Psychology 407 Computer Assignment #2

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.

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

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

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

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

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

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.

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

Race: Asian Black White

Definition

a  7  14  39
b  8  5  8
c  9  7  29
d  5  12  15

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).

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.

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.

Wall Color: Light blue Light green Deep yellow Deep red
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

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.

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

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.

Students 4th week 8th week 12th week 16th week
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

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.

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

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