Homework Problems

 

  1. A clinical researcher is interested in comparing social skills training and cognitive restructuring therapies on the mental health of depressed and anxious subjects.  Each subject will receive one treatment and then the other one month apart.  After each treatment, the subjects will have their mental health evaluated.  Because the depressed subjects are residing at the local in-patient facility while the anxious subjects are at a local state university, the two types of subjects must be treated separately.  To save time and money the researcher decides to run both types of subjects in groups: two groups of depressed subjects and two groups of anxious subjects.

 

    1. What is the design of this experiment?  Write it out using symbols.  Which effects are fixed?  Which are random?  Why?

b.     Write out the Cornfield-Tukey table.

    1. Construct the estimated mean square table for this design.
    2. Note the appropriate F ratios to test each effect.

                                                             i.      Answer

 

  1. Another researcher is interested in the effects of three different drugs on anxiety and depression.  Using a battery of assessment devices, she selects four groups of subjects for treatment: depressed anxious subjects, depressed non-anxious subjects, non-depressed anxious subjects, and non-depressed non-anxious subjects.  Each subject will receive each of the three drugs one week apart (in counterbalanced orders) after each drug is administered, another battery of tests will be given.

 

    1. What is the design of this experiment?  Write it out using symbols.  Which effects are fixed?  Which are random?  Why?
    2. Write out the Cornfield-Tukey table.
    3. Construct the estimated mean square table for this design.
    4. Note the appropriate F ratios to test each effect.

                                                             i.      Answer

 

  1. A social psychologist is interested in the effects of empathy instructions on helping behavior.  She believes that empathic ability and the similarity of the person needing help to the potential helper may influence helping behavior.  To test her hypotheses, she divides the subjects into two groups by empathic ability (high/low).  Half of each group receives "emotional empathy" instructions and half receives "cognitive empathy" instructions.  Then, the subjects in half of each of these groups are exposed to a situation in which they may choose to help a similar confederate; the other half of each group is exposed to a situation in which the subjects may choose to help a dissimilar confederate.  The amount of help rendered is then measured.

 

a.     What is the design of this experiment?  Write it out using symbols.  Which effects are fixed?  Which are random?  Why?

b.     Write out the Cornfield-Tukey table.

c.     Construct the estimated mean square table for this design.

d.     Note the appropriate F ratios to test each effect.

                                                             i.      Answer

 


  1. The data for the experiment in problem 3 are printed in the table below.  Assume that all factors (except subjects) are fixed and conduct the appropriate analysis.  If there are significant effects, find the significant differences and interpret them.

 

Empathy

Instructions

Similar

Dissimilar

High

Emotional

18

12

 

 

19

8

 

 

14

6

 

 

14

6

 

 

12

4

 

 

10

2

 

Cognitive

16

10

 

 

12

6

 

 

18

5

 

 

12

4

 

 

8

2

 

 

10

1

Low

Emotional

16

8

 

 

18

4

 

 

16

6

 

 

10

4

 

 

8

1

 

 

12

2

 

Cognitive

19

10

 

 

16

10

 

 

16

8

 

 

16

8

 

 

14

9

 

 

12

8

 

Answer

 

  1. The Department of Transportation has hired you to determine whether driver errors increase at night purely because it is dark and whether the effect of darkness is affected by the type of vehicle (truck, automobile, motorcycle).  You decide to run an experiment.  First you randomly select maneuvers.  Next you randomly select motorcyclists, truck drivers, and automobile drivers.  Each driver performs the same maneuvers in daylight and in darkness. 

a.     What is the structural model for this experiment?

b.     Write out the expected mean square table.

c.     Identify the correct error terms.

                                                             i.      Answer

 

  1. To investigate the effects of social factors on health, researchers randomly assign monkeys to live in either a stable social group or to be moved every month into new social groups (unstable).  Half of the monkeys are male and half are female.  A measure of cardiovascular health is taken after 1 year.  Higher numbers on this measure indicate greater disease potential.  Assume that all factors are fixed except subjects. 

a.     What is the structural model for this experiment?

b.     Write out the E(MS) table.

c.     Analyze these data. 

d.     Test the male/unstable cell against the mean of the other 3. 

e.     Interpret your results.

 

                                 Social Condition 

                   Stable                               Unstable

          Male             Female         Male             Female

          .23               .34               .54               .39

          .17               .62               .68               .23

          .26               .54               .70               .27

          .32               .30               .76               .49

          .41               .51               .58               .53

          .38               .44               .87               .42

          .49               .41               .81               .34

                                                             i.      Answer

 


  1. The director of a psychology department clinic is interested in determining whether there are gender differences between male and female graduate students in the severity ratings given to clients.  Each of the 6 graduate students (3 men, 3 women) in the general practicum are asked to rate each of their 4 clients on a standard severity measure (high=bad).  Each student sees different clients.

