STAT 530, Fall 2024
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Homework 4b
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Problem 1:

An educational testing expert was asked to judge (on a scale of 0 to 100) how dissimilar were pairs of standardized tests.  
The following R code produces the resulting dissimilarity matrix for six kinds of standardized test.

tests.diss <- 100*round(1-cov2cor(ability.cov$cov),2)
print(tests.diss)

Descriptions of the six tests are as follows: 

general: a non-verbal measure of general intelligence using Cattell's culture-fair test.
picture: a picture-completion test
blocks: block design
maze: mazes
reading: reading comprehension
vocab: vocabulary

Find a two-dimensional multidimensional scaling solution, plot the tests on a 2-D map, and try to interpret 
meanings for the dimensions underlying the judgments about the distinctions among the tests.  Assess how well 
the 2-D solution represents the dissimilarities among the tests, using a numerical measure.

Note that
row.names(tests.diss)
contains the vector of the test names.


Problem 2:

The following R code creates a two-way contingency table called 'recreation' where the row variable is age group,
and the column variable is favorite recreational activity (out of four options), for a sample of adults.

recreation <- matrix(c(
61,49,25,21,
60,40,26,41,
60,37,33,52,
59,29,33,55,
48,16,28,57,
78,20,50,105), byrow=T, ncol=4, nrow=6,
dimnames = list(c('18-24','25-34','35-44','45-54','55-64','65+'),
                               c('exercise','sports','charity', 'gardening')))

Verify with a chi-squared test that there is an association between age group and favorite recreational activity (explain how you know this).
Use a correspondence analysis to explain how favorite recreational activity depends on age group.
Show a plot of the two-dimensional solution and explain what can be learned from this.  
You may also use a one-dimensional solution to aid your explanation of the association.