PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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PSYC3001 Research Methods 3 2023
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
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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
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(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.
Cell sample means are as follows:
Factor B
control b1
CBT b2
Mj
Factor A placebo a1
30 32 31
drug a2
25 16 20.5
k
M 27.5 24 25.75
An experimenter is interested in carrying out an analysis on all factorial contrasts and begins with a
test of a homogeneity hypothesis (one that asserts that all factorial effect parameters are zero), in
order to determine whether it is worthwhile to proceed with the follow-up contrast analysis.
The ANOVA summary table for this analysis is
Source SS df MS F
------------------------------------------------
Between cells 1527.500 3 509.167 29.913
Error 800.000 36 22.222
------------------------------------------------
The Fc value for this overall test is F.1426; 3, 36 = 1.927, where * = 1 – (1 - .05)3 = .1426.
The homogeneity hypothesis can be rejected (F3,36 = 29.9 > 1.927).
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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(a) To be compatible with the overall F test (of homogeneity of all factorial effects), the critical
value for follow-up tests of any factorial contrast is a contrast F critical value for a single-
family analysis.
What is this contrast F critical value? State the formula for the CC and hence the value of the
CC
(b) For the above example, write the contrasts section of a PSY input file, including all factorial
contrasts.
(c) The ANOVA summary table from a PSY analysis of all factorial contrasts is given below.
Which contrasts are statistically significant by the relevant F-STP? What directional
inferences follow from this analysis?
Analysis of Variance Summary Table
Source SS df MS F
------------------------------------------------
Between
------------------------------------------------
A(drug) B1 1102.500 1 1102.500 49.613
A(b1) B2 125.000 1 125.000 5.625
A(b2) B3 1280.000 1 1280.000 57.600
B(psyc) B4 122.500 1 122.500 5.513
B(a1) B5 20.000 1 20.000 0.900
B(a2) B6 405.000 1 405.000 18.225
AB B7 302.500 1 302.500 13.613
Error 800.000 36 22.222
------------------------------------------------
(d) Below is an edited version of PSY output for the relevant Scheffé CI analysis for all factorial
contrasts.
(i) Why is the CI level set at 85.74%
(ii) What inferences follow from the CI output?
Post hoc 85.74% Simultaneous Confidence Intervals
-------------------------------------------------
Raw CIs (scaled in Dependent Variable units)
-------------------------------------------------------
Contrast Value SE ..CI limits..
Lower Upper
-------------------------------------------------------
A(drug) B1 10.500 1.491 6.916 14.084
A(b1) B2 5.000 2.108 -0.069 10.069
A(b2) B3 16.000 2.108 10.931 21.069
B(psyc) B4 3.500 1.491 -0.084 7.084
B(a1) B5 -2.000 2.108 -7.069 3.069
B(a2) B6 9.000 2.108 3.931 14.069
AB B7 -11.000 2.981 -18.169 -3.831
-------------------------------------------------------
(e) Given the above Summary Table in (c):
(i) What test outcomes and directional inferences would follow from a standard two-
factor ANOVA-model analysis?
(ii) In considering both test outcomes and CI outcomes, what does the all factorial
contrasts analysis (cell means model analysis) tell us that the standard analysis
cannot? Pay particular attention to the simple effect contrasts B(a1) and B(a2).
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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AND
(f) Had the contrasts in the analysis in (b) been planned (independently of the data), an
alternative to the F STP (and associated Scheffé analysis) would be a Bonferroni-t analysis
with k = 7 and * = 3 = .15. The Bonferroni contrast F critical for this planned contrasts
analysis is F.15/7; 1, 36 = 5.785.
What recommendation would you give regarding the choice of decision rule for this planned
contrasts analysis (i.e, Bonferroni or Scheffé)? Explain.
Q7 An experimenter is interested in testing the effects of a new drug (Drug X) on reducing anxiety
in combination with psychological treatment. Sixty-six patients (N = 66) are randomly allocated to
one of three treatment conditions (behavioural treatment, counselling or wait-list control) and all
patients are told they will be taking an active drug that helps alleviate anxiety. However, half the
participants in each treatment condition are randomly allocated to receive Drug X while the other
half receive a placebo. Thus there are six cells in the experimental design, with n = 11 patients per
cell. The dependent measure is an improvement score.
Sample means are shown below:
Behavioural treatment Counselling Control
Placebo Drug X Placebo Drug X Placebo Drug X
17 25 20 26 18 14
The experimenter considers the design to represent a single experimental factor with six levels (J =
6). He is interested in making inferences regarding the size of the Drug effect (Drug vs placebo) for
each of the treatment conditions and begins the analysis with a single-factor ANOVA F test.
The ANOVA Summary Table for this analysis is given below:
SOURCE SS df MS F
BETWEEN 1,210 5 242 7.81
ERROR 1,860 60 31
TOTAL 3,070 65
Since the obtained F of 7.81 exceeds Fc = F.05; 5,60 = 2.37, the experimenter rejects the homogeneity
hypothesis, and decides to carry out follow-up tests of the following three contrasts using the
Scheffé procedure to control the FWER at .05.
Behavioural tmt Counselling Control
Placebo Drug X Placebo Drug X Placebo Drug X
1 1 -1 0 0 0 0
2 0 0 1 -1 0 0
3 0 0 0 0 1 -1
PSY output for this analysis is given below:
Between contrast coefficients
Contrast Group...
1 2 3 4 5 6
B1 1 -1 0 0 0 0
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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B2 0 0 1 -1 0 0
B3 0 0 0 0 1 -1
Analysis of Variance Summary Table
Source SS df MS F
------------------------------------------------
Between
------------------------------------------------
B1 352.000 1 352.000 11.355
B2 198.000 1 198.000 6.387
B3 88.000 1 88.000 2.839
Error 1860.000 60 31.000
------------------------------------------------
None of the three contrasts is significant by the Scheffé procedure ( 1 × Fc = 5 × 2.37 = 11.85), and
so the experimenter concludes that Drug X has no effect on alleviating anxiety.
(a) Why is the experimenter's analysis misleading? [In answering this, you do not need to
consider confidence interval inference.]
(b) A post-hoc factorial analysis of the data, controlling the FWER is carried out instead. The
factorial analysis allows for directional inferences to be made regarding the size of the drug
effect for each treatment condition and test output for this analysis is given below.
(i) What B main effect coefficient vectors have been used to define the AB contrasts?
(ii) For nominal  = .05, the critical value for this analysis is Fc = F*, 1, 2 = F.0975, 3, 60 =
2.199. Why is * = .0975 and why is 1 = 3?
(iii) What directional inferences can be made for this analysis?
PSY output is given below.
Between contrast coefficients
Contrast Group...
