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.
• So more 0.7 will be enought

Hi dear friend This is a strange question, and it depends entirely on the number of degrees of freedom of the chi-square distribution. However, the values are generally well above 0.6.

The statistical assumptions for carrying out factor analysis are quite many. Some of the popular ones are: (a) determinant score, which checks for multicollinearity/singularity (recommended minimum value of 0.00001), Bartlett’s Test of Sphericity to confirm patterned relationship among the variables as seen from the correlation matrix (p= 0.5. et.c

Read these additional resources:

(1) Gie Yong A, Pearce S (2013). A beginner’s guide to factor analysis: Focusing on exploratory factor analysis. Tutor Quant Methods Psychol, 9, 79–94.

(2) Williams B, Onsman A, Brown T (1996). Exploratory factor analysis: A five-step guide for novices. J Emerg Prim Health Care, 19, 42–50

Thanks a lot

0.70 minimum threshold will explicate robustness of validity nomenclature.

Hi,

As per Hair et al. (2010), one needs to consider multiple criteria for assessing if the sample is appropriate for factor/component analysis:

1. The visual inspection to assess if there are enough inter-item correlations of more than 0.3.

2. You can choose to get anti-image correlation matrix, and if the absolute values in this matrix are more than 0.7, most likely your data is not suitable for factor analysis/PCA.

3. You can also see the results of Bartlett's test. This test assesses if your correlation matrix is identity matrix. In case the significance value is

KMO statistic varies between 0 and 1. Kaiser 1974 recommends accepting values greater than .5 as barely acceptable. KMO values of less than .5 should lead to more data collection or chosing variables to include.

Read, Andy, F. (2013) Discovering Statistics Using IBM SPSS for more information

KMO is the measure of Sampling Adequacy. The minimum acceptable value for KMO is 0.6. However, the ideal is above 0.8.

KMO threshold of 0.5 is appropriate based on extant literature as regards minimum threshold for robustness of factor structure

Low KMO reflect inadequate sample size for you to proceed further in your EFA procedure. Thus your results might not be reliable or your argument is not strong enough.

KMO value greater than 0.50, Eligible for factor analysis

Yes, this is eligible for factor analysis.

Generally in SPSS; Bartlett’s test of sphericity is significant (p= 0.00).

KMO does not depend on sample size, but rather depends on partial correlations (e.g., correlations between pairs of items with variance associated with all other items removed). KMO =1 if all partial correlations are zero, an unlikely outcome. However, if some pairwise correlations cannot be explained by overlap with other variables in the model, then those partial correlations may be large, and KMO is reduced. Ordinarily, if there are three or more correlated variables on each factor, KMO will be large, close to 1. However, if there are isolated pairs of items that are correlated with each other but not with other variables, KMO will suffer. A factor with only two items will generally contribute to small KMO.

You are spot on.

It seems that KMO = 0.78 and Cronbach’s Alpha = 0.75 is sufficient enough for factor analysis? Would you agree?

The KMO = 0.7 sounds good to justify the sample adequacy to do the factor analysis.

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.

Therefore according to litreture, we should have at least 0.7 KMO

so what action when you have KMO unacceptable while Bartletts is significant (p

According to Kaiser (1975), KMO > 0.9 --->> Marvelous

Between 0.8 and 0.9 --> Mmeritourious

Between 0.7 and 0.8 --> Middling

Between 0.6 and 0.7 --> Mediocre

Between 0.50 and 0.6 --> Miserable

Less than 0.5 --> Unacceptable.

However, Hair et al. (2006) suggest accepting a value > 0.5, and that values between 0.5 and 0.7 are Mediocre, and values between 0.7 and 0.8 are Good.

@Assem Abu Hatab Could you please write full references for Kaiser (1975) and Hair et al. (2006) so I could find them? Thank you!

Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2006). Multivariate Data Analysis. New Jersey: Pearson University Press

Tabachnick, B. G., & Fidell, L. S. (2007). Using Multivariate Statistics: Pearson Education Inc. Boston, MA.

Kaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36. https://doi.org/10.1007/BF02291575

Just go on, Ksenija. It's OK.

The adequacy of the sample is measured by KMO in SPSS. The sampling is adequate or sufficient if the value of Kaiser Meyer Olkin (KMO) is larger than 0.5 Field (2000), according to Pallant (2013) the value of KMO is 0.6 and above. Kaiser (1974) recommends a bare minimum of 0.5 and the value between 0.5 and 0.7 are mediocre, value between 0.7 and 0.8 are good, value between 0.8 and 0.9 are great and value between 0.9 and above are superb (Hutcheson & Sofroniou, 1999).

Dale E. Berger Thank you for explaining KMO in the best manner.

KMO does not depend on sample size, but rather depends on partial correlations (e.g., correlations between pairs of items with variance associated with all other items removed). KMO =1 if all partial correlations are zero, an unlikely outcome. However, if some pairwise correlations cannot be explained by overlap with other variables in the model, then those partial correlations may be large, and KMO is reduced. Ordinarily, if there are three or more correlated variables on each factor, KMO will be large, close to 1. However, if there are isolated pairs of items that are correlated with each other but not with other variables, KMO will suffer. A factor with only two items will generally contribute to small KMO.

Currently attempting to do my EFA but the KMO test shows I have only 0.5 sampling adequacy and R will not let me continue with this. Is there any way to carry on with the EFA or would I just need to say the sampling was not adequate and publish this in the results?