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PSYC3001 Research Methods
Practice Questions and Solutions for Final Exam
There are 9 practice questions.
Each question is representative of the difficulty of a final exam question.
However, some practice questions are longer than what you can expect for the final exam.
Allow about 40-50 minutes for each practice question (depending on length).
You may find the provided Statistical Tables and Formulae (provided separately in the Final Exam
section on Moodle) helpful in answering these questions. Students can choose to refer to these
materials during the actual online final exam.
NOTES: These practice questions are from previous years where the final exam was attended in
person. These questions are appropriate as practice/revision for the 2022 online final exam.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
2
Q1 An experiment is carried out to evaluate three new treatments for social anxiety (NT1, 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
(a) Suppose that before the experiment was conducted, the psychologist had decided to base
the analysis on the following five contrasts, controlling the familywise error rate at the .05
level:
NT1 NT2 NT3 ST C
1 1 1 1 1 -4
2 1 1 1 0 -3
3 1 1 1 -3 0
4 1 1 -2 0 0
5 1 -1 0 0 0
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(ˆ )
1 1 1 1 1 -4 3781.25
2 1 1 1 0 -3 4800.00
3 1 1 1 -3 0 1518.75
4 1 1 -2 0 0 37.50
5 1 -1 0 0 0 12.50
(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.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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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.
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 isons
Dependent Variable: time
LSD
-8.00000* 2.53640 .002 -13.0528 -2.9472
-23.00000* 2.53640 .000 -28.0528 -17.9472
-2.00000 2.53640 .433 -7.0528 3.0528
-3.00000 2.53640 .241 -8.0528 2.0528
8.00000* 2.53640 .002 2.9472 13.0528
-15.00000* 2.53640 .000 -20.0528 -9.9472
6.00000* 2.53640 .021 .9472 11.0528
5.00000 2.53640 .052 -.0528 10.0528
23.00000* 2.53640 .000 17.9472 28.0528
15.00000* 2.53640 .000 9.9472 20.0528
21.00000* 2.53640 .000 15.9472 26.0528
20.00000* 2.53640 .000 14.9472 25.0528
2.00000 2.53640 .433 -3.0528 7.0528
-6.00000* 2.53640 .021 -11.0528 -.9472
-21.00000* 2.53640 .000 -26.0528 -15.9472
-1.00000 2.53640 .695 -6.0528 4.0528
3.00000 2.53640 .241 -2.0528 8.0528
-5.00000 2.53640 .052 -10.0528 .0528
-20.00000* 2.53640 .000 -25.0528 -14.9472
1.00000 2.53640 .695 -4.0528 6.0528
(J) group
2.00
3.00
4.00
5.00
1.00
3.00
4.00
5.00
1.00
2.00
4.00
5.00
1.00
2.00
3.00
5.00
1.00
2.00
3.00
4.00
(I) group
1.00
2.00
3.00
4.00
5.00
Mean
Dif ference
(I-J) Std. Error Sig. Low er Bound Upper Bound
95% Conf idence Interval
The mean dif ference is signif icant at the .05 level.*.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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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
-------------------------------------------------------
[1 1 -4 1 1] B1 -19.750 2.005 -23.745 -15.755
[1 -3 0 1 1] B2 -6.333 2.071 -10.459 -2.208
[2 0 0 -1 -1 B3 -2.500 2.197 -6.876 1.876
[0 0 0 1 -1] B4 -1.000 2.536 -6.053 4.053
-------------------------------------------------------
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) a1: Drug X