1 2 3 4 5 6
A(b1) B1 1 -1 0 0 0 0
A(b2) B2 0 0 1 -1 0 0
A(b3) B3 0 0 0 0 1 -1
A B4 1 -1 1 -1 1 -1
AB1 B5 1 -1 -1 1 0 0
AB2 B6 1 -1 0 0 -1 1
AB3 B7 0 0 1 -1 -1 1
Analysis of Variance Summary Table
Source SS df MS F
------------------------------------------------
Between
------------------------------------------------
A(b1) B1 352.000 1 352.000 11.355
A(b2) B2 198.000 1 198.000 6.387
A(b3) B3 88.000 1 88.000 2.839
A B4 183.333 1 183.333 5.914
AB1 B5 11.000 1 11.000 0.355
AB2 B6 396.000 1 396.000 12.774
AB3 B7 275.000 1 275.000 8.871
Error 1860.000 60 31.000
------------------------------------------------
(c) Comment on the reasons for any difference in the conclusions that follow from the
experimenter’s analysis and the analysis in (b).
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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Q8 The effects of age and alcohol on driving performance are examined in a 3  (4) factorial study.
Errors in driving performance of sixty participants are recorded on a driving simulator under each of
four levels of blood alcohol concentration. An equal number of participants are drawn from three
age groups (J = 3, p = 4, n = 20, N = 60).
Factors and factor levels are:
Between Ss Factor: (Age) b1: 20 yrs
b2: 40 yrs
b3: 60 yrs
Within Ss Factor: w1: 0 BAC
(Blood Alcohol Concentration w2: .03 BAC
w3: .06 BAC
w4: .09 BAC
(a) A standard factorial trend analysis of orthogonal polynomial contrasts is planned for each
factor. Tests are to be carried out controlling the FWER at .05.
Complete the analysis and draw appropriate conclusions.
Table of cell means:
w1 w2 w3 w4 Mj
b1 4.80 6.30 10.85 19.00 10.23
b2 4.30 6.30 8.20 12.35 7.79
b3 5.00 6.35 7.45 8.55 6.84
Mk 4.70 6.32 8.83 13.30
Plot of cell means:
PSY output is given below.
0
2
4
6
8
10
12
14
16
18
20
0 0.03 0.06 0.09
E
rr
o
rs
BAC
20 yrs
40 yrs
60 yrs
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
14
Analysis of Variance Summary Table
Source SS df MS F
------------------------------------------------
Between
------------------------------------------------
Lin B1 462.570 1 462.570 17.093
Quad B2 29.925 1 29.925 1.106
Error 1542.492 57 27.061
------------------------------------------------
Within
------------------------------------------------
Lin W1 2405.501 1 2405.501 220.977
B1W1 626.846 1 626.846 57.584
B2W1 7.656 1 7.656 0.703
Error 620.488 57 10.886
Quad W2 121.838 1 121.838 13.905
B1W2 119.111 1 119.111 13.594
B2W2 3.649 1 3.649 0.416
Error 499.442 57 8.762
Cubic W3 3.308 1 3.308 0.508
B1W3 0.046 1 0.046 0.007
B2W3 2.545 1 2.545 0.390
Error 371.471 57 6.517
------------------------------------------------
(b) Suppose instead a planned factorial contrast analysis had been carried out that includes the
same contrast coefficient vectors as the standard analysis, plus linear and quadratic
components of trend across BAC levels for each age group. The PSY input file contains the
following coefficient vectors:
Between contrast coefficients
Contrast Group...
1 2 3
Lin B1 1 0 -1
Quad B2 1 -2 1
*20 yrs* B3 1 0 0
*40 yrs* B4 0 1 0
*60 yrs* B5 0 0 1
*** Caution ***
B3 coefficients do not sum to zero
B4 coefficients do not sum to zero
B5 coefficients do not sum to zero
Within contrast coefficients
Contrast Measurement...
1 2 3 4
Lin W1 -3 -1 1 3
Quad W2 1 -1 -1 1
Cubic W3 -1 3 -3 1
(i) How many families of contrasts will there be for this analysis and what contrasts will
be included in each family? Which parts of the summary table provide valid statistics
for contrasts?
(ii) What is the contrast Fc for this analysis? (Can use Tables to find this value).
AND
(iii) What directional inferences can be made? Comment on the inclusion of simple
effects in this analysis.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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PSY test output:
Analysis of Variance Summary Table
Source SS df MS F
------------------------------------------------
Between
------------------------------------------------
Lin B1 462.570 1 462.570 17.093
Quad B2 29.925 1 29.925 1.106
*20 yrs* B3 8384.513 1 8384.513 309.834
*40 yrs* B4 4852.391 1 4852.391 179.311
*60 yrs* B5 3739.429 1 3739.429 138.184
Error 1542.492 57 27.061
------------------------------------------------
Within
------------------------------------------------
Lin W1 2405.501 1 2405.501 220.977
B1W1 626.846 1 626.846 57.584
B2W1 7.656 1 7.656 0.703
B3W1 2223.123 1 2223.123 204.223
B4W1 678.993 1 678.993 62.374
B5W1 137.886 1 137.886 12.667
Error 620.488 57 10.886
Quad W2 121.838 1 121.838 13.905
B1W2 119.111 1 119.111 13.594
B2W2 3.649 1 3.649 0.416
B3W2 221.113 1 221.113 25.235
B4W2 23.166 1 23.166 2.644
B5W2 0.319 1 0.319 0.036
Error 499.442 57 8.762
Cubic W3 3.308 1 3.308 0.508
B1W3 0.046 1 0.046 0.007
B2W3 2.545 1 2.545 0.390
B3W3 0.303 1 0.303 0.046
B4W3 5.534 1 5.534 0.849
B5W3 0.061 1 0.061 0.009
Error 371.471 57 6.517
------------------------------------------------
Q9 A study is designed to address combating homophobia among male juvenile offenders who
have been convicted of gay hate-crimes, for example acts of physical assault against LGBT (lesbian,
gay, bisexual and transgender) victims. As part of sentencing conditions, all offenders have been
required to undertake an anger management course; however, alternative programs may be more
effective than anger management alone.
Sixty-four male juvenile offenders are randomly allocated to one of four treatment conditions (J =
4, n = 16, N = 64):
T1 (AM) Anger Management (AM) program only
T2 (Education + AM) Educational program (a series of reading materials which addresses
and challenges stereotypic beliefs about LGBT individuals) to be used
in conjunction with the Anger Management program.
T3 (Video) Video program (video interviews with LGBT survivors of hate crimes).
T4 (Contact + Video) Contact program (face-to-face workshops with LGBT survivors of hate
crimes) to be used in conjunction with the Video program
The dependent variable is an attitude measure on which a high score indicates a more favourable
attitude towards LGBT individuals. The researcher considers a difference of 5 units on the attitude
measure to be the smallest difference of clinical importance.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
16
Sample means and sums of squares within are given below.
T1: M1 = 18
T2: M2 = 21 SSW = SSE = 5,100
T3: M3 = 28
T4: M4 = 31
(a) The researcher carries out a planned contrast analysis, controlling the FWER at .05. What
inference follows from the test output for this analysis? Make explicit the decision rule that
you are using and why? PSY output for this analysis is given below.
