Name ______________________________________

You will be using the Glutting data set (the same data set you used for the second exam) for all the calculations you are supposed to do, as well as for the computer output contained here. Here are some brief descriptions of the subtests from the WISC-III along with their symbols.

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).

For each of the following questions, please answer the question with a Yes or No response, and then provide a single ANOVA table using the following model that you would publish to support your answer.

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Analysis of Variance

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Source Sum of Squares Df Mean Square F-Ratio P-Value PRE

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Model 0.0295587 1 0.0295587 124.879 1.0E-4 .7483

Residual 0.00994133 42 2.36698E-4

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Total 0.0395 43

1. Is VIQ a reliable predictor of children’s Listening Comprehension (LISTEN)?

2. Is PIQ a reliable predictor of children’s Listening Comprehension (LISTEN)?

3. Are VIQ and PIQ scores taken together reliable predictors of the child's Listening comprehension (LISTEN) score on the achievement test?

4. Is PIQ in addition to VIQ a significant predictor of LISTEN?

4. Using Helmert contrasts is there a significant difference in FSIQ between the different REGIONS in the U.S.? Is this what you would expect?

5. 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. 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 of each subtest.

common specific error reliability

PC .77

INF .84

CD .79

SM .81

PA .76

ARITH .78

BD .87

VOC .87

OA .69

SS .76

COMP .77

DS .85

MZ .70

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

6. 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. 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

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

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TOTAL 102 70 73 55 300

End Discriminant Analysis Output.

Have a very nice summer. I hope you learned some things from the course.

Here is the data:

