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        Psychology 407

        Computer Assignment \#2


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I.  In the hand-out from class on Split-plot factorial designs,
Table 12.10-1 gives the computational procedures for a SPF2.22
design.  The source table is given in Table 12.10-2.  Redo this
analysis using GLM and compare the results to those in Table
12.10-2.

\bigskip

II.  In a study on school integration, 158 graduating seniors were
asked the following question:

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The word ``integration'' often has a different meaning for different
people.  Here are several possible meanings for the word:

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a) Integration is the free association of people of different races
on the basis of mutual or like interests.

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b)  Integration is the forced mixing of people of different races.

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c)   Integration is the open acceptance of another person and
his/her racial and cultural heritage.

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d)  Integration is all people having equal social value (may marry
outside of their own races, join social clubs, etc.), and receiving
equal justice under the law.

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The distribution of responses according to race of the student is
shown below:

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\begin{tabular}{cccc}

Race:  & Asian & Black & White \\ \hline

Definition & & & \\

a & 7 & 14 & 39 \\

b & 8 & 5 & 8 \\

c  & 9 & 7 & 29 \\

d  & 5 & 12 & 15 \\

\end{tabular}

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Using the BASIC module, input the contingency table itself (i.e.,
you should have 12 ``cases'' in your data file).  Using TABLES,
provide as output the frequency table and the row, column, and
row/column percentages.  Use OUTPUT = LONG (i.e., set your
preferences), and get the Pearson Chi-square statistics and its
$p$-value (plus a lot of other stuff).

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In the log-linear option (LOGLIN), fit the model without interaction
and compare the results to what you obtained previously.  Obtain
tables of both raw and standardized residuals.  Interpret the
results.

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III.  In a study in which the effects of color upon test performance
was being studied, the data in the following table were obtained. In
this study, 40 students were assigned at random to one of four
identical rooms; identical except that wall colors were different.
Two of the rooms were painted with cool colors, and the other two
with warm colors.  During the experimental period, students studied
a section on French history following the French Revolution and
extending up to the accession of Napoleon to the Imperial Throne.
Students were instructed to study only in the assigned study room.
The criterion variable is the score on a 60-item multiple choice
test.

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\begin{tabular}{ccccc}

Wall Color: & Light blue  &  Light green &  Deep yellow  &  Deep red
\\ \hline

  & 41  & 46 & 40 & 28 \\



&  45 & 47 & 40 & 30 \\



& 45 & 49 & 41 & 30 \\



& 46 & 49 & 42 & 31 \\



&  48 & 51 & 43 & 31 \\



& 50 & 55 & 44 & 36 \\



& 56 & 55 & 46 & 39 \\



& 56 & 58 & 50 & 41 \\



& 57 & 59 & 52 & 42 \\



& 57  & 60 & 58 & 44 \\ \hline



\end{tabular}

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Using NPAR and considering just the ``cool'' colors separately,
carry out both a Mann-Whitney (as a special case of the
Kruskal-Wallis test) and a Wald-Wolfowitz runs test.  Redo  for the
``warm'' colors.  Interpret.

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Carry out a Kruskal-Wallis test on all four  treatments and a
one-way ANOVA.  Compare the results.

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IV.  The data given below (the number of errors in 50 problems) are
derived from a study in which 10 students taking a course in high
school business math were given a test to measure their recall of
7-digit numbers. The tests were given at the end of the 4th, 12th,
and 16th week of the course. It is hypothesized that, with increased
exposure to arithmetic and numbers during the taking of business
math, digit-span memory would also increase.

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\begin{tabular}{ccccc}

Students & 4th week  &  8th week  & 12th week  &  16th week \\ [2ex]
\hline

1 & 38 & 30 & 10 & 8 \\


2 & 32 & 30 & 9 & 5 \\


3  &  37 &  33 & 15  & 10 \\


4 & 35 & 41 & 22 & 12 \\


5  & 31 & 33 & 28 & 20 \\


6  & 36 & 20 & 8 & 2 \\


7  & 29 & 5 & 6 & 1 \\


8  & 46 & 33 & 32 & 29 \\


9  &  41 &  45 & 28 & 32 \\


10 & 46 & 40  & 27 & 29 \\


\end{tabular}

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Using NPAR and considering only the 4th and 8th week data, carry out
both a sign and a Wilcoxon test.  Compare the results to a paired
$t$-test.

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Evaluate the complete data set using Friedman's test and compare the
results to a Model III ANOVA.

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Moving to the CORR module, obtain   Pearson, Gamma, Spearman, and
$\mathrm{Tau}_{b}$ coefficients between all pairs of the 4 time
periods.  What consistencies do you see in the pattern of the
obtained coefficients?  Interpret.

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