Between contrast coefficients
Contrast Group...
1 2 3 4
B1 1 1 -1 -1
B2 1 -1 0 0
B3 0 0 1 -1
Analysis of Variance Summary Table
Source SS df MS F
------------------------------------------------
Between
------------------------------------------------
B1 1600.000 1 1600.000 18.824
B2 72.000 1 72.000 0.847
B3 72.000 1 72.000 0.847
Error 5100.000 60 85.000
------------------------------------------------
(b) What inference follows from the raw confidence intervals (given below)?
95% Simultaneous Confidence Intervals
------------------------------------------------
The CIs refer to mean difference contrasts,
with coefficients rescaled if necessary.
Rescaled Between contrast coefficients
Contrast Group...
1 2 3 4
B1 0.500 0.500 -0.500 -0.500
B2 1.000 -1.000 0.000 0.000
B3 0.000 0.000 1.000 -1.000
Raw CIs (scaled in Dependent Variable units)
-------------------------------------------------------
Contrast Value SE ..CI limits..
Lower Upper
-------------------------------------------------------
B1 -10.000 2.305 -15.677 -4.323
B2 -3.000 3.260 -11.028 5.028
B3 -3.000 3.260 -11.028 5.028
-------------------------------------------------------
(c) Verify that the planned contrasts in (a) are mutually orthogonal.
(d) Suppose that the researcher had carried out a planned contrast analysis (for the contrasts in
part a and b) controlling the PCER (rather than the FWER) at .05. What inferences (based on
tests and CIs) would follow for this analysis?
(e) Briefly comment on the reasons for any difference in outcome between this analysis and the
analysis in part a and b.

PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
17
Solutions
Q1
(a) Planned contrast analysis, however k = J and so compare Bonferroni and Scheffé Contrast Fc
values and use procedure with smaller value.
Bonferroni Fc = F.05/5, 1, 120 = 6.85; Scheffé Fc = 1  F.05;4,120 = 4  2.45 = 9.8. Bonferroni value
smaller, so use Bonferroni procedure.
(b) MSE = 60,000/120 = 500
Bonferroni SSc = F.05/5, 1, 120  MSE = 6.85  500 = 3425.
Reject H0: 1 = 0 and H0: 2 = 0, cannot reject H0 for all other planned contrasts.
Receiving either a treatment (1) or a new treatment (2) leads to higher average social
comfortableness (SC) ratings compared to not receiving a treatment. No inference can be made
regarding the difference in effectiveness between NTs over STs (3), nor between new treatments
(4 and 5).
(c) MSB = 5350/4 = 1337/5, MSE = 500 (see above), F = 1337.5/500 = 2.675.
Fc = F.05;4,120 = 2.45, reject homogeneity H0 of equal population means and infer that average SC
ratings differ between treatment conditions.
Scheffe SSc = 1  F.05;4,120  MSE = 4  2.45  500 = 4900.
Because F is close to Fc, any significant interpretable contrast will have coefficients close to those
of maximal contrast (where SS for maximal contrast = SSB = 5350).
The maximal contrast has coefficients (cj = Mj - M) of 5, 6, 4, -4, -11, suggesting the following
contrasts (whose SS would be 'close' to those of maximal contrast):
1: 2 2 2 –3 -3 SS(ˆ 1 ) = 4687.5
2: 1 1 1 0 –3 SS(ˆ 2 ) = 4800 (this is the maximal interpretable contrast, ie the
interpretable contrast with largest SS)
3: 1 1 0 0 -2 SS( 3ˆ ) = 4537.5
All other interpretable contrasts will have SS smaller than these three. Hence, no interpretable
contrast can be declared significant, so (in spite of rejection of homogeneity hypothesis) no
meaningful directional inference regarding the effect of treatments on social anxiety can be made.
(d) In this case, given the pattern of means and the nature of the planned contrasts, the
difference in outcome between the Bonferroni and Scheffé analyses is due entirely to power (Bonf
SSc = 3425 is considerably smaller than Scheffé SSc = 4900). The planned contrasts asked the
'right' questions of the data in that the two significant contrasts 1 and 2 were appropriate given
the way the means turned out. 3 was also appropriate (in hindsight) in that the new treatment
means were all higher than the standard treatment mean (although this difference could not be
declared significant by the planned procedure).
For the post-hoc analysis of this data set Scheffé SSc = 4900, and with SSB = 5350, this did not
leave much room to find a significant interpretable contrast. In fact none of the interpretable
contrasts with coefficients close to max could be declared significant (a fact which is established
with the contrast 1 1 1 0 -3). The post-hoc analysis (Scheffé) provides an unrestricted choice of
contrasts and allows for the testing of contrasts that do justice to the pattern of means. However,
because Scheffé is a conservative STP (by virtue of its flexibility) and has a higher SSc, relative to
Bonferroni (in this case), none of the interpretable contrasts could be declared significant (even
though the overall F test was significant).
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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The planned analysis in (a) included a contrast (2) which on a post-hoc basis turned out to be the
maximal interpretable contrast, and so the difference in outcome between the two analyses
comes down to the difference in decision rules. 2 could be declared significant by a Bonferroni
decision rule but not by a Scheffé decision rule. The planned analysis provided a more powerful
test of 2, than if 2 had been examined in the context of a post-hoc analysis.
Q2
(a) For these data, the ANOVA F test is significant (at .05 level) indicating that average compliance
times depend upon the type of exercise. Psychologist A would conclude from the LSD multiple
comparisons that average time spent exercising is higher, by at least practically important amount,
for walking compared to either riding an exercise bike, jogging or aerobics; and higher, but not
necessarily by an important amount, for walking compared to swimming. Swimming leads to
longer average time spent exercising compared to either riding an exercise bike or jogging, but not
necessarily by a practically important amount.
No pairwise difference of practical importance in average time spent exercising is found between
aerobics, jogging, and riding.
The Fisher’s Least Significant Difference procedure (“protected” t-test procedure) is problematic
because it does not control the FWER at . It is an example of a sequential test procedure, where
the first stage (ANOVA F test) is followed by .05-level t-tests. The ANOVA F test controls the Type I
error rate at  for a test of the homogeneity hypothesis; but it does not provide ‘protection’
against inflation of the familywise Type I error rate for the second stage t-tests (on all pairwise
comparisons, unless all population means are homogeneous).
(b) A valid alternative MCP strategy (if only comparisons are of interest) is the Tukey procedure,
for which the ANOVA F test is irrelevant (and even though SPSS would produce an ANOVA F test, it
would not be reported as part of a Tukey analysis).
The Tukey procedure controls the FWER at , and in this case, allows for same directional (and
importance) inference as in (a), except that no directional inference can be made between 2 and
4, and an inference of no practical importance cannot be made for 1 vs 5.
