My sample consists of 112 subjects (and there are 20 variables to be included in the analyses)...
Hi Hilde Pape
This is a frequently asked question. Here is some good answers:
https://www.researchgate.net/post/What_is_the_optimum_sample_size_for_factor_analysis#:~:text=If%20you%20have%2020%20variables,more%20reliable%20and%20acceptable%20results.
https://www.researchgate.net/post/What_is_the_minimum_sample_size_for_factor_analysis
Hello Hilde,
The facetious answer to a question about "minimum" sample size would be 3 cases (why not 2? to assure that correlations can differ from 0, +1, or -1).
The real answer is, it depends.
The usual, "rule of thumb" guidelines for exploratory factor analysis would be 10-20 cases per measured variable. For confirmatory factor analysis, the comparable guideline would be 10-20 cases per hypothesized parameter in your model.
More cases is better, especially as the number of variables increases. The reasons are: (a) bigger N of cases yields more stable estimates of the correlations among the variables; and (b) with more variables, the number of inter-relationships that must be estimated increases. With 50 variables, you are estimating 50 * 49 / 2 = 1225 separate relationships (as well as 50 variances), so that's asking a lot of your data.
The best advice would be to run simulations, but doing so requires a declaration of what the possible structures might be (and, in the case of EFA, we don't have the luxury of this knowledge).
Good luck with your work!
You don't say what kind of factor analysis. If you have no constraints on loadings, then the 10-20 guidance as a minimum is appropriate. Before you conduct this analysis, do you have ideas about how the variables may relate (once you run any analysis, you can't do this)? Using a more restricted models where fewer loadings are estimated may be possible with the small sample.
Hilde Pape, you have received some good advice up above. Some time ago, I investigated the issue you raise and came up with a variety of recommendations that have been made in the literature. I incorporated them in an article that was published at the end of last year (I can give you the reference if you like; it's open access), but after considering a number of rules of thumb, I wrote:
Other, more complex, methods for determining a satisfactory sample size exist. These methods are based on size of communalities, number of items in the factors, and size of loadings.
One of the articles I cited in support of that statement is the following:
Gaskin, C. J., & Happell, B. (2014). On exploratory factor analysis: A review of recent evidence, an assessment of current practice, and recommendations for future use. International Journal of Nursing Studies, 51, 511–521. https://doi.org/10.1016/j.ijnurstu.2013.10.005
I commend it to you.
For an efa the KMO would be a good test fir judginh factor analysis .For the cfa we generally say k into 10 would be a good number ,here k would be the number of items in the questionnaire
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