Question

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.

Answer 1

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.