(c) As expected, average time spent exercising is highest for walking compared to average of
other conditions (B1), and this difference is of practical importance. Further, compliance is greater
for swimming compared to average of other conditions (not including walking; B2), but this
difference may not be of practical importance. Differences in compliance times between riding,
jogging and aerobics are not of practical importance.
Advantage of orthogonal contrasts – parsimonious (account for all between group variability in
smallest number of contrasts) and avoids contradictions and redundancies in inference. PCER
allows for greater power/precision. Similar to Tukey, the analysis allows for an inference of
practical importance (B1), as well as an inference of no practical importance (for B3, B4).
Disadvantage compared to Tukey – although analysis in (c) allows only for a single inference of
practical importance (that walking leads to greater compliance when compared to exercise times
pooled across other exercise types), the analysis of four orthogonal contrasts doesn’t allow us to
know whether walking is better than each of the other exercise types (which is something a
pairwise comparisons analysis can tell us).
Overall, the end result is much the same between (b) and (c); either analysis method identifies
that walking is better than any other exercise type (either pooled, as in c; or separately, as in b).
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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Q3 (a) Calculations for ANOVA Summary Table
2 = JK(n – 1) = 3 4 10 = 120; MSE = SSE/2 = 4246/120 = 35.383
SS(A) = 11  4(12 + 0 + -12)= 88; MS(A) = 88/2 = 44
SS(B) = 11  3(22 + 12 + -12+ -22) = 330; MS(B) = 330/3 = 110
MS(AB) = 1782/6 = 297
F(A) = 44/35.383 = 1.244, F(B) = 110/35.383 = 3.109, F(AB) = 297/35.383 = 8.394
SOURCE SS df MS F
A 88 2 44.000 1.244
B 330 3 110.000 3.109
AB 1782 6 297.000 8.394
ERROR 4246 120 35.383
TOTAL 6446 131
A: Fc = F 05;2, 120 = 3.07 F(A) < 3.07, non-significant A main effect.
B: Fc = F 05;3, 120 = 2.68 F(B) > 2.68, B main effect significant.
AB: Fc = F 05;6, 120 = 2.17 F(AB) > 2.17, AB effect significant.
Conclude: Averaged across drug factor, eating disorder behaviour differs, on average, across levels
of the treatment factor (B main effect); in addition, the nature (and magnitude) of the treatment
effect on behaviour depends on the type of drug condition (AB interaction).
(b) Scheffe STP for B and AB contrasts.
B: SSc = 3  2.68  35.383 = 284.48
Coefficients of maximal B main effect contrast (Mk – M) are: 2 1 -1 -2 and suggest the
interpretable contrast B1 = 1 1 -1 -1.
[Note: We can calculate SS(B1) using either marginal means (which is quicker by hand and shown
below) or cell means approach.]
1
ˆ B = 30 + 29 – 27 – 26 = 6; SS(B1) = 11 3(6)
2/4 = 297 > SSc = 284.48
B1 significant: Averaged across drug factor, receiving a behavioural treatment leads to lower level
of eating disorder behaviour on average than not receiving a behavioural treatment.
[Note: B1 is the only interpretable B main effect contrast that can be declared significant. The next
contender is 1 0 0 -1 with SS = 264. Even if 1 0 0 -1 had been significant, including it in the analysis
would not really add anything to the inference provided by B1. Without any further calculation, we
can assert that no other B main effect contrast orthogonal to B1 can be declared significant, and so
B1 captures the ‘bulk’ of the B main effect.]
AB: SSc = 6  2.17  35.383 = 460.687
Coefficients of maximal AB contrast (Mjk – Mj – Mk + M)
4 3 -3 -4
2 1 -2 -1
-6 -4 5 5
suggest the interpretable AB contrast, A1 (1 1 -2) with B1 (1 1 -1 -1).
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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1 1 -1 -1 [Note: since tests required here
not CI, no need for interaction
scaling.]
1 1 1 -1 -1
1 1 1 -1 -1
-2 -2 -2 2 2
1 1
ˆ A B = (35 + 32 + 33 + 30) – 2(23 + 24) – (25 + 25 + 23 + 25) + 2(31 + 30) =60
SS(A1B1) = 11(60)2/24 = 1650 > 460.687.
Table of Means (averaged across collapsed cells to reflect A1B1):
b1,b2 b3,b4
a1,a2 32.5 24.5
a3 23.5 30.5
The direction of the drug effect (whether receiving a drug increases or decreases eating disorder
behaviour compared to a placebo) depends upon whether treatment is behavioural or non-
behavioural. Receiving a behavioural treatment leads to a better outcome with an active drug than
a placebo, whereas receiving a non-behaviour treatment leads to a better outcome with a placebo
rather than an active drug.
ie Receiving a drug enhances the effectiveness of the behavioural treatment, but inhibits the
effectiveness of the non-behavioural treatments in reducing eating disorder behaviour.
[Note: A1B1 (with SS = 1650) accounts for most of the AB effect (SS = 1782), and any AB contrast
orthogonal to A1B1 cannot be declared significant.]
Alternatively, the AB contrasts: A2 (1 0 -1) with B1, and A3 (0 1 -1 ) with B1 are also suggested by
Mjk-Mj-Mk+M, and both A2B1 (SS = 1589.5) and A3B1 (SS = 929.5) are significant. Substituting
these two AB contrasts for A1B1 would allow, perhaps, a ‘cleaner’ interpretation, whereby
receiving either Drug X or Drug W enhances the positive effect of behavioural treatments (and
inhibits the positive effect of the non-behavioural treatments).
[Further note: The ‘open ended’ nature of this question (“carry out tests on any contrasts you think
appropriate”) could distract some students into spending a lot of time carrying out unnecessary
calculation for part (B). In fact, the pattern of means is quite adequately accounted for by two (or
three) contrasts only. More contrasts could be included in the analysis, however, they would not
really add to the story conveyed by B1 and A1B1 (or A2B1 and A3B1).]
(c) Here are two possibilities:
(i) A1 ( ½ ½ -1) with B1 ( ½ ½ -½ -½) was found significant in Part B.
The cell coefficients for A1B1 (interaction scaling) are
½ ½ -½ -½
½ ¼ ¼ -¼ -¼
½ ¼ ¼ -¼ -¼
-1 -½ -½ ½ ½
The sample value of A1B1 (interaction scaling) is
= [ (35 + 33 + 32 + 30)/4 – (25 + 23 + 25 + 25)/4] – [(23 + 24)/2 – (31+ 30)/2]
= [32.5 – 24.5] – [23.5 – 30.5] = 8 – (-7) = 15
SEA1B1 = 2.197; Scheffe CC = √(6  2.17) = √13.02 = 3.608
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
21
95% post hoc SCI for A1B1: Lower limit = 15 – (2.197  3.608) = 15 – 7.927 = 7.073
Upper limit = 15 + (2.197  3.608) = 15 + 7.927 = 22.927
(ii) A2 ( 1 0 -1) with B1 ( ½ ½ -½ -½) was found significant in Part B.
