Question

A study was conducted to see how people reacted to certain facial expressions. A sample group of n=36n=36 was randomly divided into six groups. Each group was assigned to to view one picture of a person making a facial expression. Each group saw a different picture, and the different expressions were (1) Surprised (2) Nervous (3) Scared (4) Sad (5) Excited (6) Angry. After viewing the pictures, the subjects were asked to rank the degree of dominance they inferred from the facial expression they saw. (The scale ranged from -10 to 10) The data collected is summarized in the table below.

Surprised	Nervous	Scared	Sad	Excited	Angry
0.20.2	−1−1	1.81.8	00	1.31.3	0.50.5
−1−1	0.20.2	1.91.9	1.71.7	0.80.8	−0.3−0.3
−0.7−0.7	−2−2	0.70.7	−1.3−1.3	0.60.6	1.21.2
0.90.9	−1.4−1.4	−2−2	0.40.4	−2−2	−0.8−0.8
0.40.4	1.11.1	−0.3−0.3	0.20.2	1.61.6	−1.1−1.1
00	1.71.7	−0.0999999999999999−0.0999999999999999	1.41.4	−0.0999999999999999−0.0999999999999999	1.11.1

Complete the following ANOVA table

Source	df	SS	MS	FF
Expressions
Error
Total

Answer 1

I input the data set in MS Excel and use the "Anova: Single Factor" option under Data > Data Analysis to carry out this one way Anova analysis and complete the following Anova table. The output is given below.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Surprised	6	-0.2	-0.0333	0.4987
Nervous	6	-1.4	-0.2333	2.1547
Scared	6	2.0	0.3333	2.1547
Sad	6	2.4	0.4000	1.1560
Excited	6	2.2	0.3667	1.6907
Angry	6	0.6	0.1000	0.9560
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1.9556	5	0.3911	0.2725	0.9246	2.5336
Within Groups	43.0533	30	1.4351
Total	45.0089	35

The Anova table is thus given below.

Source	df	SS	MS	F
Expressions	5	1.9556	0.3911	0.2725
Error	30	43.0533	1.4351
Total	35	45.0089

(I have rounded the SS, MS and F values to four places of decimal. Please round them to the required number of decimal places.)