Q1 An experiment is carried out to evaluate three new treatments for social anxiety (NT 1, NT2 and NT3 ). One hundred and twenty five subjects are randomly assigned to each of five conditions (N =  125, J = 5, n = 25): NT1, NT2, NT3, the standard treatment (ST), and a waiting list control (C).             The dependent variable is a measure of social comfortableness (the extent to which participants    feel comfortable and at ease in social situations), where a high score indicates a high level of           comfortableness in social situations.

Sample means and sums of squares (between, within and total) are given below.

NT1 :     M1 = 33                                            SSB =      5,350

NT2 :     M2 = 34                               SSW = SSE =    60,000

NT3 :     M3 = 32                                           SST =     65,350

ST:        M4 = 24

C:          M5 = 17

What test procedure would you choose for this analysis and why?

(b) Complete this analysis and draw appropriate conclusions. Contrast SS are given below.

NT1

NT2

NT3

ST

C

SS(八 )

(c) Suppose that the experimenter had decided to begin the analysis with a .05 level ANOVA F test, and to test contrasts with a procedure compatible with the F test. Carry out this          analysis and draw appropriate conclusions.

(d) Comment on the reasons for any differences in outcome between the analyses in (b) and

(c).

Q2 A study is conducted to determine which of five exercise programs for potential heart disease    sufferers will be easiest for patients to maintain, and hence lead to a high compliance and low drop- out rate.  Eighty patients are randomly allocated to one of five exercise programs (J = 5, n = 16, N =  80):

Group 1:  riding an exercise bike;

Group 2:  swimming;

Group 3:  walking;

Group 4: jogging on a mini trampoline;

Group 5:  working out to a low-impact aerobics video.

All patients are requested to complete at least 30 minutes of exercise each day over a four week period.  The dependent variable is the average number of minutes spent exercising per day.  A    difference of 10 minutes spent exercising is considered the smallest difference of practical            importance.

It is expected that walking will be the most compliant exercise program compared to each of the other types; swimming will be the next most compliant, followed by riding an exercise bike; and little difference in compliance is expected between jogging and working out to a video.

Sample means:      M1 = 8         M2 = 16         M3 = 31         M4 = 10         M5 = 11

(a) Psychologist A (not a graduate of UNSW) analyses the data with SPSS and chooses Analyze -

Compare Means – One Way Anova, and then post hoc option, LSD with -level of .05.

Multiple Com par is ons

Dependent Variable: time

LSD

*. The mean diff erence is signif ic ant at the .05 lev el.

What conclusions would Psychologist A draw from this analysis? What is problematic (invalid) about this analysis?

(b) Psychologist B (a graduate of UNSW) analyses the data in SPSS and chooses Analyze -

Compare Means – One Way Anova, and then post hoc option, Tukey with -level of .05.

Multiple Com par is ons

Dependent Variable: time

Tukey HSD

*. The mean difference is signif ic ant at the .05 lev el.

How does this analysis differ from (a)? What conclusions would Psychologist B draw from this analysis?

(c) Psychologist C plans a set of orthogonal contrasts relevant to the expected outcomes, and controls the PCER at .05. What inference follows for this analysis?

Individual 95% Confidence Intervals

-----------------------------------

Raw CIs (scaled in Dependent Variable units)

-------------------------------------------------------

Contrast

Value

SE

..CI limits..

Lower       Upper

-------------------------------------------------------

-23.745

-10.459

-6.876

-6.053

-------------------------------------------------------

In what way might this analysis in (c) be advantageous/disadvantageous to the analysis in (b)?

Q3 version 1 A 3 4 factorial experiment is carried out to determine the long term effects of a combined drug and psychological treatment program for eating disorder The factors and factor levels are:

A (Drug)

B (Treatments) -

a1 :  Drug X

a2 :  Drug W

a3 :  placebo

b1 : hypnosis

b2 : one-to-one counselling

b3 : a behavioural treatment emphasising

b4 : a behavioural treatment emphasising

social supports

lifestyle changes

One hundred and thirty-two participants (identified as having an eating disorder) are randomly    assigned to one of the twelve cells of the design  (J = 3, K = 4, n = 11, N = 132). The dependent      variable is a measure of eating disorder behaviour, 12 months after the completion of treatment.

Cell means are given below.

a1 a2 a3

Mk

b1                          b2                          b3                          b4

30                29                27                26

Mj

29

28

27

28

For this example, SSE = 4,246 and SS(AB) = 1782.

