What Is KMO? How to Read and Handle KMO in EFA

What Is KMO

KMO, short for Kaiser-Meyer-Olkin Measure of Sampling Adequacy, indicates whether your data are suitable for exploratory factor analysis, or EFA. When you open the SPSS output, you usually find KMO in the KMO and Bartlett's Test table, directly above the Bartlett test results.

KMO does not measure questionnaire quality, replace Cronbach's Alpha, or tell you how many factors will be extracted. It assesses whether the observed variables have enough common correlation to be grouped into latent factors. In principle, KMO compares the sum of squared correlations between variables with the sum of squared correlations plus the sum of squared partial correlations. The smaller the partial correlations are compared with the observed correlations, the higher the KMO.

In quantitative research, you usually read KMO together with Bartlett's Test of Sphericity. KMO answers whether the data have enough overall association, while Bartlett's Test checks whether the correlation matrix differs from an identity matrix. Read these two rows together before moving to Total Variance Explained and the rotated matrix.

The Meaning of KMO in Quantitative Research

When you run EFA, you are checking whether the observed variables form factor groups that match the structure proposed by your theoretical model. For example, five observed variables measuring service quality should have a clear enough relationship for SPSS to treat them as expressions of a common concept. KMO helps you check this initial condition.

If KMO is low, the variables may have scattered relationships, their correlations may be too weak to extract stable factors, or the sample may not fit the number of variables. An acceptable KMO only indicates that the data are more suitable for continuing with EFA. You still need to examine Bartlett's Test, factor loading, communality, eigenvalue, the number of factors, and the theoretical content.

KMO also helps you decide whether to stop and inspect the data or continue running EFA. It is not an automatic permission to retain every variable. A dataset with a good KMO can still contain variables with low loadings, high cross-loadings, or low communality. You can read more about communality to understand how much of each variable's variance is explained by the extracted factors.

KMO is commonly used in SPSS EFA and other factor analysis procedures. If your study uses CFA, the assessment logic is different because you need to examine measurement model fit. Keep EFA separate from CFA, since the two procedures have different objectives and output tables.

What KMO Value Is Acceptable

The minimum threshold commonly used is KMO of 0.5 or above. Kaiser proposed interpretation bands ranging from barely adequate to excellent, but you should not look at one number and make a conclusion about the entire scale. The table below gives the thresholds and sources you can use when explaining the result in Chapter 4.

In many theses, KMO of 0.5 or above is treated as the minimum acceptable condition and Bartlett's Test is expected to have Sig. below 0.05. Report this together with the actual values from your output, such as KMO = 0.782 and Bartlett's Test with Sig. = 0.000. Do not write that a high KMO proves that your research model is correct, because KMO evaluates whether the data are suitable for EFA.

Some local methodology references also present KMO together with Bartlett when explaining EFA, including (Hoàng Trọng and Chu Nguyễn Mộng Ngọc, 2008). You can compare your department's or supervisor's preferred reporting style with this source and (Kaiser, 1974), while keeping the values from your own SPSS file.

How to Read KMO in the Output

After running EFA in SPSS, find the table named KMO and Bartlett's Test. This table usually has two parts. The upper part is Kaiser-Meyer-Olkin Measure of Sampling Adequacy. The lower part is Bartlett's Test of Sphericity, with the columns Approx. Chi-Square, df, and Sig.

Read the KMO Row

Take the number from the row Kaiser-Meyer-Olkin Measure of Sampling Adequacy. For example, if the value is 0.782, the data meet the minimum level because the value is above 0.5 and falls in the fair range under the interpretation of (Kaiser, 1974). Do not use the number in the Approx. Chi-Square column to conclude whether KMO is acceptable.

Read Bartlett's Test

In the Bartlett's Test of Sphericity section, focus on the Sig. column. If Sig. = 0.000 in SPSS, write p < 0.001 in your thesis because the software rounds the value to three decimal places. This result provides sufficient evidence to reject the assumption that the correlation matrix is an identity matrix under the criterion used in EFA.

Illustrative SPSS Output

The following table shows the form of SPSS output. This is illustrative output, not the result of a specific study, and you should not copy it into your thesis instead of the values in your own file.

With this illustrative table, you can conclude that the data are suitable for continuing with EFA because KMO = 0.782, which is above 0.5, and Bartlett's Test has Sig. = 0.000, which is below 0.05. You must then continue reading Total Variance Explained and Rotated Component Matrix. KMO does not tell you the final number of factors.

You can run EFA at Analyze > Dimension Reduction > Factor. Move the observed variables you want to examine into the Variables box, select Descriptives and check KMO and Bartlett's test of sphericity, then choose the extraction method and rotation that fit your research design. For an overview of the full process, see the guides to EFA and principal component analysis.

How to write this in your thesis

You can adjust the following sentence using your actual values: “The EFA results show that the KMO value was [KMO] and that Bartlett's Test of Sphericity was statistically significant, with Sig. = [Sig.]. Since KMO was [greater than or equal to 0.50] and Sig. was [less than 0.05], the data were suitable for exploratory factor analysis according to the criterion of (Kaiser, 1974).”

What to Do When KMO Is Not Acceptable

If KMO is below 0.5, do not edit the number in the output or remove a variable simply to make the table look better. Work through the checks in order, save every run, and record the reason for removing each variable. EFA rarely produces the expected structure on the first run, especially when the questionnaire contains several scales or the data come from a heterogeneous sample.

