# Interpreting results of a factor analysis

I performed factor analysis on R using factanal. Following advice I found on this tutorial, I chose the number of factors as being the number of principal components that capture 90% of the variability. I got the following table of results:

               Factor1 Factor2 Factor3 Factor4 Factor5 Factor6 Factor7 Factor8 Factor9
Proportion Var   0.309   0.099   0.066   0.059   0.044   0.038   0.015   0.008   0.007
Cumulative Var   0.309   0.408   0.474   0.533   0.577   0.615   0.630   0.638   0.645

Test of the hypothesis that 9 factors are sufficient.
The chi square statistic is 30148.02 on 3732 degrees of freedom.
The p-value is 0


I tried with one factor and I got a p-value of 0 as well...

1. Why is the cumulative var smaller than with 9 PCs for a pca?
2. How can I interpret the above table to choose the correct number of factors? (since the p-value is the same for 1 of 9 factors)

• Thus PCA will tend to need fewer PC's than FA needs factors to explain the same amount of variation in the data This statement is a bit slippery. Since FA explains only common variability it thus has its ceiling limiting variation below 100% that it can explain, while for PCA the limit is 100%. – ttnphns May 28 '14 at 12:55