STA2201s01 Assignment Nine

Hand in Thursday March 29

The data file twinpsych.dat contains educational test scores for a sample of high school age identical and fraternal twin pairs. Members of each twin pair were of the same sex. The variables are:

• SEX: 0=Male, 1=Female
• IDENT: 0=Fraternal 1=Identical
• PROGMAT1: Progressive matrices (puzzle) score for twin 1
• REASON1: Reasoning score for twin 1
• VERBAL1: Verbal (reading and vocabulary) score for twin 1
• PROGMAT2: Progressive matrices (puzzle) score for twin 2
• REASON2: Reasoning score for twin 2
• VERBAL2: Verbal (reading and vocabulary) score for twin 2

Ignoring gender and identical vs. fraternal status (not a good idea in general, but this is just one of the many things we could do with these data) we want to test whether there are any linear relationships among these variables. That is, we want to test simultaneouslywhether any of the off-diagonal elements of the correlation matrix (or equivalently, the variance-covariance matrix) are different from zero.

1. First, plot the data. Use the S function pairs to make a matrix of scatterplots.
2. Please do the significance test two ways.
   • A large-sample likelihood ratio test, assuming multivariate normality.
   • A randomization test using m=1000 randomizations.
   In each case, please circle the value of your test statistic and the corresponding p-value. Do you conclude that the variables are inter-correlated? Write the answer to this on your printout.

You will hand in your picture, and also the printouts for question two.