One Way Within Groups ANOVA A researcher studying people with a fear of public s
ID: 3376225 • Letter: O
Question
One Way Within Groups ANOVA
A researcher studying people with a fear of public speaking assessed their fear of public speaking as a function of the size of the audience. The researcher asked each participant to read a paragraph aloud to three different audience sizes, a small audience (10 people), a medium-sized audience (30 people), and a large audience (100 people). Participants fear levels were assessed after each exposure and were measured on a scale from 0 (no fear) to 30 (extreme fear).
Participants’ Level of Fear when Speaking in front of Audiences of Differing Sizes
Participant
Small Audience
Medium Audience
Large Audience
1
7
15
22
2
16
18
28
3
3
18
26
4
9
13
29
Source
SS
df
s2
F
Between-groups
618.50
Subjects
62.00
Residual
Total
754.00
1) What is the F statistic.
2) What is the F critical value?
3) Calculate the effect size.
4) Perform post-hoc comparisons. What is the HSD value?
5) What should you conclude?
Participant
Small Audience
Medium Audience
Large Audience
1
7
15
22
2
16
18
28
3
3
18
26
4
9
13
29
Explanation / Answer
Solution 1:
Option B is correct.
From excel output, the F-statistics for treatments is 25.25.
Solution 2:
Option d is correct.
Using F-tables, the critical value at a = 0.05 with 2 and 6 degrees of freedom is
F (0.05, 2, 6) = 5.14
Solution 3:
Option a is correct.
Effect size = SS between/SS total
Effect size = 618.50/754
Effect size = 0.82
Solution 4:
Option b is correct.
HSD = q(a, k, n - k)*sqrt(MSE/n)
HSD = q (0.01, 3, 6)*sqrt(12.250/4)
HSD = 9.779*1.75
HSD = 17.01
Solution 5:
Option b is correct.
Participants’ level of fear was significantly greater, on average, when speaking in front of a large audience compared to when speaking in front of small audiences and medium audiences.
EXCEL output
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