3. A researcher begins with a sample of 60 subjects and randomly assigns 12 to each of 5 treatment conditions. Based on his reading of other studies in the area, the researcher predicts that group 3 will obtain a significantly different mean from group 1, and that group 4 will obtain a significantly higher mean than group 1. a) Given the following data (note that some subjects have dropped out) are the researcher's predictions supported with a ≤.01? Group 1 Group 2 Group 3 Group 4 Group 5 n₁ 8 10 10 12 12 X-bar; 43.5 S₁ 5.6 5.4 8.7 b) After collecting and inspecting the data, the researcher decides to perform three more tests. Specifically, he wishes to see whether X-bar3 is significantly different from X-bar2; whether X-bars is significantly different from X-bar2; and whether X-bar4 is significantly greater than X-bar2. Perform whichever statistical analyses are necessary and, if appropriate, use the procedure that allows each comparison to be tested with a ≤.01. 45.2 6.3 61.8 77.3 66.7 7.5

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Answer question 3 Answers: 3 a) 3 vs. 1, t = 5.53, Reject Ho, prediction is supported: group 3 obtained a significantly higher mean score than group 1; 4 vs. 1, t = 10.608, Reject Ho, prediction is supported: group 4 obtained a significantly higher mean score than group 1; b) F = 43.696, Reject Ho, at least 2 means differ significantly; 3 vs. 2, q = 7.583, Reject Ho, the mean scores of groups 3 and 2 differ significantly; 5 vs. 2, q = 9.822, Reject Ho, the mean scores of groups 5 and 2 differ significantly; 4 vs. 2, no test valid because post hoc tests cannot be 1-tailed.
Psychology 2211 Assignment 5.
1. Subjects were randomly assigned to one of four groups in an exploratory study of the effect of different drugs on
motion sickness. The data provided below were subjected to an analysis of variance, resulting in FOBT = 10.0.
n₁ = 8
n₂=7
n3 = 10
n4=7
x-bar₁ = 12.0 x-bar₂ = 6.5 x-bar3 = 13.1 x-bar4 = 8.5
First, determine whether the ANOVA is significant (with a ≤.01), and, if so, determine whether there is a
significant difference between the mean scores of groups 2 and 3, 2 and 4, and 2 and 1, using the post hoc
procedure that allows you to use a ≤.01 for each comparison.
2. Subjects were randomly assigned to one of four treatment conditions. After treatment, the following data were
obtained:
n₁ = 8
n₂ = 10
n3=7
n₁=9
x-bar₁ = 6.5 x-bar2 = 5.5 x-bar3 = 8.75 x-bar4 = 12.0
In addition, the standard deviation of the scores of all 34 subjects was 3.50.
a) Before the experiment, the researcher predicted that group 3 would obtain a significantly higher mean than
group 2, and that there would be no significant difference between the means of groups 1 and 2. Perform the
appropriate test(s) to determine whether these predictions were borne out. (a ≤.05)
b) After the data had been collected, the researcher wished to determine whether there was a significant difference
between x-bar4 and x-bar₁, and between x-bar3 and x-bar₁. Using a ≤.05, perform the necessary test(s) and, when
comparing these means, use whichever valid procedure gives you the smallest critical value.
3. A researcher begins with a sample of 60 subjects and randomly assigns 12 to each of 5 treatment conditions. Based
on his reading of other studies in the area, the researcher predicts that group 3 will obtain a significantly different
mean from group 1, and that group 4 will obtain a significantly higher mean than group 1.
a) Given the following data (note that some subjects have dropped out) are the researcher's predictions supported
with a ≤.01?
Group 1 Group 2 Group 3 Group 4
8
10
10
12
X-bar; 43.5
S₁
5.6
b) After collecting and inspecting the data, the researcher decides to perform three more tests. Specifically, he
wishes to see whether X-bar3 is significantly different from X-bar2; whether X-bars is significantly different from
X-bar2; and whether X-bar4 is significantly greater than X-bar2. Perform whichever statistical analyses are
necessary and, if appropriate, use the procedure that allows each comparison to be tested with a ≤.01.
n₁
45.2
6.3
61.8
5.4
77.3
Group 5
12
66.7
8.7
7.5
Answers
1. 2 vs. 3, q= 6.74, Reject Ho, the mean scores of groups 2 and 3 differ significantly; 2 vs. 4, q=2.04, Do not reject
Ho, there is no evidence for a significant difference between the mean scores of groups 2 and 4; 2 vs. 1, q= 5.62,
Reject Ho, the mean scores of groups 2 and 1 differ significantly.
2. a) 3 vs. 2, t= 2.720, Reject Ho, group 3 obtained a significantly higher mean score than group 2; 1 vs. 2, t=.870,
Do not reject Ho, there is no evidence for a significant difference between the mean scores of groups 1 and 2.
b) F = 12.92, Reject Ho, at least 2 means differ significantly; 4 vs. 1, q = 6.56, Reject Ho, the mean scores of
groups 4 and 1 differ significantly; 3 vs. 1, q=2.68, Do not reject Ho, there is no evidence for a significant
difference between groups 3 and 1.