(a) Construct a two-way ANOVA summary table and carry out overall tests for the A, B and A

B effects, controlling the familywise error rate at .05, and draw appropriate conclusions.

(b) Using a test procedure commensurate with the analysis in (A), carry out tests on any follow-

up contrasts you think appropriate, controlling FWER at .05. Provide a concise account of directional inferences that follow from your test outcomes.

(c) Calculate the post-hoc 95% CI limits for one AB contrast that allows for a directional inference.

You may find the following table useful.

For this data set, SEs for all      interpretable AB product         contrasts are given as follows:

{m,r}

A    {2,1}

{1,1}

B

{3,1}          {2,2}          {2,1}          {1,1}

Q4 A 4 3 factorial experiment is carried out to examine the effectiveness of different treatment approaches for child obesity. The experimenters are interested in the combined effects of              Exercise/Diet programs with psychological treatments.

The factors and factor levels are:

A (Treatments) -

B (Exercise/Diet)

a1 : a behavioural treatment emphasising lifestyle changes

a2 : one-to-one counselling

a3 : family counselling

a4 : no treatment

b1 :  Exercise and Diet

b2 :  Diet only

b3 :  Exercise only

One hundred and thirty-two participants children diagnosed as obese, according to age relevant      body mass index (BMI) norms, are randomly assigned to one of the twelve cells of the design  (J = 4, K = 3, n = 11, N = 132). After being on the program for six weeks, measures are taken relating to       participants' physical activity, fitness and BMI. The dependent variable is a composite measure         indicating improvement.

The experimenters plan a contrast analysis, controlling the familywise error rate at .05. Planned contrasts include: four A main effect contrasts, two B main effect contrasts, and eight AB            interaction contrasts (each the product of an A contrast with a B contrast).

The following coefficient vectors refer to factor levels for the A and B main effect contrasts:

a1 a2 a3 a4 b1 b2 b3

b3

Exercise only

25

(a) For all contrasts in the analysis, write down the coefficient vectors referring to cell means

that would appear in the PSY input file.

(b) Test output is given on the next page. What directional inferences follow for the planned

contrasts? Clearly state the decision rule you are using.

Analysis of Variance Summary Table

Source        SS      df       MS           F

------------------------------------------------

Between

------------------------------------------------

------------------------------------------------

(c) Raw 95% SCI output (edited) is given below. Verify from the table of cell means that the contrast value for A1B1 is -7.50.

Raw CIs (scaled in Dependent Variable units)

-------------------------------------------------------

Contrast

Value

SE

..CI limits..

Lower       Upper

(d) A difference of 2 improvement points is considered to be the smallest difference of clinical importance, what inferences (if any) can be made, based on the Raw 95% CIs above,           regarding clinically important effects?

(e) The 95% SCI table above cannot be generated from a running a single PSY input file. Why

not? In order to generate the above 95% SCI output in PSY, describe the steps you would need to take.

[Hint: What CC and scaling method would be appropriate for each family of contrasts?].

Q5 Psychologist A and Psychologist B have been engaged by a university committee to conduct a study designed to tackle the problem of plagiarism in students’ written assessments.

Forty-four students are randomly allocated to one of four conditions (J = 4, n = 11, N = 44):

T1 (Education + Practice)

T2 (Education only)

T3 (Writing task)

T4 (Control)

Educational program which explains plagiarism and gives              students written practice tasks focussing on reducing plagiarism.

Education only program explaining plagiarism to students.

Program that does not directly address plagiarism, but gives students practice at a neutral writing task.

Control condition.

At the end of the treatment programs, all students complete a task in which they are given three     journal articles to read and asked to provide a 500 word written summary. The dependent variable  is a ‘similarity index’ which measures the percentage degree of overlap in the wording between a    student’s essay and the published articles. For example, a similarity index of 50% indicates that 50% of the essay shares the same wording as the published articles.

The two psychologists consider a reduction of 10% for the similarity index (ie a difference of 10 units) to be the smallest difference of practical importance.

(a) Prior to collecting data, Psychologist A plans to base the analysis on tests of the following

three comparisons, controlling the familywise error rate at the .05 level:

1 2 3

T1                T2                T3                T4

(i) What is the most efficient test procedure for this analysis and why? Make explicit the decision rule you would use.   Complete this analysis and make directional

inferences, where appropriate.