STAT 530, Fall 2022
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Homework 7
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ALL students should do both of the following problems:

IMPORTANT NOTE: For EACH of these problems, write a couple of sentences 
explaining in words what substantive conclusions about the data
that you can draw from the plots and/or analyses.

PROBLEM 1:  
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Use Hotelling's T^2 test and the data in the test score data set (scores on math and reading tests
given to a sample of girls and a sample of boys) to test for a difference in the mean score vector 
of the boys and the mean vector of the girls.

The following R code will read in the data:

testdata <- read.table("http://people.stat.sc.edu/hitchcock/testscoredata.txt", header=T)
attach(testdata)
testdata.noIDs <- testdata[,-1]  #to remove the ID numbers


PROBLEM 2:  
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Consider the 'hsb' data set that we have studied in class.  Suppose our goal is to
compare the mean vectors (where the variables are the scores on: read, write, math, science, socst)
among the different levels of 'ses' (high, middle, and low socioeconomic classes).

hsb <- read.table("http://people.stat.sc.edu/hitchcock/hsbdata.txt", header=T)
attach(hsb)

hsb.prob4 <- hsb[,c(5,8,9,10,11,12)]

hsb.numeric <- hsb[,c(8,9,10,11,12)]

###############################################

(a) Conduct the MANOVA F-test using Wilks' Lambda to test for a difference in 
(read, write, math, science, socst) mean vectors across the three ses classes.
Use a 0.05 significance level, and give the P-value of the test.

(b) Check to see whether the assumptions of your test are met.  Do you believe 
your inference is valid?

(c) Examine the sample mean vectors for each group.  Informally comment on the 
differences among the groups in terms of the specific variables.


FUN EXTRA CREDIT PROBLEM:
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In class we studied Box's M-test for testing the equality of several covariance matrices.
This test was named after George Box (same person as with the Box-Cox transformation, and for those
who took my time series class, recall the Ljung-Box test and the Box-Jenkins method).
For an extra credit point: Whose daughter did George Box end up marrying?
And for a little more extra credit, write an imaginary dialogue between George and the father
of his future wife when he came to the daughter's house to take her out on a date.  The funnier, the better!