3. a) 3 vs. 1, t= 5.53, Reject Ho, prediction is supported: group 3 obtained a significantly higher mean score than
group 1; 4 vs. 1, t= 10.608, Reject Ho, prediction is supported: group 4 obtained a significantly higher mean score
than group 1; b) F= 43.696, Reject Ho, at least 2 means differ significantly; 3 vs. 2, q= 7.583, Reject Ho, the
mean scores of groups 3 and 2 differ significantly; 5 vs. 2, q=9.822, Reject Ho, the mean scores of groups 5 and 2
differ significantly; 4 vs. 2, no test valid because post hoc tests cannot be 1-tailed.
Transcribed Image Text:Psychology 2211 Assignment 5. 1. Subjects were randomly assigned to one of four groups in an exploratory study of the effect of different drugs on motion sickness. The data provided below were subjected to an analysis of variance, resulting in FOBT = 10.0. n₁ = 8 n₂=7 n3 = 10 n4=7 x-bar₁ = 12.0 x-bar₂ = 6.5 x-bar3 = 13.1 x-bar4 = 8.5 First, determine whether the ANOVA is significant (with a ≤.01), and, if so, determine whether there is a significant difference between the mean scores of groups 2 and 3, 2 and 4, and 2 and 1, using the post hoc procedure that allows you to use a ≤.01 for each comparison. 2. Subjects were randomly assigned to one of four treatment conditions. After treatment, the following data were obtained: n₁ = 8 n₂ = 10 n3=7 n₁=9 x-bar₁ = 6.5 x-bar2 = 5.5 x-bar3 = 8.75 x-bar4 = 12.0 In addition, the standard deviation of the scores of all 34 subjects was 3.50. a) Before the experiment, the researcher predicted that group 3 would obtain a significantly higher mean than group 2, and that there would be no significant difference between the means of groups 1 and 2. Perform the appropriate test(s) to determine whether these predictions were borne out. (a ≤.05) b) After the data had been collected, the researcher wished to determine whether there was a significant difference between x-bar4 and x-bar₁, and between x-bar3 and x-bar₁. Using a ≤.05, perform the necessary test(s) and, when comparing these means, use whichever valid procedure gives you the smallest critical value. 3. A researcher begins with a sample of 60 subjects and randomly assigns 12 to each of 5 treatment conditions. Based on his reading of other studies in the area, the researcher predicts that group 3 will obtain a significantly different mean from group 1, and that group 4 will obtain a significantly higher mean than group 1. a) Given the following data (note that some subjects have dropped out) are the researcher's predictions supported with a ≤.01? Group 1 Group 2 Group 3 Group 4 8 10 10 12 X-bar; 43.5 S₁ 5.6 b) After collecting and inspecting the data, the researcher decides to perform three more tests. Specifically, he wishes to see whether X-bar3 is significantly different from X-bar2; whether X-bars is significantly different from X-bar2; and whether X-bar4 is significantly greater than X-bar2. Perform whichever statistical analyses are necessary and, if appropriate, use the procedure that allows each comparison to be tested with a ≤.01. n₁ 45.2 6.3 61.8 5.4 77.3 Group 5 12 66.7 8.7 7.5 Answers 1. 2 vs. 3, q= 6.74, Reject Ho, the mean scores of groups 2 and 3 differ significantly; 2 vs. 4, q=2.04, Do not reject Ho, there is no evidence for a significant difference between the mean scores of groups 2 and 4; 2 vs. 1, q= 5.62, Reject Ho, the mean scores of groups 2 and 1 differ significantly. 2. a) 3 vs. 2, t= 2.720, Reject Ho, group 3 obtained a significantly higher mean score than group 2; 1 vs. 2, t=.870, Do not reject Ho, there is no evidence for a significant difference between the mean scores of groups 1 and 2. b) F = 12.92, Reject Ho, at least 2 means differ significantly; 4 vs. 1, q = 6.56, Reject Ho, the mean scores of groups 4 and 1 differ significantly; 3 vs. 1, q=2.68, Do not reject Ho, there is no evidence for a significant difference between groups 3 and 1. 3. a) 3 vs. 1, t= 5.53, Reject Ho, prediction is supported: group 3 obtained a significantly higher mean score than group 1; 4 vs. 1, t= 10.608, Reject Ho, prediction is supported: group 4 obtained a significantly higher mean score than group 1; b) F= 43.696, Reject Ho, at least 2 means differ significantly; 3 vs. 2, q= 7.583, Reject Ho, the mean scores of groups 3 and 2 differ significantly; 5 vs. 2, q=9.822, Reject Ho, the mean scores of groups 5 and 2 differ significantly; 4 vs. 2, no test valid because post hoc tests cannot be 1-tailed.
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