 (Field, 2018; Hair et al., 2019).
What KMO tells you
Exploratory factor analysis only makes sense if the items share common variance. KMO compares the size of the ordinary correlations between items with the size of their partial correlations, that is, what remains of each correlation after the other items are controlled for. If items cluster into factors, the partial correlations are small relative to the ordinary ones, and KMO approaches 1. If correlations are diffuse, partial correlations are large and KMO falls. In formula terms, KMO = Σr² / (Σr² + Σpartial²), summed over all item pairs.
Kaiser's (1974) labels
| KMO | Kaiser's description |
|---|---|
| .90 and above | Marvellous |
| .80 – .89 | Meritorious |
| .70 – .79 | Middling |
| .60 – .69 | Mediocre |
| .50 – .59 | Miserable |
| Below .50 | Unacceptable |
Kaiser's original paper used the American spelling "marvelous"; the labels are often quoted word for word, so keep them in quotation marks if you use them. The .50 floor is repeated in standard textbooks (Field, 2018; Hair et al., 2019), which is why many theses say "KMO should exceed .50" while others, preferring a safer margin, use .60.
Bartlett's test and item-level MSA
Bartlett's (1954) test of sphericity checks whether the correlation matrix differs from an identity matrix, one in which items are unrelated. With survey samples of a few hundred it is almost always significant, so it is a necessary but weak check. The more useful diagnostic is the diagonal of the anti-image correlation matrix, which gives each item's own MSA. Items with MSA below .50 should be considered for removal before extraction (Field, 2018).
Worked example
A student runs EFA on 16 items from 220 respondents. Summed over all item pairs, the squared correlations total 4.20 and the squared partial correlations total 0.90.
KMO = 4.20 / (4.20 + 0.90) = 4.20 / 5.10 = .82.
That is "meritorious" (Kaiser, 1974). Bartlett's test gives χ²(120) = 1,834.6, p < .001; the degrees of freedom are p(p − 1)/2 = 16 × 15 / 2 = 120. The anti-image matrix shows that 15 items have MSA between .71 and .89, but item Q9 has an MSA of .46. Q9 also has a low communality. The student removes Q9 and re-runs: KMO rises slightly and the 15 items load cleanly on four factors. The write-up would read:
The Kaiser-Meyer-Olkin measure verified sampling adequacy, KMO = .82, "meritorious" according to Kaiser (1974), and Bartlett's test of sphericity was significant, χ²(120) = 1,834.6, p < .001. Item Q9 was removed because its individual MSA (.46) fell below .50 (Field, 2018).
Note the APA formatting: no leading zero for KMO and p, because they cannot exceed 1, and a comma as the thousands separator in the chi-square value.
What to do when KMO is low
- Remove items with low MSA one at a time, starting with the lowest, and re-check.
- Check reverse-coded items. An unrecoded item correlates negatively with its neighbours and lowers sampling adequacy.
- Check sample size. KMO tends to be lower with small samples relative to the number of items.
- Question the item pool. If items come from unrelated constructs with few items each, factor analysis may not be the right method.
Run it free
The free survey data analysis tool runs EFA with KMO, Bartlett's test, item MSA, communalities and rotated loadings, and labels each value against its source. Its output is checked against the R package psych.
FAQ
Is a KMO of .55 acceptable?
It passes the .50 floor but Kaiser called it "miserable". Look at item MSA values and try to improve it before proceeding.
Does KMO depend on sample size?
Indirectly. It is computed from correlations, but small samples give noisier partial correlations, which usually lowers KMO.
Do I need KMO for CFA?
No. KMO is a pre-check for exploratory factor analysis. Confirmatory models are judged on fit indices and loadings.
Bartlett's test is significant but KMO is .48. Can I continue?
No. Bartlett's test is a weak check; a KMO below .50 means the data are not suitable for factor analysis as they stand.
References
- Bartlett, M. S. (1954). A note on the multiplying factors for various χ² approximations. Journal of the Royal Statistical Society: Series B (Methodological), 16(2), 296–298.
- Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
- Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate data analysis (8th ed.). Cengage Learning.
- Kaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36. https://doi.org/10.1007/BF02291575