Psychology 407 Computer Assignment #1

An experiment was carried out to study the effect of a small lesion introduced into a particular structure in a rat’s brain on its ability to perform in a discrimination problem. The particular structure studied is bilaterally symmetric, so that the lesion could be introduced into the structure on the right side of the brain, the left side, both sides, or neither side (a control group). Four groups of randomly selected rats were formed, and given the various treatments. Originally, the control group contained 7 rats and each of the experimental groups had 14 rats, but due either to death or postoperative incapacity, only the following numbers were actually observed in the discrimination situation. The experimenter was prepared to assume that loss of rats during the study was a purely random event, which had no bearing on the results. The final data were as shown below.

Treatment I II III IV
20 24 20 27
18 22 22 35
26 25 30 18
19 25 27 24
26 20 22 28
24 21 24 32
26 34 28 16
18 21 18
32 23 25
23 25
22 18

30 32

a) Obtain the basic descriptive summary statistics for the four treatment groups (Use the STATS module and the BY command). Also, obtain the basic descriptive summary statistics aggregated over all four treatment groups.

b) Carry out the usual single-factor analysis-of-variance in different ways, and compare the consistency of the results.

i) Use the automatic coding of the dummy variables using the CATEGORY command in ANOVA.

ii) Using multiple regression in GLM, construct zero-one indicator variables and fit the model (without an additive constant).

iii) Using multiple regression in GLM, construct dummy variables that reflect the use of a weighted mean in constructing the additive constant in the ANOVA model.

c) Interpret the results substantively and discuss what further analyses might be warranted and how they might be conducted, e.g., post-hoc tests.

A sociologist selected a random sample of 45 adjunct professors who teach in the evening division of a large metropolitan university for a study of special problems associated with teaching in the evening division. The data collected include the amount of payment received by the faculty member for teaching a course during the past semester. The sociologist classified the faculty members by subject matter of course (Factor A) and highest degree earned (Factor B). The earnings per course (in thousand dollars) follow:

Factor B: Bachelor’s Master’s Doctorate

Factor A

Humanities  1.7  1.8  2.5
1.9  2.1  2.7

2.9 2.5 2.6 2.8 2.7 2.9

Social sciences  2.5  2.7  3.5
2.3  2.4  3.3
2.6  2.6  3.6
2.4  2.4  3.4

2.5

Engineering  2.7  2.9  3.7
2.8  3.0  3.6
2.8  3.7
2.7  3.8

3.9

Management  2.5  2.3  3.3
2.6  2.8  3.4

3.3 3.5 3.6

a) Using STATS and the BY command (several times), obtain the basic descriptive summary statistics for Factor A alone, Factor B alone, and for the combination of Factor A and Factor B. Also, obtain the basic descriptive summary statistics aggregated over all cells in the design.

b) Carry out a two-way ANOVA using ANOVA and the CATEGORY command, and interpret substantively. Graph the means and interpret the results in terms of the graph.

c) The analysis carried out in (a) is based on a particular dummy coding of the categories, which you can save and look at (see ANOVA and SAVE/MODEL). Do so, and show numerically that the tests used in (a) could be obtained alternatively by testing sets of regression coefficients against zero (using the simultaneous tests as discussed in GLM).

Several different methods of teaching the FORTRAN programming language are to be compared. However, the experimenter had reason to believe that general ability of the students might also affect their achievement under any given method. It was considered desirable to remove the possible linear effects of general ability on programming achievement though use of the analysis of covariance. The subjects were twenty female college freshmen who were assigned at random to five groups, each representing a different method of teaching this material. Prior to the experimental sessions, each subject was given a general ability test (score x) and, after the training, achievement was measured (score y). No student had prior experience with programming languages. The results are shown below (each x and y value has been reduced by 100 for computational convenience; this has no effect whatsoever on the final analysis). The desire of the experimenter was to treat the general ability score as the concomitant variable, and to ask if differences due to method exist even after adjustment for general ability.

Groups: 1  2  3  4  5
x y x y x y x y x y
10 18 22 40 30 38 35 25 11 15
20 17 31 22 31 40 37 45 16 17
15 23 16 28 18 41 41 50 19 20
12 19 17 31 22 40 30 51 25 23

a) Obtain the basic descriptive summary statistics for the five treatment groups for both the covariate and the dependent measure (use the STATS module and the BY command). Also, obtain the basic descriptive summary statistics aggregated over all five groups.

b) Carry out an analysis-of-covariance on these data, testing first for the homogeneity of regression slopes. Provide the adjusted group means and show how they relate to Kutner, et al. on page 931 (22.22). Are they the same? Comment. Interpret the results substantively.

c) Redo the analyses in (a) from first principles using the general linear model with 0-1 indicator variables. In particular, show how the comparison of Full and Reduced models allows one to test: (i) the homogeneity of regression slopes; (ii) assuming homogeneity of regression slopes, that the adjusted group means are or are not significantly different from each other.