RACE REGION FSIQ VIQ PIQ PC INF CD SM PA ARITH BD VOC OA SS COMP DS MZ LISTEN

1 1 115 124 103 10 14 6 15 12 13 12 14 12 9 14 14 13 114

1 1 107 118 94 9 13 11 14 9 14 8 12 8 12 12 13 9 89

1 1 117 123 108 14 13 9 14 10 13 13 14 10 8 15 8 4 108

1 1 112 122 100 9 14 13 17 10 14 9 13 9 13 10 19 12 127

1 1 105 107 102 12 12 8 11 13 11 13 12 5 14 10 10 9 105

1 1 129 124 130 12 15 15 14 12 18 19 12 14 17 11 16 14 107

1 1 108 105 111 9 11 10 11 14 10 11 12 14 13 10 11 8 82

1 1 99 98 102 9 8 12 11 14 9 9 10 7 16 10 11 10 105

1 1 115 105 125 13 11 19 10 17 10 10 12 9 13 11 11 9 120

1 1 100 99 102 9 10 9 10 11 10 12 11 10 9 8 10 10 89

1 1 125 125 120 11 14 11 13 16 12 11 16 16 12 16 10 10 138

4 1 126 134 112 11 17 13 13 11 18 14 14 10 17 17 15 14 131

4 1 110 105 115 14 12 18 12 10 8 8 12 11 15 10 10 12 95

3 1 126 122 126 16 13 11 14 14 13 10 15 18 10 13 10 9 128

1 1 128 121 132 16 14 12 15 15 15 16 12 15 18 11 11 13 115

2 1 109 111 106 10 12 14 14 11 9 10 13 9 18 11 17 9 131

1 1 97 90 106 7 9 16 9 11 4 8 9 12 15 10 7 11 94

1 1 121 133 103 14 16 9 17 8 18 13 12 8 10 15 14 15 109

1 1 114 114 112 15 11 11 16 8 12 11 14 14 12 9 12 10 118

1 1 98 98 99 7 9 12 11 8 8 11 11 11 10 9 10 7 93

1 1 106 101 110 9 9 12 13 10 7 10 11 16 5 11 12 7 101

1 1 110 108 111 15 10 8 13 10 12 11 11 14 8 11 6 9 83

1 1 107 105 110 16 9 11 13 7 12 10 8 13 10 12 9 10 96

2 1 78 85 75 9 8 9 7 4 8 7 9 1 9 5 7 1 86

1 1 123 123 119 11 13 7 17 17 14 14 12 15 14 13 13 15 71

2 2 122 119 120 15 15 15 15 15 11 10 13 10 7 12 11 16 130

2 2 104 102 106 12 13 13 8 8 11 11 12 10 6 8 10 11 130

2 2 76 81 74 2 7 7 7 7 8 8 7 5 7 4 8 4 98

3 2 109 112 104 10 12 8 11 12 16 11 10 12 7 11 17 10 101

2 2 78 75 84 8 7 13 4 5 1 7 8 5 4 8 11 14 83

2 2 85 87 86 7 5 10 8 9 9 4 6 9 16 10 13 10 104

1 2 89 87 94 10 10 11 5 13 9 8 5 3 7 9 12 14 103

1 2 95 89 104 9 10 12 8 13 8 9 7 10 13 7 9 14 110

1 2 114 112 115 7 14 17 13 16 12 9 10 12 15 11 11 11 127

1 2 119 112 123 12 13 11 12 13 11 16 12 15 10 12 10 18 105

1 2 77 74 84 8 6 10 7 5 4 5 6 10 5 4 7 9 81

1 2 104 106 102 13 11 11 9 7 7 9 14 11 9 14 15 9 99

1 2 77 75 82 11 6 9 5 5 6 3 5 8 5 6 9 8 96

1 2 95 91 100 11 9 11 8 10 11 8 7 10 14 7 9 14 112

1 2 94 101 87 11 7 10 8 8 13 9 10 2 7 13 7 7 116

1 2 100 93 108 10 10 12 11 11 7 12 7 11 15 9 14 19 104

1 2 130 127 129 16 15 14 16 16 13 13 15 12 13 14 13 18 132

4 2 86 89 84 7 6 10 5 11 9 5 10 5 9 10 7 9 108

1 2 97 97 98 13 11 9 12 13 5 9 9 4 15 10 9 11 84

1 2 88 80 100 10 6 13 9 9 6 9 7 9 10 4 10 8 81

1 2 122 131 107 12 13 12 17 10 10 10 19 11 11 17 14 6 114

2 2 107 107 106 15 10 13 10 8 11 10 11 8 12 14 13 8 113

2 2 101 104 98 11 10 12 9 8 9 8 12 9 12 13 7 15 115

2 2 78 79 81 7 5 6 6 8 8 7 4 7 7 8 7 6 84

3 2 104 111 96 10 11 6 11 12 12 7 12 12 10 13 8 9 101

2 3 98 100 96 9 11 10 9 11 13 9 9 8 9 8 13 5 118

4 3 123 119 125 16 15 13 15 9 13 15 14 15 13 9 10 11 133

2 3 68 74 65 3 7 3 5 6 2 1 6 8 5 7 6 6 79

1 3 89 93 86 10 9 6 8 8 9 7 8 8 10 10 7 12 86

2 3 81 90 74 2 3 8 9 9 7 4 9 6 13 13 7 6 104

2 3 95 93 98 10 10 15 8 6 7 8 10 9 12 9 9 6 85

1 3 111 112 108 15 15 9 12 9 12 11 11 12 9 10 13 5 113

1 3 112 94 130 16 6 7 12 18 10 14 8 17 6 9 8 19 102

2 3 81 84 81 2 9 7 5 10 9 4 8 12 6 5 10 5 92

2 3 72 81 68 4 7 8 8 2 1 3 9 6 8 8 5 5 76

2 3 99 107 91 8 15 6 10 10 10 11 12 8 7 9 8 18 116

2 3 81 91 73 2 9 6 9 9 8 3 9 8 9 7 11 8 95

1 3 103 101 104 10 14 7 9 12 10 10 10 14 8 8 12 12 101

2 3 78 72 90 1 3 10 6 12 6 10 6 9 8 4 9 10 74

2 3 88 90 89 8 9 5 11 11 11 8 7 9 6 3 7 8 97

2 3 79 85 77 5 10 5 5 9 6 8 8 4 6 8 6 8 83

2 3 84 92 79 5 7 14 9 9 11 4 8 1 11 8 15 8 90

2 3 87 85 91 8 9 12 9 11 8 7 8 5 17 3 9 4 98

1 3 110 113 106 12 11 14 13 10 12 10 13 8 13 12 8 6 107

1 3 84 81 90 11 9 9 6 7 10 5 5 10 10 3 10 12 89

1 3 97 99 96 10 9 6 10 11 9 11 13 9 13 8 10 12 74

1 3 108 106 110 15 13 7 11 12 8 10 11 13 9 12 11 12 93

1 3 133 126 136 18 16 13 13 15 17 16 14 15 11 12 11 15 123

2 3 93 85 103 14 11 6 7 11 8 9 6 12 11 5 7 13 96

1 3 118 121 112 15 13 10 13 13 12 11 14 10 8 15 15 14 112

3 4 92 94 91 6 7 8 11 8 7 12 11 9 8 9 10 15 108

3 4 81 80 86 8 5 5 8 5 7 11 4 10 5 8 7 10 86

2 4 65 70 66 3 5 5 6 6 5 2 1 6 4 6 6 9 94

2 4 73 72 78 1 4 6 10 8 4 11 6 6 6 1 5 9 76

3 4 75 71 82 6 5 6 4 6 8 9 5 9 12 2 9 5 87

3 4 69 63 79 5 3 8 1 5 8 7 2 8 6 3 8 17 82

3 4 81 78 87 8 5 9 5 6 9 8 6 9 10 5 6 12 84

1 4 92 90 96 6 9 9 11 11 9 9 6 12 7 6 10 9 104

3 4 110 108 111 14 11 10 14 9 12 15 13 10 11 7 15 12 124

1 4 99 94 106 6 9 11 10 11 11 13 6 13 13 9 12 11 102

3 4 84 84 87 11 7 6 9 4 7 8 8 11 10 5 7 9 86

3 4 96 97 96 11 8 9 12 10 9 7 9 10 13 9 10 9 103

1 4 106 99 113 11 7 10 10 14 9 11 8 14 11 15 18 13 131

2 4 88 84 95 11 4 7 10 10 9 5 6 13 6 7 7 11 76

3 4 79 79 83 4 6 12 4 10 8 7 3 4 5 10 6 9 88

3 4 71 80 68 1 5 11 7 2 7 8 5 1 11 8 5 11 83

3 4 68 64 77 7 3 5 4 5 7 7 2 7 9 2 6 8 69

1 4 76 78 79 10 5 6 7 1 6 8 6 8 6 6 7 8 84

1 4 111 115 104 17 12 3 15 11 13 12 13 10 6 10 16 10 135

3 4 80 82 81 7 5 8 7 5 7 6 7 9 7 8 7 7 97

3 4 93 94 93 6 7 9 9 8 10 15 8 6 10 11 6 12 86

3 4 83 80 89 9 5 8 7 8 7 8 6 8 6 7 7 13 99

1 4 81 87 79 9 11 6 6 6 10 3 5 9 9 6 14 7 85

1 4 80 81 82 8 7 8 7 7 10 5 8 8 8 1 8 4 75

1 4 103 98 108 4 10 15 10 10 7 11 10 16 17 11 18 15 113