The cell coefficients for A1B1 (interaction scaling) are
½ ½ -½ -½
1 ½ ½ -½ -½
0 0 0 0 0
-1 -½ -½ ½ ½
Sample value of A2B1 is = [ (35 + 33)/2 – (25 + 23)/2] – [(23 + 24)/2 – (31+ 30)/2]
= [(34 – 24) – (23.5 – 30.5)] = 10 – (-7) = 17
SEA2B1 = 2.5366; Scheffe CC = √(6  2.17) = √13.02 = 3.608
95% post hoc SCI for A2B1: Lower limit = 17 – (2.536  3.608) = 17 – 9.15 = 7.85
Upper limit = 17 + (2.536  3.608) = 17 + 9.15 = 26.15
Q4 (a) Contrast coefficient vectors for PSY input file, given the following order of cells:
a1b1 a1b2 a1b3 a2b1 a2b2 a2b3 a3b1 a3b2 a3b3 a4b1 a4b2 a4b3
A1 1 1 1 1 1 1 1 1 1 -3 -3 -3
A2 2 2 2 -1 -1 -1 -1 -1 -1 0 0 0
A3 1 1 1 0 0 0 -1 -1 -1 0 0 0
A4 0 0 0 1 1 1 -1 -1 -1 0 0 0
B1 2 -1 -1 2 -1 -1 2 -1 -1 2 -1 -1
B2 0 1 -1 0 1 -1 0 1 -1 0 1 -1
A1B1 2 -1 -1 2 -1 -1 2 -1 -1 -6 3 3
A1B2 0 1 -1 0 1 -1 0 1 -1 0 -3 3
A2B1 4 -2 -2 -2 1 1 -2 1 1 0 0 0
A2B2 0 2 -2 0 -1 1 0 -1 1 0 0 0
A3B1 2 -1 -1 0 0 0 -2 1 1 0 0 0
A3B2 0 1 -1 0 0 0 0 -1 1 0 0 0
A4B1 0 0 0 2 -1 -1 -2 1 1 0 0 0
A4B2 0 0 0 0 1 -1 0 -1 1 0 0 0

(b) Planned, FWER contrast analysis
Bonferroni decision rule Reject H0:  = 0 if F() > contrast Fc, where
A: contrast Fc = F.05/4, 1, 120 = 6.43 B: contrast Fc = F .05/2, 1, 120 = 5.15
AB: contrast Fc = F.05/8, 1, 120 = 7.75. Significant contrasts: A1, A3, A4, B1 and A1B1.
Directional inferences:
A: Averaged across the Diet/Exercise factor, greater average improvement for children receiving a
treatment than not (A1), and for those receiving either behavioural treatment (A3) or one-to-one
counselling (A3) compared to family counselling.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
22

B1: Averaged across the Treatment factor, children who receive a combined Exercise/Diet
program show greater average improvement compared to children receiving a single program.
A1B1: The magnitude of the B1 effect (advantage of a combined Exercise/Diet program over a
single program) is greater for children who do not receive a psychological treatment, than for
children who do.
(c) 1 1 1( 1) 1( 2, 3)ˆ ˆ ˆA B A b A averaged across b b  = −
where 11 21 31
1( 1) 41
32 30 31
ˆ 32 1
3 3
A b
M M M
M
+ + + +
= − = − = −
12 22 32 13 23 33 42 43
1( 2, 3)
ˆ
6 2
32 31 25 29 29 22 23 20
28 21.5 6.5
6 2
A b b
M M M M M M M M

+ + + + + +
= −
+ + + + + +
= − = − =
thus, 1 1ˆ 1 6.5 7.5A B = − − = −
Note: The A1B1 coefficients associated with the above calculation are the produce of the A1
coefficient vector (⅓ ⅓ ⅓ -1) with the B1 coefficient vector (1 -½ -½)
With this method you get the same answer as above:
1 1
1 1 1
ˆ (32 30 31) 32 (32 31 25 29 29 22) (23 20)
3 6 2
31 32 28 21.5 7.5
A B = + + − − + + + + + + +
= − − + = −
(d) The only (unequivocal) CI inference of clinical importance follows for B1, ie the improvement
advantage of a combined Exercise/Diet program over a single program is at least of clinical
importance.
For A1, A3, and A4, the average improvement shown by children who receive a treatment
(compared to those who don’t), or who receive a behavioural treatment or one-to-one counselling
compared to family counselling, may or may not be of clinical importance.
The difference in the magnitude of the B1 (Exercise/Diet) effect for those receiving treatment
compared to those not, may be a clinically important effect (and could be quite large) but this is
not established by the CI.
(e) In the above 4 x 3 design, a separate CC is required for each family of contrasts (A, B and AB
contrasts). Further, the default mean difference scaling is not appropriate for AB contrasts.
Consequently, a single run through PSY, where all 14 contrasts are included in the PSY input file
and the “Bonferroni-t” option chosen, with default Mean Difference scaling, would result in CI
output with a single CC based on k = 14 (rather than different CCs for A, B and AB) and
inappropriate scaling for the AB contrasts.
To obtain appropriate CI output from PSY at least 3 runs are required.
ie 1A1B1 B1
1 -½ -½
⅓ ⅓ -
1
6 - 16
A1 ⅓ ⅓ -
1
6 - 16
⅓ ⅓ -
1
6 - 16
-1 -1 ½ ½
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
23
1. One run for A main effect contrasts (either including only A contrasts in the input file
and choose Bonferroni-t option; or keep all contrast in the input file and enter User
Supplied CC = 6.43 =2.536)
2. One run for B main effect contrasts (same method as above, except CC = 5.15 =
2.269).
3. One run for AB contrasts (same method as above, except CC = 7.75 = 2.784, AND
choose Interaction scaling option, Between Order = 1).
Q5 (a) (i) The analysis is planned and the number of comparisons (k = 3) is fewer than the set of
all comparisons (which would be 6 in this case). Test procedures that are valid (control the FWER
at ) are Bonferroni, Scheffe and Tukey.
However the most efficient test procedure (in this case) is Bonferroni (because k < J-1 and k is less
than 6). This statement can be verified by comparing CC’s for these 3 procedures:
Bonferroni CC =  F.05/3, 1, 40 = 6.24 = 2.498
Scheffe CC = (1  F.05, 3, 40 ) = (3 2.84) = 2.919
Tukey CC = q*.05, 4, 40 = 2.68 ie Bonferroni CC is smallest.
Decision Rule: Reject H0:  = 0 if F() > Bonferroni contrast Fc = F.05/3, 1, 40 = 6.24.
