Question

In: Statistics and Probability

Researchers in mental health fields are often interested in evaluating the effectiveness of using food images...

Researchers in mental health fields are often interested in evaluating the effectiveness of using food images to enhance positive mood. Adapting a typical design from such studies, suppose we have participants rate their mood change on a standard self-report affect scale after viewing images of "comfort" foods, fruits/vegetables (F/V), and random non-food images (used as a control group). The results are given in the table at right for this hypothetical study.

Images
Control F/V Comfort
Foods
0 0 3
0 1 2
1 2 3
3 2 5
0 1 0

(a) Complete the F-table. (Round your answers to two decimal places.)

Source of
Variation
SS df MS Fobt
Between
groups
Between
persons
Within
groups (error)
Total


(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05. Select all that apply.)

Participants rated a significantly larger mood change after viewing images of comfort foods compared with the mood change after viewing images of fruits/vegetables. Participants rated a significantly larger mood change after viewing images of fruits/vegetables compared with the mood change after viewing control images. Participants rated a significantly larger mood change after viewing images of comfort foods compared with the mood change after viewing control images. There were no significant differences between any of the groups.

Solutions

Expert Solution

a)

Anova: Two-Factor Without Replication
SUMMARY Count Sum Average Variance
subject 1 3 3 1 3.000
subject 2 3 3 1 1.000
subject 3 3 6 2 1.000
subject 4 3 10 3 2.333
subject 5 3 1 0 0.333
subject 6
Control 5 4 1 1.700
F/V 5 6 1 0.700
comfort foods 5 13 3 3.300
ANOVA
Source of Variation SS df MS F P-value F crit
Rows 16.40 4 4 5.125 0.0241 3.84
Columns 8.93 2 4 5.583 0.0304 4.46
Error 6.40 8 1
Total 31.73 14

a)

Source of
Variation
SS df MS Fobt
Between
groups
8.93 2 4.47 5.58
Between
persons
16.40 4 4.10 5.13
Within
groups (error)
6.40 8 0.80
Total 31.73 14

b)

Level of significance 0.05/3 = 0.0167
Numerator d.f. 3
Denominator d.f. 8
MSE 0.80
t-critical value,t(α/2,df) 3.0158

critical value=tα/2,df √(MSE(1/ni+1/nj))

if absolute difference of means > critical value,means are significnantly different ,otherwise not                      
                      

population mean difference critical value result
µ1-µ2 0.40 1.71 means are not different
µ1-µ3 1.80 1.71 means are different
µ2-µ3 1.40 1.71 means are not different

b)

participants rated a significantly larger mood change after viewing images of comfort foods compared with the mood change after viewing control images.


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