Ed Psy 507 Final Exam
Name ______________________________________
You will be using some of the WISCIII standardization data for all the calculations you are supposed to do. This data was used for the computer output contained here. However, in order to use the Student version of Statlets, I have had to remove three of the WISCIII subtests, and divide the data into two sections. Below are some brief descriptions of the WISCIII subtests along with their symbols. In the data set that you use for calculations, SS DS, and MZ were eliminated.
Picture Completion (PC) - A set of colorful pictures of common objects and scenes each of which is missing an important part which the child identifies.
Information (INF) - A series of orally presented questions that tap the child's knowledge about common events, objects, places and people.
Coding (CD) - A series of simple shapes (Coding A) or numbers (Coding B), each paired with a simple symbol. The child draws the symbol in its corresponding shape (Coding A) or under its corresponding number (Coding B), according to a key.
Similarities (SM) - A series of orally presented pairs of words for which the child explains the similarity of the common objects or concepts they represent.
Picture Arrangement (PA) - A set of colorful pictures, presented in mixed-up order, which the child rearranges into a logical story sequence.
Arithmetic (ARITH) - A series of arithmetic problems which the child solves mentally and responds to orally.
Block Design (BD) - A set of modeled or printed two-dimensional geometric patterns which the child replicates using two-color cubes.
Vocabulary (VOC) - A series of orally presented words which the child orally defines.
Object Assembly (OA) - A set of puzzles of common objects, each presented in a standardized configuration, which the child assembles to form a meaningful whole.
Comprehension (COMP) - A series of orally presented questions that require the child's solving of everyday problems or understanding of social rules and concepts.
Symbol Search (SS) - A series of paired groups of symbols, each pair consisting of a target group and a search group. The child scans the two groups and indicates whether or not a target symbol appears in the search group.
Digit Span (DS) - A series of orally presented number sequences which the child repeats verbatim for Digits Forward and in reverse order for Digits Backwards.
Mazes (MZ) - A set of increasingly difficult mazes, printed in a response booklet, which the child solves with a pencil.
Scores from these subtests can be grouped into intelligence quotients. In general, three intelligence quotients are available a Verbal IQ (VIQ) and Performance IQ (PIQ) and an overall measure of intelligence the Full Scale IQ (FSIQ). These IQs along with other descriptive information (Region, Race etc.) are contained in the first of the two data sets.
Use the first data set to solve problems 1 through 3. This data set can be found by clicking here.
1. Are VIQ and PIQ scores reliable predictors of the child's Listening comprehension (LISTEN) score on the achievement test? Provide a summary statement and ANOVA table.
2. Is PIQ in addition to VIQ a significant predictor of LISTEN? Provide a summary statement and ANOVA table.
3. Using Helmert contrasts is there a significant difference in FSIQ between the different REGIONS in the U.S.? Is this what you would expect? Provide a summary statement and ANOVA table.
4. Using the following Factor Analysis output from the data provided to us by Glutting, answer these questions. Note you may need to conduct some procedures other than Factor by yourself to answer some questions.
a. How many factors would typically be derived by most researchers.
b. Using a colored pen or pencil, circle the variables in the appropriate place on the output below that should be included if one were naming each factor.
c. How much variance is explained by the total number of derived factors? _________
d. Using the average reliability measures reported below, calculate the common, error, and specific variance for each subtest. Note we had to reduce this data set to 10 variables. Pretend you only have these 10 subtests instead of the original 13.
| Common | Specific | Error | Reliability | |
| PC | ____ | ____ | ____ | .77 |
| INF | ____ | ____ | ____ | .84 |
| CD | ____ | ____ | ____ | .79 |
| SM | ____ | ____ | ____ | .81 |
| PA | ____ | ____ | ____ | .76 |
| ARITH | ____ | ____ | ____ | .78 |
| BD | ____ | ____ | ____ | .87 |
| VOC | ____ | ____ | ____ | .87 |
| OA | ____ | ____ | ____ | .69 |
| COMP | ____ | ____ | ____ | .77 |
FACTOR ANALYSIS OUTPUT FROM SYSTAT — Here we use the original 13 subtest scores
FACTOR ANALYSIS OUTPUT FROM SYSTAT LATENT ROOTS (EIGENVALUES)
