Question

a) The worksheet "Counts8Year" provides the number Top30 TV shows aired on each network by year. Run a two-way ANOVA without replication using the data in columns A to E of the "Counts8Year" worksheet. (Do not include row 1 and check labels.) Two hypothesis tests will be performed, one for the Year (row) factor and the other for the Network (column) factor. What is the value of the test statistic, F_calc, for the test on the Network factor? Provide your answer with 2 decimal places.

.

b) R-square (R²) is the proportion of the variation in the data (number of top 30 shows) that can be explained by the factors (year and network). Compute R² = 1 - SSE/SST.   Provide your answer with 4 decimal places.  

.

c) What is the conclusion of the ANOVA hypothesis test at a 5% significance level?  (Click to select)At least one pair of network means differ. At least one pair of the yearly means differ.None of the network means differ. None of the yearly means differ.All of the network means differ. All of the yearly means differ.None of the network means differ. At least one pair of yearly means differ.At least one pair of network means differ. None of the yearly means differ.None of the network means differ. All of the yearly means differ.All of the network means differ. None of the yearly means differ.

.

d) Based on the ANOVA test results, which means are significantly different? (Click to select)Years 2015 and 2016ABC, CBSFOX, NBCCBS, NBCABC, FOXABC, NBCCBS, FOXNo pairs of means differ significantlyABC, CBS, FOX, NBC

.

e) Which of the following methods/test would NOT be appropriate for testing the assumptions of this ANOVA test?

Number of Shows in Top 30 for the last 8 Years
Year	ABC	CBS	FOX	NBC
2016	4	15	4	9
2015	6	19	1	4
2014	6	17	2	5
2013	6	18	3	3
2012	7	17	4	2
2011	8	16	3	3
2010	9	15	5	1
2009	8	15	5	3

Answer 1

1. The worksheet "Counts8Year" provides the number Top30 TV shows aired on each network by year. Run a two-way ANOVA without replication using the data in columns A to E of the "Counts8Year" worksheet. (Do not include row 1 and check labels.) Two hypothesis tests will be performed, one for the Year (row) factor and the other for the Network (column) factor.

What is the value of the test statistic, F_calc, for the test on the Network factor? Provide your answer with 2 decimal places.

.F=71.73

b) R-square (R²) is the proportion of the variation in the data (number of top 30 shows) that can be explained by the factors (year and network). Compute R² = 1 - SSE/SST.   Provide your answer with 4 decimal places.  

.R square = 1-(71.73/87.91)

=0.1841

1. What is the conclusion of the ANOVA hypothesis test at a 5% significance level?  (Click to select)

At least one pair of network means differ.

.

None of the yearly means differ.

.

1. Based on the ANOVA test results, which means are significantly different? (Click to select)Years 2015 and 2016

ABC, CBS

CBS, NBC

ABC, FOX

ABC, NBC

CBS, FOX

.

Excel Addon Megastat used.

Randomized blocks ANOVA
	Mean	n	Std. Dev
	6.750	8	1.581	ABC
	16.500	8	1.512	CBS
	3.375	8	1.408	FOX
	3.750	8	2.435	NBC
	8.000	4	5.228	year2016
	7.500	4	7.937	year2015
	7.500	4	6.557	year2014
	7.500	4	7.141	year2013
	7.500	4	6.658	year2012
	7.500	4	6.137	year2011
	7.500	4	5.972	year2010
	7.750	4	5.252	year2009
	7.594	32	5.650	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatments	900.84	3	300.281	71.73	3.34E-11
Blocks	0.97	7	0.138	0.03	.9999
Error	87.91	21	4.186
Total	989.72	31
Post hoc analysis
p-values for pairwise t-tests
		FOX	NBC	ABC	CBS
		3.375	3.750	6.750	16.500
FOX	3.375
NBC	3.750	.7176
ABC	6.750	.0034	.0080
CBS	16.500	2.10E-11	3.61E-11	4.46E-09
Tukey simultaneous comparison t-values (d.f. = 21)
		FOX	NBC	ABC	CBS
		3.375	3.750	6.750	16.500
FOX	3.375
NBC	3.750	0.37
ABC	6.750	3.30	2.93
CBS	16.500	12.83	12.46	9.53
critical values for experimentwise error rate:
		0.05	2.79
		0.01	3.53