a2: Drug W
a3: placebo
B (Treatments) - b1: hypnosis
b2: one-to-one counselling
b3: a behavioural treatment emphasising social supports
b4: a behavioural treatment emphasising lifestyle changes
Multiple Com par isons
Dependent Variable: time
Tukey HSD
-8.00000* 2.53640 .019 -15.0899 -.9101
-23.00000* 2.53640 .000 -30.0899 -15.9101
-2.00000 2.53640 .933 -9.0899 5.0899
-3.00000 2.53640 .761 -10.0899 4.0899
8.00000* 2.53640 .019 .9101 15.0899
-15.00000* 2.53640 .000 -22.0899 -7.9101
6.00000 2.53640 .136 -1.0899 13.0899
5.00000 2.53640 .290 -2.0899 12.0899
23.00000* 2.53640 .000 15.9101 30.0899
15.00000* 2.53640 .000 7.9101 22.0899
21.00000* 2.53640 .000 13.9101 28.0899
20.00000* 2.53640 .000 12.9101 27.0899
2.00000 2.53640 .933 -5.0899 9.0899
-6.00000 2.53640 .136 -13.0899 1.0899
-21.00000* 2.53640 .000 -28.0899 -13.9101
-1.00000 2.53640 .995 -8.0899 6.0899
3.00000 2.53640 .761 -4.0899 10.0899
-5.00000 2.53640 .290 -12.0899 2.0899
-20.00000* 2.53640 .000 -27.0899 -12.9101
1.00000 2.53640 .995 -6.0899 8.0899
(J) group
2.00
3.00
4.00
5.00
1.00
3.00
4.00
5.00
1.00
2.00
4.00
5.00
1.00
2.00
3.00
5.00
1.00
2.00
3.00
4.00
(I) group
1.00
2.00
3.00
4.00
5.00
Mean
Dif ference
(I-J) Std. Error Sig. Low er Bound Upper Bound
95% Conf idence Interval
The mean dif ference is signif icant at the .05 level.*.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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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.
b1 b2 b3 b4 Mj
a1 35 33 25 23 29
a2 32 30 25 25 28
a3 23 24 31 30 27
Mk 30 29 27 26 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:
B
{m,r} {3,1} {2,2} {2,1} {1,1}
A {2,1} 2.536 2.197 2.690 3.106
{1,1} 2.929 2.536 3.106 3.587
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) - a1: a behavioural treatment emphasising lifestyle changes
a2: one-to-one counselling
a3: family counselling
a4: no treatment
B (Exercise/Diet) 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.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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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
A1 1 1 1 -3 B1 2 -1 -1
A2 2 -1 -1 0 B2 0 1 -1
A3 1 0 -1 0
A4 0 1 -1 0
The cell means are as follows:
(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
------------------------------------------------
A1 B1 396.000 1 396.000 12.153
A2 B2 198.000 1 198.000 6.077
A3 B3 412.500 1 412.500 12.660
A4 B4 264.000 1 264.000 8.102
B1 B5 697.125 1 697.125 21.395
B2 B6 166.375 1 166.375 5.106
A1B1 B7 309.375 1 309.375 9.495
A1B2 B8 0.458 1 0.458 0.014
A2B1 B9 24.750 1 24.750 0.760
A2B2 B10 0.917 1 0.917 0.028
A3B1 B11 132.000 1 132.000 4.051
A3B2 B12 0.000 1 0.000 0.000
A4B1 B13 206.250 1 206.250 6.330
A4B2 B14 2.750 1 2.750 0.084
Error 3910.000 120 32.583
------------------------------------------------
(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.
b1
Exercise/Diet
b2
Diet only
b3
Exercise only
Mj
a1 Behavioural 32 32 29 31
a2 one-to-one 30 31 29 30
a3 family 31 25 22 26
a4 no treatment 32 23 20 25
Mk 31.25 27.75 25 28
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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Raw CIs (scaled in Dependent Variable units)
-------------------------------------------------------
Contrast Value SE ..CI limits..