(or alternatively, if SS(ˆ ) > SSc = F.05/3, 1, 40  MSE = 6.24  286.2 = 1785.89)
None of 3 comparisons can be declared significant (all F’s < 6.24), so no directional inference can
be made regarding the effect of either Treatment (Education + practice, Education only or Writing
Task) compared to the control condition on average Similarity Index (SI) scores.
(ii) The smallest difference of practical importance is 10 DV units.
In line with the test output for which no directional inference could be made for each of the 3
comparisons, the 95% simultaneous CI limits do not establish practically important treatment
effects. The CI limits for B1 and B2 indicate that, compared to the Control condition, the Education
program (either with Practice, B1; or without Practice, B2) may reduce average SI scores by as
much as a practically important effect (lower limits of -36 and -32, respectively, indicate the
possibility of a reduction of more than 10%). Alternatively, the treatment effect size may only be a
trivial reduction or even a trivial increase in average SI scores (upper limits of 0. 03 and.4.03
respectively).
For B3, the CI limits indicate the difference in average SI scores between the Writing Task and the
Control condition is estimated with poor precision and could be anything (from a trivial to an
important effect, in one or the other direction).
(b) (i) Post hoc contrast analysis, hence only Scheffe procedure is appropriate.
Decision Rule: Reject H0:  = 0, if F() > Scheffe contrast Fc = 1  F.05, 3, 40 = 3 2.84 = 8.52
(alternatively, Reject H0:  = 0, if SS(ˆ ) > SSc = 8.52  286.2 = 2438.42)
Coefficients of maximal contrast are Mj – M, where M = 108/4 = 27.
M1 – M = 16 – 25.5 = -9.5
M2 – M = 20 – 25.5 = -5.5
M3 – M = 32 – 25.5 = 6.5
M4 – M = 34 – 25.5 = 8.5
Coefficient vector is [ –9.5 –5.5 6.5 8.5]
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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Coefficients of maximal contrast suggest following interpretable contrast [ –1 –1 1 1].
or [1 1 –1 –1]. Applying the latter coefficients:
ˆ 16 20 32 34 30 = + − − = −
211( 30)
ˆ( ) 2475
4
SS 
−
= = > SSc = 2438.42
Can reject H0 for this contrast. Receiving the Education program (averaged across those who
receive Practice and those who don’t) leads to reduced average SI scores compared to not
receiving the Education program.
(ii) Mean difference scaling [½ ½ –½ –½], ˆ 15 = − and SE = 5.101 (value given in test paper)
Scheffe CC = (1  F.05, 3, 40 ) = (3 2.84) = 2.919.
95% Scheffé simultaneous CI limits for this contrast:
  –15  (2.919  5.101)
 –15  (14.89)
 ( –29.89, –0.11)
The CI indicates that SI is reduced for those who receive the Education program (compared to
those who don’t); however, the practical importance of this effect is not established by the CI.
(iii) A plausible set of contrasts that accounts for all of SSB (ie J – 1 orthogonal contrasts), and that
includes the contrast 1 1 -1 -1, is:
1: 1 1 -1 -1
2: 1 -1 0 0
3: 0 0 1 -1
(c) The planned analysis in (a) was restricted to comparisons comparing each treatment with the
control condition. The analysis in (b) was unrestricted and thus the psychologist was able to
include in the analysis a complex contrast that best reflected the pattern of differences between
the means. The pattern of sample means indicated two subsets of means: one comprising M1 and
M2, and the other comprising M3 and M4. In other words, the two education programs had a
similar impact on SI scores (similar means) as did the two other conditions (writing task and
control).
In this case, the complex contrast in (b) that best reflected the pattern of means could be
declared significant by a Scheffe (post hoc) procedure, whereas none of the comparisons in (a)
could be declared significant by the Bonferroni procedure (even though the Bonferroni procedure
was the most efficient for the planned analysis). The reason for the difference in outcome (of
these two analyses) is not to do with difference in power (or precision) of Bonferroni procedure
compared to Scheffe procedure but to do with the difference in power (and precision) afforded a
complex contrast rather than a comparison (in this particular case).
A more powerful test of the effectiveness of the Education programs was accomplished by
pooling participants’ SI scores across the two Education conditions and comparing these with the
remaining participants’ SI scores (22 participants vs 22 participants); rather than comparing one
type of Education treatment with the control condition (11 participants vs 11 participants). This
complex contrast was suggested by the pattern of means (and coefficients of maximal contrast)
Q6
(a) Scheffé contrast F critical value 3F.1426; 3, 36 = 3  1.927 = 5.781. CC = √3 × .1426;3,36 = 2.404
NOTE: Unlike a single-factor ANOVA-model analysis of the data (which has the same summary
table), this analysis is restricted to factorial contrasts. The F-STP associated with the above F test
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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must use the same critical F value for tests on all implied null hypotheses, including those on
contrasts.
(b) [BetweenContrasts]
1 1 -1 -1 A(drug)
1 0 -1 0 A(b1)
0 1 0 -1 A(b2)
1 -1 1 -1 B(psyc)
1 -1 0 0 B(a1)
0 0 1 -1 B(a2)
1 -1 -1 1 AB
(c) Significant contrasts: A, A(b2), B(a2), AB
Those receiving drug have lower levels of depression than those receiving placebo, when averaged
across the treatment factor (A) or when combined with CBT [A(b2)] and the magnitude of this drug
simple effect is greater than when combined with Control condition (AB). Similarly, receiving CBT
lowers depression compared to Control condition in combination with drug rather than placebo
[B(a2) and AB].
(d) (i) The F STP for the single family of all factorial contrasts has a FWER (or EWER) of * = 1 – (1-
.05)3 = .1426. Post-hoc SCIs commensurate with the F STP have a non-coverage error rate of .1426,
which corresponds to a confidence level of 100(1-*)% = 100  .8574 = 85.74%.
(ii) CI inference – smallest difference of practical importance is 5 DV units.
Positive impact of drug in lowering depression (compared to placebo) is an important effect,
either averaged across treatment factor (A) or when combined with CBT [A(b2)likely to be a very
large effect]. However, the importance of difference in magnitude of drug effect in combination
with CBT compared to in combination with Control (AB) is not established (it may be important).
Positive impact of CBT (compared to Control) in lowering depression is not established as
important in combination with the drug (although this effect may be important).
(e) (i) Standard Analysis – Fc = 4.116 (interpolating from Table; or use F.05; 1, 30 -= 4.17).
Significant contrasts: A, B and AB. Inference – same directional inference as above, as well as CBT
lowers depression compared to control (averaged across drug factor).
(ii) Even though the contrast Fc = 5.781 (for analysis in (b)) is larger than F.05; 1, 36 = 4.116 (and
hence analysis in b is less powerful than standard analysis), the all factorial contrasts analysis is
worth considering as an alternative to the standard analysis. The all factorial contrasts analysis
provides direct inferences on simple effect contrasts (which in this case provide more information
about the effects of two factors, than does standard analysis, see below). The larger contrast Fc is
the price to be paid to access inferences for simple effects.