1 2 3 4 5
5.861 1.188 1.078 0.802 0.713
6 7 8 9 10
0.641 0.491 0.474 0.455 0.410
11 12 13
0.364 0.302 0.221
COMPONENT LOADINGS
1 2 3
PC 0.692 0.281 0.138
INF 0.818 0.067 -0.221
CD 0.479 -0.691 0.077
SM 0.793 0.193 -0.219
PA 0.595 0.175 0.029
ARITH 0.758 -0.045 -0.104
BD 0.745 0.073 0.289
VOC 0.823 0.079 -0.308
OA 0.668 0.249 0.322
SS 0.549 -0.616 0.168
COMP 0.701 0.075 -0.246
DS 0.546 -0.307 -0.191
MZ 0.397 0.066 0.733
VARIANCE EXPLAINED BY COMPONENTS
1 2 3
5.861 1.188 1.078
PERCENT OF TOTAL VARIANCE EXPLAINED
1 2 3
45.085 9.139 8.291
ROTATED LOADINGS
1 2 3
PC 0.582 0.026 0.486
INF 0.795 0.245 0.174
CD 0.139 0.827 0.094
SM 0.813 0.119 0.198
PA 0.525 0.077 0.324
ARITH 0.654 0.332 0.221
BD 0.487 0.249 0.587
VOC 0.846 0.228 0.104
OA 0.462 0.060 0.627
SS 0.174 0.794 0.221
COMP 0.715 0.188 0.104
DS 0.444 0.482 -0.012
MZ -0.016 0.152 0.822
VARIANCE EXPLAINED BY ROTATED COMPONENTS
1 2 3
4.260 1.914 1.953
PERCENT OF TOTAL VARIANCE EXPLAINED
1 2 3
32.767 14.722 15.026
END OF FACTOR OUTPUT
5. Using the following discriminant analysis output, answer these questions?
a. Were we able to significantly discriminate between the four different races using the WISC-III subtest scores? Is this what you would expect? How would you explain these results?
b. How many significant discriminant functions are there?
c. Using a colored marker circle the variables that would be used to name the discriminant function(s).
d. Irrespective of your answer to part a, would you say that for practical purposes that the subtests can discriminate between the races? Why or Why not.
Discriminant Analysis Output
MULTIVARIATE TEST STATISTICS
MULTIVARIATE TEST STATISTICS
WILKS' LAMBDA = 0.728
F-STATISTIC = 2.441 DF = 39, 841 PROB = .343690E-05
PILLAI TRACE = 0.299
F-STATISTIC = 2.439 DF = 39, 858 PROB = .343003E-05
HOTELLING-LAWLEY TRACE = 0.337
F-STATISTIC = 2.440 DF = 39, 848 PROB = .344791E-05
THETA = 0.138 S = 3, M = 4.5, N =141.0 PROB = 0.001
TEST OF RESIDUAL ROOTS
ROOTS 1 THROUGH 3
CHI-SQUARE STATISTIC = 92.164 DF = 39 PROB = .341014E-05
ROOTS 2 THROUGH 3
CHI-SQUARE STATISTIC = 48.938 DF = 24 PROB = 0.002
ROOTS 3 THROUGH 3
CHI-SQUARE STATISTIC = 18.641 DF = 11 PROB = 0.068
CANONICAL CORRELATIONS
1 2 3
0.372 0.315 0.249
DEPENDENT VARIABLE CANONICAL COEFFICIENTS
STANDARDIZED BY CONDITIONAL (WITHIN GROUPS) STANDARD DEVIATIONS
1 2 3
PC 0.401 0.305 -0.391
INF 0.449 -0.786 0.259
CD 0.269 -0.537 -0.746
SM 0.241 0.140 0.032
PA 0.230-.866886E-03 0.674
ARITH -0.082 0.510 -0.220
BD 0.078 0.040 -0.203
VOC -0.490 -0.125 0.110
OA 0.105 0.311 -0.017
SS 0.010 0.272 0.146
COMP 0.034 -0.183 0.197
DS 0.145 -0.100 0.181
MZ 0.050 0.391 -0.018
CANONICAL LOADINGS (CORRELATIONS BETWEEN CONDITIONAL
DEPENDENT VARIABLES AND DEPENDENT CANONICAL FACTORS)
1 2 3
PC 0.744 0.263 -0.181
INF 0.760 -0.297 0.198
CD 0.496 -0.385 -0.534
SM 0.659 0.038 0.222
PA 0.601 0.052 0.576
ARITH 0.538 0.203 -0.018
BD 0.619 0.177 -0.111
VOC 0.491 -0.146 0.158
OA 0.567 0.340 0.034
SS 0.436 0.079 -0.084
COMP 0.506 -0.146 0.121
DS 0.452 -0.088 0.153
MZ 0.383 0.465 -0.060
TABLE OF GROUP (ROWS) BY PREDICT (COLUMNS)
FREQUENCIES
1.000 2.000 3.000 4.000 TOTAL
-----------------------------------------
1.000 85 41 48 37 211
2.000 4 24 8 10 46
3.000 10 4 17 2 33
4.000 3 1 0 6 10
-----------------------------------------
TOTAL 102 70 73 55 300
End Discriminant Analysis Output.
Have a very nice summer. I hope you learned some things from the course.