Under what conditions is Kaiser's criterion considered accurate?

• A. When the number of variables is less than 30 with communalities greater than 0.7, or when the sample size exceeds 250 and the average communality is at least 0.6
• B. When the number of variables is greater than 50 with high communalities
• C. When the sample size is very large
• D. When the data are normally distributed

Answer: (A)

Kaiser's criterion is a simple rule of thumb for deciding how many factors to keep in factor analysis, based on eigenvalues greater than 1. It works best when the data show stable, well-explained variance by the factors. Specifically, it tends to be accurate under two practical conditions: either you have fewer than about 30 variables and the communalities are high (greater than 0.7), or you have a large sample size (more than 250) and a reasonably high average communality (at least 0.6). High communalities mean each variable shares a lot of its variance with the underlying factors, which makes the eigenvalues more reflective of the true structure; a large sample size reduces sampling error in those eigenvalues. If you have many variables with moderate or low communalities, or if the sample is small, the criterion can mislead you about the correct number of factors. Simply having a very large sample doesn’t fix low communalities, and normal distribution of the data isn’t the determining factor here.