The standard analysis establishes a significant difference between A(b1) and A(b2) [and similarly
between B(a1) and B(a2)], implied by the significant AB contrast. However, from the standard
analysis alone, we do not know the magnitude (nor statistical significance) of each simple effect.
From the simple effects analysis we can infer:
A(b2): Genuine anti-depressant medication produces a clinically important positive effect in
combination with CBT, compared to a placebo.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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A(b1): Without CBT, it is unclear whether genuine anti-depressant medication produces a positive
effect (it may produce a clinically important effect, however it may be no more effective than a
placebo).
(f) Note that for a planned analysis, * is a slightly larger value than that for the F-STP (.1426)
because .15 is the per-experiment error rate (PEER) associated with a standard planned analysis,
and the Bonferroni-t procedure controls the PEER exactly. (Note: EWER < PEER when k > 1)
In this case, the Bonferroni-t contrast F critical (5.785) is only marginally larger than the Scheffé
contrast F critical (5.781), and so there is no increase in precision or power (in any substantial
sense) and no advantage to using the Bonferroni-t procedure for a planned analysis.
Q7
(a) The experimenter’s analysis is misleading because the outcome (rejection of homogeneity
hypothesis) suggests that improvement depends (in some way) on drug/treatment levels.
However, examining the ‘simple effect’ follow-up contrasts in the context of a single factor post-
hoc analysis did not allow for any further inference to be made. No directional inference could be
made for the Drug effect combined with either of the 3 treatment conditions.
The manner in which the experimenter has analysed the data has not capitalised on statistical
power. The experimenter has carried out a post-hoc analysis appropriate for a single factor
between-subjects design, with J = 6. However, given the nature of the experimental conditions
(and the questions of interest to the experimenter) a more appropriate and efficient way to
conceptualise the research design is as a 2  3 between-subjects factorial design. A factorial
analysis of the data that allows for Drug simple effect contrasts will provide more power for
hypothesis tests (and greater precision for CIs).
For example, the contrast Fc for a post-hoc analysis of a single all-factorial-contrasts family would
be contrast Fc = 5  F.1426; 5, 60 and this value is smaller than the value for a single factor analysis,
namely contrast Fc = 5  F.05, 5, 60. The reason we know this to be the case is because F.1426; 5, 60 must
be smaller than F.05, 5, 60 = 2.37. Similarly, an A(B) analysis would utilise a contrast Fc = 3  F.0975; 3, 60
and this value would be smaller than contrast Fc = 5  F.05, 5, 60.
As well, a factorial analysis of the data allows for AB contrasts to be included which address
whether the magnitude of the drug effect differs across treatment conditions (important
questions to consider, given the nature of the design).
(b) (i) What B main effect coefficient vectors have been used to define the AB contrasts?
Coefficients referring to levels of Factor B (Treatment)
b1 (Behavioural) b2 (Counselling) b3 (Control)
B1 1 -1 0
B2 1 0 -1
B3 0 1 -1
Coefficients referring to cells:
a1b1 a2b1 a1b2 a2b2 a1b3 a2b3
B1 1 1 -1 -1 0 0
B2 1 1 0 0 -1 -1
B3 0 0 1 1 -1 -1
(ii) For nominal  = .05, the critical value for this analysis is Fc = F*, 1, 2 = F.0975, 3, 60 = 2.199. Why
is * = .0975?
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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The post-hoc factorial analysis in part (b) defines a single A(B) family of factorial contrasts that
include A main effect contrast, A(b) simple effect contrasts and AB interaction contrasts. As this
single (non-standard) family contains two standard families A and AB, each of which would have a
FWER of .05 in a standard analysis. Setting FWER = .05 for this single non-standard family would
lead to an unnecessarily conservative analysis. The algorithm for defining FWER for this non-
standard A(B) family comes from the expression for the experimentwise error rate (EWER) across
two standard families (A and AB, in this case), namely 1 – (1 – .05)2 = .0975. In other words, the
FWER for the A(B) family is set at the same level as the EWER for two standard families.
and why is 1 = 3?
Short answer: 1 = K(J-1) = 3(1) = 3 (but this doesn’t really answer the ‘why’ part).
Longer answer: For the A(B) effect, SS[A(B)] = SS(between cells) – SS(B), that is, SS for A(B) effect
is what’s left over from SS between cells when we take away the SS for B effect.
Thus the degrees of freedom for the A(B) effect is what’s left over from between cells df when we
take away df for B effect. ie 1 = dfA(B) = dfcells – dfB = 5 – 2 = 3.
Algebraically, dfA(B) = (JK – 1) – (K -1) = JK – K = K(J-1)
(iii) Scheffé contrast Fc = 1 × Fc = 3 × 2.199 = 6.597. Significant contrasts are A(b1), AB2 and AB3.
For those receiving behavioural treatment, average improvement is greater in combination with
drug than with placebo [A(b1)], and size of this drug effect (for behavioural treatment condition) is
greater than for control condition (AB2). Although a drug effect is not established for counselling
condition [A(b2)] nor control condition [A(b3)], there is a difference between the counselling and
control conditions in the magnitude of the drug effect (AB3). From the cell means – we can infer
that Drug X leads to greater improvement (compared to placebo) when combined with
counselling, but leads to lower improvement when combined with control condition.
(c) For the analysis in (a) the one-way Scheffé contrast Fc = 11.85 (appropriate for a J = 6
between-subjects design with  = .05, 1 = 5 and 2 = 60). However, for the factorial analysis in (b),
the Scheffé contrast Fc = 6.597 (for  = .0975, 1 = 3 and 2 = 60), and hence the factorial analysis
has more power to detect drug (and treatment) effects.
With regard to the inferences of interest to the experimenter, none of the three contrasts in (a)
could be declared significant by the one-way Scheffé procedure (applicable for J = 6). However,
the smaller contrast Fc for the factorial analysis in (b) allowed for a directional inference to be
made for A(b1), indicating a positive drug effect when combined with behaviour treatment.
The factorial analysis also allowed for two more inferences, for AB2 and AB3, indicating that the
size of the drug effect was greater for behavioural treatment than the control condition, and
greater for counselling than control condition. Interestingly, had the analysis in (a) included the
same contrasts as in (b), only AB2 would have been significant.
Q8 (a) Between Ss main effect contrasts: Fc = F.05/2, 1, 57 = 5.3 (PSY probability calculator) or Fc 
F.05/2, 1, 50 = 5.34 (from Tables).
Within Ss main effect contrasts: Fc = F.05/3, 1, 57 = 6.085 (PSY probability calculator) or Fc  F.05/3, 1, 50
= 6.14 (from Tables).
B  W interaction contrasts: Fc = F.05/6, 1, 57 = 7.472 (PSY probability calculator) or Fc  F.05/6, 1, 50 =
7.44 (from Tables).
The analysis yields significant contrasts for B1, W1 and W2, B1W1 and B1W2.