 

a.     Write out the structural model for this design.

b.     Write out the expected mean square table.  Be sure to identify the correct error term for each effect.  Calculate the degrees of freedom for each effect.  Identify the correct degrees of freedom for each F ratio.

c.     Conduct a standard analysis.

d.     Determine whether there are gender differences.

e.     Interpret your results.

 

Gender

 

Grad Student

Clients

 

Male

 

1

49

40

31

40

 

 

2

42

48

52

58

 

 

3

42

46

50

54

 

 

 

 

 

 

 

Female

 

4

54

60

64

70

 

 

5

44

54

54

64

 

 

6

57

62

66

71

 Answer

 

  1. A clinical psychologist is interested in studying the effects of four prototypical relationship orientations on marital satisfaction.  Couples are recruited and divided into four classifications based on self reports of relationship orientation: husband cooperative/wife cooperative, husband cooperative/wife exchange, husband exchange/wife cooperative, husband exchange/wife exchange.  Each couple is then asked to discuss two types of issues, a Husband Issue and a Wife Issue.  Each member of each couple then completes a measure of the helpfulness of the discussion.

 

Orientation                                     Husband Issue                   Wife Issue

1             Couple 1       H

                                  W      

                         2       H

                                  W

2                       3

                         4

3

4

 

a) If the researcher was interested in analyzing the effects of the prototypical orientations and issue types on the average satisfaction of couples:

a.  What is the design of this experiment?  Write it out using symbols.  Which effects are fixed?  Which are random?  Why?

b.  Write out the Cornfield-Tukey table.

c.  Construct the estimated mean square table for this design.

d.  Note the appropriate F ratios to test each effect

b) If the researcher was interested in analyzing the effects of the prototypical orientations, and issue types on each member of the couple:

 a.  What is the design of this experiment?  Write it out using symbols.  Which effects are fixed?  Which are random?  Why?

b.  Write out the Cornfield-Tukey table.

c.  Construct the estimated mean square table for this design.

d.  Note the appropriate F ratios to test each effect

c) If you feel the need for a challenge,

a.  Determine the design that would be needed if the researcher were to be interested in analyzing the effects of the orientations, issue types, and gender on each member of each couple. Write it out using symbols.  Which effects are fixed?  Which are random?  Why?

b.  Write out the Cornfield-Tukey table.

c.  Construct the estimated mean square table for this design.

d.  Note the appropriate F ratios to test each effect

 

Answer 

 

  1. An organizational psychologist is interested in the effect of four different types of management style on job satisfaction.  To study the effects of these types of management styles, she locates four different organizations, each which uses a different management style.  Within each organization she obtains job satisfaction ratings from the members of two groups.  Her data are presented below.
    1. What is the structural model for this experiment? 
    2. Write out the E(MS) table.
    3. Analyze these data; if there are significant effects, find where the significant differences lie.
    4. Interpret your results.

 

a.     Style             Group   Ratings         Style        Group       Ratings

 

b.     Democratic   1       19 41 28 40    Autocratic            5    18 38 24  17

      2       44 38 39 36                               6    11  6   6    2

c.     Laissez-faire 3       38 19 44 40    Republican           7     3 10 14  25

     4        35 31 26 27                                8    14   8  7   39

 

Answer

 

  1. A researcher is interested in the differential effects of state and trait anxiety on cognitive performance on easy versus hard mathematical and verbal tasks.  She administers the Texas Trait Anxiety Inventory to a group of subjects and finds a bimodal distribution so she divides the subjects into those high and low in trait anxiety.  Half of each of these groups of subjects are then assigned to the high state anxiety manipulation and half are assigned to the low state anxiety manipulation.  Each subject then receives a test with problems ranging from very easy to very hard.  The score on each type of problem for each subject is presented below. 

a.     Assume that all of the factors except subjects are fixed.  Complete the expected mean squares table for this design.

b.     Analyze these data and present a summary of your results that includes a table of means and an ANOVA table. 

c.     Test for trends in the effect of test difficulty.  DO NOT ATTACH PRINT OUT.

 

Trait

State

VEasy

MEasy

MHard

VHard

High

High

18

14

12

6

High

High

19

12

8

4

High

High

14

10

6

2

High

Low

16

12

10

4

High

Low

12

8

6

2

High

Low

18

10

5

1

Low

High

16

10

8

4

Low

High

18

8

4

1