PSY2PRM ASSIGNMENT 2 - ANOVA
A Twelve to Fifteen Word Title Goes Here and Includes the Contention of Essay/Report
Melissa Middleton
19018793
Submitted in partial fulfilment of the requirements for PSY2PRM
School of Psychological Science
La Trobe University
2018
PSY2PRM ASSIGNMENT 2 - ANOVA
DATA
Electronic gaming (pokies) is a popular gambling pursuit. The return rate is about 85c for
every dollar gambled, and there are many ways by which this payout rate can be achieved
(Great…for the pokie owner obviously). One could program the machine to deliver many
small wins or a few big wins within a very large set of spins.
Scenario: A pokie machine manufacturer hired you, a psychologist, to find out whether many
small wins or a few big wins is more exciting to the gambler. According to the Small-Win
payout theory, many small wins would be more effective in keeping the level of excitement
elevated (so people keep playing). On the other hand, according to the Big-Win payout
theory, a few big wins could be more exciting and reinforcing than many small wins which
may be viewed as boring.
The manufacturer also thinks that women might prefer many small wins to a few big wins but
men might prefer a few big wins to many small wins. As such, the manufacturer also wants to
know if there are sex differences in people’s excitement levels to these two different payout
schedules. If there is a sex difference, then the manufacturer could build electronic gaming
machines, or even the kinds of games, that appeal specifically to men and women.
So, you went to the dark side (by trying to help an entrepreneur extract $ from people!) and
designed an experiment with 80 participants divided into four equal groups.
Group 1 are 20 men who received many small wins. (M/SW)
Group 2 are 20 men who received a few big wins. (M/BW)
Group 3 are 20 women who received many small wins. (W/SW)
Group 4 are 20 women received a few big wins. (W/BW)
You think that men like to play pokies just as much as women but, just in case, you ask all
participants to rate how much they like the pokies (10-point likert scale- 0= ‘not at all’ to 10 =
‘enormously’). All participants started with 1000 credits on a 5c machine and had to play for
200 spins/turns on two specially programmed versions of the game (many small wins, a few
big wins) in which the outcome is identical at the end of the 200 spins (say, 850 credits
remaining).
Heart rate was recorded at one-minute intervals and, then averaged across the session, to be
used as a score of excitement, where a higher averaged heart rate score is assumed to indicate
a higher level of excitement.
PSY2PRM ASSIGNMENT 2 - ANOVA
Q1 Check your assumption that the sample of men and women do not differ in how
much they like to play the pokies. What statistical test will you use to compare these
means?
(a) Report the test that you have selected, naming the independent and dependent
variables.
(b) Report, in APA format, the results of the test.
An Analysis of Variance (ANOVA) was performed to test for differences between mean
ratings of liking to play the pokies as the independent variable between sex (men and women)
as the independent variable.
The results of the mean ratings of liking to play the pokies between men and women were not
statistically significant, η² = .005, F(1, 78) = 0.404, p =.527.
PSY2PRM ASSIGNMENT 2 - ANOVA
Q2 Let us say your assumption is correct, and you proceed to an analysis of excitement.
Report tests of the assumptions that:
(a) Heart rate (HR) scores are normally distributed within each of the four groups.
(b) The variances of HR are homogeneous between the groups.
The Kolmogorov-Smirnov test results indicate that the assumption of normality of
distribution is tenable for heart rate in each of the four groups.
The Levene test result also indicates that the assumption of homogeneity of variance was also
tenable for heartrate in each of the four groups, F(3, 76) = 1.80, p = .15.
PSY2PRM ASSIGNMENT 2 - ANOVA
Q3 In regard to descriptive statistics:
Construct, in APA format, a table of sample sizes, means and standard deviations of HR
for each group.
Group 1 are 20 men who received many small wins. (M/MSW)
Group 2 are 20 men who received a few big wins. (M/FBW)
Group 3 are 20 women who received many small wins. (W/MSW)
Group 4 are 20 women received a few big wins. (W/FBW)
Table 1
The Sample Size, Mean and Standard Deviation of Mean Heart Rate in Groups
Group
n
M
SD
M/MSW
M/FBW
W/MSW
W/FBW
20
20
20
20
75.50
81.80
86.85
76.35
3.89
6.04
6.68
8.36
Q4 Plot a bar chart with 95% CI, in APA format, of the mean HR of each group. (10
marks)
PSY2PRM ASSIGNMENT 2 - ANOVA
Conduct a test of mean HR between all four groups (i.e., one-way design) (Q.5), with
appropriate post-hoc comparisons (Q.6) between the means (to control the Type I error
rate).