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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Averaged across BAC levels, average driving errors decrease in a constant manner as age increases
(B1).
Averaged across age levels, average driving errors increase in a constant manner as BAC increases
(W1).
However, the magnitude of the linear BAC effect decreases by a constant amount as age increases
(B1W1). In other words, the amount by which errors increase across BAC levels decreases by a
constant amount for each 20 year increment in age. The consequence of this is that alcohol has a
bigger impact on younger participants because the increase in errors across BAC levels occurs
more rapidly for younger participants.
Averaged across age levels, driving errors increase more rapidly as BAC levels increase (W2,
quadratic trend), that is, driving errors increase across BAC levels at an increasing rate. The
increment in driving errors between BAC levels of .03 and .06 is much greater than between 0 and
.03. Similarly, the increment in errors between BAC levels of .06 and .09 is much greater than
between 0.03 and 0.06.
Further, the size of this quadratic trend across BAC levels decreases by a constant amount with
age (B1W2). That is, the increasing rate of increase of driving errors across BAC levels becomes less
pronounced (by a constant amount) as age increases. In other words, alcohol has a stronger effect
on younger drivers – the faster rate in which driving errors increase across BAC levels is much
steeper for younger drivers than older drivers.
(b) (i) The factorial contrasts included in the PSY analysis are B and W main effect contrasts, W(b)
simple effect contrasts, and BW interaction contrasts. The PSY input file makes no provision for
B(w) simple effects contrasts. We can define two families for this analysis: B main effect family
(FWER = .05), and non-standard simple effects family W(B) with FWER = .10 containing W, W(b)
and BW contrasts. Valid contrasts from the PSY Summary Table are:
B main effect contrasts: B1, B2.
W main effect contrasts: W1, W2, W3.
W simple effect contrasts: B3W1, B4W1, B5W1, B3W2, B4W2, B5W2, B3W3, B4W3, B5W3.
BW interaction contrasts; B1W1, B1W2, B1W3, B2W1, B2W2, B2W3.
Output is for B3, B4 and B4 is meaningless.
(ii) For B family, k = 2 and Fc = F.05/2, 1, 57 = 5.3 (PSY probability calculator) or Fc  F.05/2, 1, 50 = 5.34
(from Tables).
For W(B) family, k = 18 and Fc = F.10/18; 1, 57 = F.05/9; 1, 57 = 8.309 (from PSY) or Fc  F.05/9, 1, 50 = 8.40
(from Tables).
(iii) Significant contrasts with same directional inferences as in part (a) are B1, W1, W2, B1W1 and
B1W2.
Significant simple effect contrasts:
B3W1 = W1(b1), B4W1 = W1(b2), B5W1 = W1(b3). The significant positive linear trend in driving
errors across increasing amounts of alcohol is evident for each age group.
B3W2 = W2(b1). The significant quadratic trend in driving errors across increasing amounts of
alcohol is evident for 20 year old age group (but not for older age groups).
The simple effects analysis allows us to see that the significant B1W2 interaction is being driven by
the W2 quadratic trend for younger drivers, but not for older drivers. Whilst cell means indicate a
quadratic pattern across BAC levels for each age group, we are only able to make a directional
inference (that errors increase at an increasing rate across BAC levels) for 20 year olds. The B1W2
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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contrast implies that the W2 effect is not consistent across levels of B, and test outcomes for the
W2(b) simple effect contrasts verify this fact.
The test outcomes of W1(b) contrasts do not allow us to verify the nature of the B1W1 interaction
because we have obtained a significant test outcome for each simple effect contrast and we can
make (at best) a directional inferences for each. We would need interval estimates of each simple
trend effect size in order to provide insight into the nature of the B1W1 effect (beyond that
indicated by the pattern of means).
Q9 (a) Planned analysis controlling FWER = .05, both Bonferroni and Scheffe procedures are valid
BUT since k = 3 = J – 1, Bonferroni contrast Fc will be smaller (necessarily) than Scheffe contrast
Fc, so use Bonferroni decision rule:
Reject H0:  = 0 if F() > F.05/3, 1, 60 = 6.07. B1 significant (FB1 = 18.824 > 6.07), but not B2 and B3
(F’s < 6.07).
Directional inference for B1: Average attitude measure is higher, indicating a more favourable
attitude towards LGBTs, after watching video interviews with LGBT survivors of hate crimes (with
or without real-life contact) compared to participating in an anger management program.
Unable to make directional inference regarding the impact on attitude of adding an educational
component to the anger management program (B2) or of adding a real-life contact component to
the video program (B3).
(b) B1: The size of the video program effect (more favourable attitude from watching video that
from anger management program) may or may not be clinically important.
B2 and B3: The effect of adding an educational component to the anger management program or
the effect of adding a real-life component to the video program may have a zero or trivial effect,
or could have a clinically important effect (in one or the other direction). CIs too imprecise to be
informative.
(c) c1c2 = (1  1) + (1  -1) + (-1  0) + (-1  0) = 1 - 1 = 0
c1c3 = (1  0) + (1  0) + (-1  1) + (-1  -1) = -1 + 1 = 0
c2c3 = (1  0) + (-1  0) + (0  1) + (0  -1) = 0
(d) Planned, PCER = .05. Contrast Fc = F.05, 1, 60 = 4.00. B1 significant, B2 and B3 n.s. Same
directional inference can be made as in Q1 (a). CC =  F.05, 1, 60 = 4.00 = 2.
Individual 95% CI limits (can use sample value and SE given in PSY output):
B1: 1  -10  (2.305  2) = -10  (4.61) = (-14.61, -5.39)
B2: 2  -3  (3.26  2) = -3  (6.52) = (-9.52, 3.52)
B3: 3  (-9.52, 3.52) same as B2
B1: The size of the video program effect (more favourable attitude from watching video that from
anger management program) is clinically important.
B2 and B3: The effect of adding an educational component to the anger management program or
the effect of adding a real-life component to the video program may be a trivial effect (in one or
the other direction) but could be a clinically important effect (favouring the combined program).
(e) The difference in outcome between the two analyses is due to the different choice of error
rate unit. The first analysis controlled the FWER at .05, whereas the second analysis controlled the
PCER at .05 (and since the planned contrasts were orthogonal both approaches were valid).
PSYC3001 Research Methods 3 – Practice for Final Exam Dr Melanie Gleitzman and Dr Sonny Li
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A PCER analysis always provides more powerful tests and more precise (narrower) CIs than a
FWER analysis (in this case, FWER CC = 6.07 = 2.46 whereas PCER CC = 4 = 2). Although no
difference was found between the two analyses in test outcomes (or directional inferences that
followed), a difference was apparent in the CI inference that could be made.
In particular, for B1, the greater precision afforded by the individual 95% CI over the simultaneous
95% CI allowed for a stronger inference of clinical importance (rather than a weaker inference of
‘may or may not be clinically important’).