Exploratory factor analysis of turtle data

Question

I'm learning a bit about exploratory factor analysis working with some datasets, but some doubts came in mind.

I'm using this data to practice turtle data. I have two groups of turtles: male and female and measures of 3 variables length, width and height.

The output of factor model using R is

  Uniquenesses:
        length     width     height 
    0.017 0.026 0.053 

    Loadings:
      Factor1
    length 0.991  
    width 0.987  
    height 0.973  

               Factor1
SS loadings      2.904
Proportion Var   0.968

The degrees of freedom for the model is 0 and the fit was 0 

The above result, shows that a single factor is good enough to describe the covariance structure of the data. Then I calculated the factor scores using the regression option and did a plot of it

(1) Clearly there are differences between males and females, but what conclusions could I draw from the scores?

(2) In this case I have a single factor and can't do a biplot, how I could check what variable is the one that most differentiates males and females?

(3) I used some rotation (varimax and promax) and results were the same that I get without rotation. Is it because I have a single factor?

(4) Is there any difference between use Regression Scores and Barlett scores?

Answer 1

That's four questions. I will take them one at a time:

(1) Clearly there are differences between males and females, but what conclusions could I draw from the scores?

First, if you are interested in differences between males and females, I'd look at a parallel boxplot and a t-test. However, one conclusion is clear: While both males and females can have negative or small positive scores, only males have scores over about 1. Since the variables all have positive loadings, this means that large turtles are all male.

(2) In this case I have a single factor and can't do a biplot, how I could check what variable is the one that most differentiates males and females?

With length, width and height, this is unlikely to be fruitful because the 3 variables are likely to be highly correlated. I haven't checked the correlations, but you could easily do so. If you really wanted to do this, you could run 3 t-tests comparing males and females on the 3 variables and seeing which had the largest t.

(3) I used some rotation (varimax and promax) and results were the same that I get without rotation. Is it because I have a single factor?

Yes. With only one factor, there is nothing to rotate.

(4) Is there any difference between use Regression Scores and Barlett scores?

I don't know.