Lower Upper
-------------------------------------------------------
A1 B1 4.000 1.147 1.090 6.910
A2 B2 3.000 1.217 -0.086 6.086
A3 B3 5.000 1.405 1.436 8.564
A4 B4 4.000 1.405 0.436 7.564
B1 B5 4.875 1.054 2.483 7.267
B2 B6 2.750 1.217 -0.012 5.512
A1B1 B7 -7.500 2.434 -14.275 -0.725
A1B2 B8 -0.333 2.811 -8.156 7.490
A2B1 B9 -2.250 2.582 -9.436 4.936
A2B2 B10 0.500 2.981 -7.798 8.798
A3B1 B11 -6.000 2.981 -14.298 2.298
A3B2 B12 0.000 3.442 -9.581 9.581
A4B1 B13 -7.500 2.981 -15.798 0.798
A4B2 B14 -1.000 3.442 -10.581 8.581
-------------------------------------------------------
(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) Educational program which explains plagiarism and gives
students written practice tasks focussing on reducing plagiarism.
T2 (Education only) Education only program explaining plagiarism to students.
T3 (Writing task) Program that does not directly address plagiarism, but gives
students practice at a neutral writing task.
T4 (Control) 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:
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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T1 T2 T3 T4
1 1 0 0 -1
2 0 1 0 -1
3 0 0 1 -1
(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.
Means and sums of squares are as follows:
M1 = 16 SSB = 2,585
M2 = 20 SSE = 11,448
M3 = 32 SST = 14,033
M4 = 34 (Grand Mean) M = 25.5
Between contrast coefficients
Contrast Group...
1 2 3 4
B1 1 0 0 -1
B2 0 1 0 -1
B3 0 0 1 -1
Analysis of Variance Summary Table
Source SS df MS F
------------------------------------------------
Between
------------------------------------------------
B1 1782.000 1 1782.000 6.226
B2 1078.000 1 1078.000 3.767
B3 22.000 1 22.000 0.077
Error 11448.000 40 286.200
------------------------------------------------
(ii) 95% confidence interval output commensurate with the test procedure you should
have used in Part a(i) is given below. What can be said about the practical
importance of treatment effects for these three contrasts?
95% Simultaneous Confidence Intervals
------------------------------------------------
The CIs refer to mean difference contrasts,
with coefficients rescaled if necessary.
The rescaled contrast coefficients are:
Rescaled Between contrast coefficients
Contrast Group...
1 2 3 4
B1 1.000 0.000 0.000 -1.000
B2 0.000 1.000 0.000 -1.000
B3 0.000 0.000 1.000 -1.000
Raw CIs (scaled in Dependent Variable units)
-------------------------------------------------------
Contrast Value SE ..CI limits..
Lower Upper
-------------------------------------------------------
B1 -18.000 7.214 -36.026 0.026
B2 -14.000 7.214 -32.026 4.026
B3 -2.000 7.214 -20.026 16.026
-------------------------------------------------------
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
9
(b) Suppose Psychologist B examines the data before deciding which contrasts to test and finds
only one interpretable significant complex contrast (controlling FWER at .05).
(i) State the decision rule for this analysis. Carry out a test of significance and make an
inference for the one interpretable complex contrast that can be declared significant
by the appropriate test procedure.
[Hint: Look at the coefficients of maximal contrast and/or pattern of sample means.]
(ii) Construct a 95% simultaneous CI for this contrast (commensurate with the test
procedure you used in Part b(i) above). What conclusion follows for this CI?
ˆSE values for different {m,r}
contrasts are provided (you may
find these calculations useful):
{m,r} {1,1} {1,2} {1,3} {2,2}
ψˆSE 7.214 6.247 5.890 5.101
(iii) Psychologist B wants to report the findings with a set of contrasts that accounts for
all of SSB and includes the one significant contrast from Part b(i). Define a plausible
set of contrasts that meets Psychologist B’s requirement (you do not need to carry
out this analysis).
AND
(c) Briefly discuss the reasons for differences in outcome between the two analyses conducted
by Psychologist A and Psychologist B.
Q6 A 2 2 factorial experiment (J = 2, K = 2, n = 10, N = 40) is carried out to examine the combined
effects of drug and psychological treatment on depression.
The dependent variable is a depression scale on which a relatively high score indicates a relatively
high level of depression. A difference of 5 raw score units on this scale is regarded as a clinically
important difference.
