Statistics How To

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:
Kaiser-Meyer-Olkin


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.

  • In SPSS: Run Factor Analysis (Analyze>Dimension Reduction>Factor) and check the box for”KMO and Bartlett’s test of sphericity.” If you want the MSA (measure of sampling adequacy) for individual variables, check the “anti-image” box. An anti-image box will show with the MSAs listed in the diagonals.
    measures-of-sampling-adequacy

    The test can also be run by specifying KMO in the Factor Analysis command. The KMO statistic is found in the “KMO and Bartlett’s Test” table of the Factor output.
  • In R: use the command KMO(r), where r is the correlation matrix you want to analyze. Find more details about the command in R on the Personality-Project website.
  • In Stata, use the postestimation command estat kmo.

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.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

Comments are now closed for this post. Need help or want to post a correction? Please post a comment on our Facebook page and I'll do my best to help!
Kaiser-Meyer-Olkin (KMO) Test for Sampling Adequacy was last modified: October 15th, 2017 by Andale

13 thoughts on “Kaiser-Meyer-Olkin (KMO) Test for Sampling Adequacy

  1. Muluken

    KMO is the measure of sampling adequacy, so can I interpret the KMO index as the ratio of variables to respondents?

  2. Zena

    Hello,
    I have realized that KMO of two-item scales is always 0.5. Can we consider this acceptable? If so, I would appreciate sharing a reference that could be cited in support of accepting a KMO of 0.5 for two-item scales.
    Thank you

  3. Andale Post author

    I would be surprised if there was anything out there that showed 0.5 as acceptable. 0.5 is a poor candidate for factor analysis, two-item scale or not (it’s theoretically possible for a two-item scale to have a KMO of 1).

  4. Joeri

    What if your kmo is exactly 0.5 for a two-item scale?
    Although my kmo is 0.5, Bartlett’s test of Sphericity is 0.000, so significant.
    I have high communalities and also the scree plot etc. telling me to use only 1 component.

    Can i go directly to a reliability analysis to check if using 1 component/factor is valid?

  5. Allan

    I have failed to get KMO and the factor analysis for this data. Can some one help please?
    2 1 4 1 1
    1 2 1 3 4
    3 6 12 2 2
    6 4 2 4 4
    4 16 2 5 8
    7 5 6 6 12
    9 3 6 11 4
    7 8 10 8 11
    5 11 20 14 3
    13 12 15 11 7
    10 13 6 10 10
    11 10 6 13 9
    12 9 12 9 19
    18 7 16 7 14
    14 15 19 17 19
    16 14 14 19 18
    19 18 18 15 16
    17 16 23 23 16
    19 21 5 20 13
    15 26 26 18 14
    21 22 16 24 24
    23 19 11 25 25
    24 23 21 20 21
    22 25 27 26 22
    25 20 22 26 27
    26 24 23 22 29
    28 28 28 29 22
    27 27 25 28 29
    29 30 29 27 26
    30 29 30 30 28

  6. Andale Post author

    Sure. But it’s not the easiest choice. Check out Yu et al’s paper for an overview. If you could, I would consider other alternatives, depending on what you want to get out of your data. For only 30 items, I would think it’s probably easier to try anything but factor analysis.

  7. Andale Post author

    What do you mean that you failed?
    If you’re saying the KMO failed to recommend factor analysis, then that’s a pretty good indication you shouldn’t do it.