Check Variables and Data Coding

Open Variable View and Data View to check whether a variable was coded incorrectly, entered as a string instead of a number, or given a value outside the Likert scale. If a reverse-worded variable has not been reverse coded, its correlation with the other variables in the same scale may have the wrong direction and reduce the adequacy result. Create the reverse-coded variable according to the scale's coding scheme, then run Cronbach's Alpha and EFA again according to your study procedure.

Check Missing Values and Unusual Responses

Check the number of missing values, response rows with many blanks, and respondents who selected the same option for nearly every observed variable. You need a data-cleaning rule that was specified in advance or can be explained. Do not delete individual rows simply to increase KMO. If the actual sample is small compared with the number of variables, review your data collection plan and the basis for your sample size.

Examine the Correlation Matrix and Remove Variables With Evidence

If one variable has almost no correlation with the other variables, it may measure a different concept, contain confusing wording, or have been entered incorrectly. You can inspect Anti-image Matrices, Communalities, and Rotated Component Matrix to identify the variable that needs attention. Remove a variable only when statistical evidence and theory support the decision, then run the analysis again and record the result from each round.

Review Which Variables You Put Into EFA

Do not put demographic variables such as gender, age, or income into EFA together with the observed variables of a scale unless your research design provides a clear reason. You may run EFA separately for the dependent variable if it is measured with several observed variables, but follow the model and procedure required by your supervisor. The EFA design should also distinguish clearly between independent-variable and dependent-variable groups.

If you have checked the data, variables, and sample size but KMO remains below 0.5, report the limitation instead of removing variables repeatedly. Removing too many variables can strip the scale of its content, producing a better-looking SPSS result that becomes difficult to defend when the committee asks why the theoretical structure changed.

KMO, Bartlett's Test, and Communality

KMO, Bartlett's Test, and communality all appear in the EFA process, but they answer three different questions. KMO evaluates the overall adequacy of the data. Bartlett's Test examines the overall correlation matrix. Communality shows how much of each variable's variance is explained by the extracted factors.

A high KMO does not mean that every variable has a good factor loading. Conversely, a variable with low communality does not automatically prove that the entire EFA has failed. Read the indicators as a sequence: data adequacy, number of factors, explained variance, loadings, cross-loadings, and consistency with theory.

You also need to distinguish KMO from Cronbach's Alpha. Alpha evaluates the internal consistency of variables within a scale, while KMO evaluates whether a set of variables is suitable for EFA. Both measures can appear in the same thesis, but they do not replace each other.

Common Errors

The first error is concluding, “KMO = 0.782, so the scale is acceptable.” This sentence is too broad. KMO only shows that the data have a certain level of suitability for EFA. The scale still needs to be examined through Alpha, factor loading, communality, and the factor structure.

The second error is reporting Sig. = 0.000 as a probability equal to zero. In SPSS output, this is usually a rounded value. When you write the result, use p < 0.001 if the table displays 0.000, and report the correct Approx. Chi-Square and df if your department requires them.

The third error is using CFI, TLI, or RMSEA to conclude whether KMO is acceptable. Those measures belong to model fit assessment in CB-SEM, not to the KMO criterion in EFA. Do not use SmartPLS thresholds as a substitute for the thresholds used in SPSS EFA.

The fourth error is running EFA repeatedly without saving the syntax or the result tables from each round. When someone asks why a variable was removed, you will not remember which variable was removed at which step. Save the .spv file, record the variable name, the reason for removal, and the KMO value before and after every run.

Read more: CFA, rotated matrix, communality, principal component analysis, EFA.

Frequently asked questions

What KMO value is acceptable?

KMO of 0.5 or above is commonly treated as the minimum level for considering EFA, according to (Kaiser, 1974). You still need to check that Bartlett's Test has Sig. below 0.05 and continue reading the other output tables.

What should I do if KMO is below 0.5?

Check the coding, missing values, reverse-worded variables, unusual response rows, sample size, and the group of variables entered into EFA. You can then remove a variable when statistical and theoretical evidence supports the decision and run each round separately. If KMO remains low, report the limitation and discuss it with your supervisor instead of removing variables in bulk.

Does a high KMO mean that EFA is definitely correct?

A high KMO only shows that the data are more suitable for factor analysis. It does not guarantee the number of factors, factor loadings, or scale content. You must also examine Bartlett's Test, Total Variance Explained, Rotated Component Matrix, and communality.

How are KMO and Bartlett's Test different?

KMO assesses the overall adequacy of the sample and the correlations between variables. Bartlett's Test checks the assumption that the correlation matrix is an identity matrix through the Sig. value. The two results are usually read together in the KMO and Bartlett's Test table.

Do I need to run KMO for the dependent variable?

If the dependent variable is a concept measured by several observed variables, you may need to check the factor structure of that group according to your research design. If the dependent variable is a single variable, there is no set of observed variables on which to run EFA. Separate the variable groups and present the procedure that matches your model.

Open your SPSS file, find the KMO and Bartlett's Test table, record KMO, Approx. Chi-Square, df, and Sig., then compare them with the handling steps above before running EFA again. If you need to run the analysis on your own .sav or .csv file and check each round, you can use M4 data analysis by DoThesis.