Question

a) The worksheet "EpisodeRatings" provides ratings of 3 TV shows by a total of 108 raters. The raters were randomly assigned to view 1 of 6 episodes of 3 TV shows. Raters filled out a questionnaire consisting of 10 items answered on scale from 1 to 15. The data on the Excel worksheet are average responses to the 10 questions by the raters. Each Episode-Show combination was rated by 6 people (6 replications of each factor combination). Run a two-way ANOVA with replication on this data using Excel's Data Analysis tools. Select all of the data (including labels) and specify 6 replications (rows per sample). What is the p-value of the hypothesis test on the "Episode" factor?   Provide your answer with 4 decimal places.

.

b) What is the average rating of the Show with the lowest mean rating? Provide your answer with 2 decimal places.

.

c) What is the variance of the Episode-Show combination with the largest variability in ratings? Provide your answer with 4 decimal places.

.

d) Based on the ANOVA test results, which of the Show means are significantly different at α = 5%?  

.

e) Three "effects" were tested in this two-way ANOVA. Order the 3 effects in terms of their usefulness in the ANOVA model for explaining the variation in mean ratings (start with the most useful effect).

Episode of Show Rated	Show A Rating	Show B Rating	Show C Rating
Episode 1	10.1	10.7	10.6
	9.8	10.7	10.6
	9.4	10.4	11.3
	9.2	10.4	9.6
	8.9	10	10
	9	9.9	9.4
Episode 2	9.7	10.5	10.4
	9.6	9.8	11.1
	9.6	9.6	11.9
	9.2	9.5	9.3
	8.8	9.8	10.1
	9.2	9.7	9.7
Episode 3	9.3	9.5	9.5
	10.1	9.4	9.9
	9.8	9.9	9.4
	9	10.3	9.4
	8.7	10.4	10.1
	8.8	9.9	9.8
Episode 4	9.8	10.8	11
	10.7	10.1	10.8
	10.8	9.4	11
	9	10.1	9.4
	9.7	9.5	9
	8.9	10	9.4
Episode 5	9.2	10.8	9.7
	9.3	10.3	10.5
	9.9	10.6	11.2
	10.7	10.6	9.6
	11.5	10.8	10
	11.3	11.2	9.6
Episode 6	10	10.2	9.7
	9.7	10.6	9.4
	9.9	11.2	8.7
	9.6	10.2	9.4
	9.2	11	9.4
	9.7	11.6	8.9

Answer 1

excel steps for two way anova with replication

excel>menu>data>data analysis>two way anova with replication>enter required label

Anova: Two-Factor With Replication
SUMMARY	Show A Rating	Show B Rating	Show C Rating	Total
Episode 1
Count	6	6	6	18
Sum	56.4	62.1	61.5	180
Average	9.4	10.35	10.25	10
Variance	0.22	0.115	0.511	0.441176471
Episode 2
Count	6	6	6	18
Sum	56.1	58.9	62.5	177.5
Average	9.35	9.816666667	10.41666667	9.861111111
Variance	0.119	0.125666667	0.905666667	0.540163399
Episode 3
Count	6	6	6	18
Sum	55.7	59.4	58.1	173.2
Average	9.283333333	9.9	9.683333333	9.622222222
Variance	0.317666667	0.164	0.085666667	0.235947712
Episode 4
Count	6	6	6	18
Sum	58.9	59.9	60.6	179.4
Average	9.816666667	9.983333333	10.1	9.966666667
Variance	0.653666667	0.253666667	0.86	0.534117647
Episode 5
Count	6	6	6	18
Sum	61.9	64.3	60.6	186.8
Average	10.31666667	10.71666667	10.1	10.37777778
Variance	0.993666667	0.089666667	0.408	0.507712418
Episode 6
Count	6	6	6	18
Sum	58.1	64.8	55.5	178.4
Average	9.683333333	10.8	9.25	9.911111111
Variance	0.077666667	0.32	0.139	0.609281046
Total
Count	36	36	36
Sum	347.1	369.4	358.8
Average	9.641666667	10.26111111	9.966666667
Variance	0.4705	0.308730159	0.572
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	5.442685185	5	1.088537037	3.081249672	0.01297146	2.315689238
Columns	6.912407407	2	3.456203704	9.783246842	0.000143026	3.097698035
Interaction	10.05537037	10	1.005537037	2.846307071	0.004027979	1.937566791
Within	31.795	90	0.353277778
Total	54.20546296	107

p-value of the hypothesis test on the "Episode" factor=0.0130

average rating of the Show with the lowest mean rating=9.64

the variance of the Episode-Show combination with the largest variability in ratings=0.5720