Statistical Methods for Psychology

Exercises 623

Exercises

16.1 The following hypothetical data were obtained from poor, average, and good readers on the

number of eye fixations per line of text.

Poor Average Good

10 5 3

78 5

84 2

11 6 3

55 4

a. Construct the design matrix for these data.

b. Use any standard regression program to calculate a least-squares analysis of variance.

c. Run the analysis of variance in the traditional manner and compare your answers.

16.2 For the data in Exercise 16.1,

a. Calculate treatment effects and show that the regression model reproduces these treat-

ment effects.

b. Demonstrate that for the regression model is equal to for the analysis of variance.

16.3 Taking the data from Exercise 16.1, add the scores 5 and 8 to the Average group and the

scores 2, 3, 3, and 5 to the Good group. Rerun the analysis for Exercise 16.1 using the more

complete data.

16.4 Rerun the analysis of Exercise 16.2 for the amended data from Exercise 16.3.

16.5 A psychologist was concerned with the relationship between Gender, Socioeconomic Status

(SES), and perceived Locus of Control. She took eight adults (age 5 25 to 30 years) in each

Gender–SES combination and administered a scale dealing with Locus of Control (a high

score indicates that the individual feels in control of his or her everyday life).

SES

Low Average High

Male 10 16 18

12 12 14

819 17

14 17 13

10 15 19

16 11 15

15 14 22

13 10 20

Female 814 12

10 10 18

713 14

9921

12 17 19

515 17

812 13

7816

R^2 h^2

Adjusted Ymeans (16.5)

Homogeneity of regression (16.5)

(16.5)

True-score analysis of covariance (16.7)

Nonequivalent groups design (16.7)

Stratification (16.11)

Difference scores (16.11)

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