{"id":5091,"date":"2016-05-16T14:00:05","date_gmt":"2016-05-16T19:00:05","guid":{"rendered":"http:\/\/www.thejuliagroup.com\/blog\/?p=5091"},"modified":"2016-09-15T19:05:10","modified_gmt":"2016-09-16T00:05:10","slug":"minimum-sample-size-in-factor-analysis-other-small-sample-thoughts","status":"publish","type":"post","link":"https:\/\/www.thejuliagroup.com\/blog\/minimum-sample-size-in-factor-analysis-other-small-sample-thoughts\/","title":{"rendered":"Minimum Sample Size in Factor Analysis & Other Small Sample Thoughts"},"content":{"rendered":"

Someone handed me a data set on acculturation that they had collected from a small sample size of 25 people. There was a good reason that the sample was small – think African-American presidents of companies over $100 million in sales or Latina neurosurgeons. Anyway, small sample, can’t reasonably expect to get 500 or 1,000 people.<\/p>\n

The first thing I thought about was whether there was a valid argument for a minimum sample size for factor analysis. I came across this very interesting post by Nathan Zhao where he reviews the research on both a minimum sample size and a minimum subjects to variables ratio<\/a>.<\/p>\n

Since I did the public service of reading it so you don’t have to, (though seriously, it was an easy read and interesting), I will summarize:<\/p>\n

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  1. There is no evidence for any absolute minimum number, be it 100, 500 or 1,000.<\/li>\n
  2. The minimum sample size depends on the number of variables and the communality estimates for those variables<\/li>\n
  3. “If components possess four or more variables with loadings above .60, the pattern may be interpreted whatever the sample size used .”<\/li>\n
  4. There should be at least three measured variables per factor and preferably more.<\/li>\n<\/ol>\n

    This makes a lot of sense if you think about factor loadings in terms of what they are, correlations of an item with a factor. With correlations, if you have a very large correlation in the population, you’re going to find statistical significance even with a small sample size. It may not be precisely as large as your population correlation, but it is still going to be significantly different than zero.<\/p>\n

    So … this data set of 25 respondents that I received originally had 17 items. That seemed clearly too many for me.\u00a0 I thought there were two factors, so I wanted to reduce the number of variables down to 8, if possible. I also suspected the communality estimates would be pretty high, just based on previous research with this measure.<\/p>\n

    Here is what I did next :<\/p>\n