Figure 1. Bar chart of mean heart rate in groups.
Q5 (a) Report the test that you have selected, naming the independent and dependent
variables.
PSY2PRM ASSIGNMENT 2 - ANOVA
(b) Present the ANOVA summary table, in APA format. (10 marks)
A one-way analysis of variance was performed to test for differences between mean heart
rate as the dependent variable and groups as the independent variable
Table 2
Analysis of Variance of Mean Heart Rate Between Groups
Source
Groups
Error
Total
df
3
76
79
SS
1673.45
3153.30
4826.75
MS
557.82
41.49
F
13.44
p
<.001
η²
.35
Q.6 (a) Report the results of the ANOVA, in APA format.
(b) Report on post-hoc comparisons between means.
The results summarized in Table 2 show that differences in mean heart rate (BPM)
between groups were statistically significant, η2 = .35, F(3, 76) = 13.44, p < .001.
PSY2PRM ASSIGNMENT 2 - ANOVA
The Tukey post hoc comparison test indicates that heart rate for the M/MSW and W/FBW
were significantly different from the M/FBW and W/MSW groups. Mean heart rate in
M/MSW and W/FBW groups were not different from one another. Mean heart rate
between M/FBW and W/MSW were not different from one another.
Q7 You had forgot that you could have used a planned comparisons technique, so now you
decide to employ it to specifically address the research questions. Choose a set of contrasts
to test these hypotheses (a, b & c below), and demonstrate that these contrasts are
PSY2PRM ASSIGNMENT 2 - ANOVA
orthogonal to one another, using the mathematical method (note: you are not asked to
conduct the analysis).
(a) Big Wins are more exciting than Small Wins.
(b) Small Wins are more exciting to women than to men.
(c) Big Wins are more exciting to men than to women.
H1
H2
H3
M/FBW W/FBW >M/MSW W/MSW
W/MSW> M/MSW
M/FBW >W/FBW
The selected linear contrasts, where the sum of coefficients sum to zero for this set of three
hypotheses are
M/FBW
W/FBW
1
0
-1
1
0
1
1
2
3
M/MS
W
W/MS
W
-1
1
0
Sum of coefficients
-1
-1
0
0
0
0
Working with pairs of these hypotheses, the products of their corresponding coefficients also
sum to zero
H1*H2
H1*H3
H2*H3
0
-1
0
0
1
0
-1
0
0
1
0
0
Product of coefficients
0
0
0
Q8 Finally, you decided that a two-way design might be more appropriate to demonstrate
the interaction between sex and payout; namely, that women find many small wins more
exciting than a few big wins whereas the opposite is true for men.
PSY2PRM ASSIGNMENT 2 - ANOVA
(a) Report the test that you have selected, naming the independent and dependent
variables.
(b) Present the ANOVA summary table, in APA format.
A 2 x 2 between-subjects ANOVA was performed to heartrate between sex (Male and
Female) in payout (many small wins, few big wins). The dependent variable is excitability
(measured by heart rate). The independent between-subject variables are Sex and Payout.
Table 2
ANOVA Summary Table of Excitability (Heartrate BPM) By Sex (Men, Women) in Payout
Condition (Many Small Wins, Few Big Wins)
Source
df
Sex
Payout
Sex x Payout
Error
Total
1
1
1
76
80
SS
174.05
88.20
1411.20
3153.30
MS
F
p
174.05
88.20
1411.20
41.49
4.20
2.13
34.01
.04
.15
<.001
η ₚ²
.35
.99
.05
Q9 Regardless of the interaction result (whether significant or not), conduct a simple
main effects analysis of sex within each payout, and report on these effects.
In two comparisons of sex (men and women) within each payout condition (many small wins,
few big wins), mean heartrate (bpm) between sex differed significantly within the many small
PSY2PRM ASSIGNMENT 2 - ANOVA
wins condition η ₚ² = .29, F(1, 76) = 31.05, p < .001 and the few big wins condition η ₚ² = .
086, F(1, 76) = 7.16, p < .01.
Q10 Regardless of the interaction result, conduct a simple main effects analysis of
payout within each level of sex, and report on these effects.
In two comparisons of payout conditions (many small wins, few big wins) within each sex
(men and women), mean heartrate (bpm) in payout conditions were significantly different in
men η ₚ² = .11, F(1, 76) = 9.57, p < .01 and women η ₚ² = .26, F(1, 76) = 26.57, p < .001.
PSY2PRM ASSIGNMENT 2 - ANOVA