The following should be done in R. Game meats, including those from white-tailed
ID: 3066489 • Letter: T
Question
The following should be done in R.
Game meats, including those from white-tailed deer and eastern gray squirrels, are used as food by families, hunters, and other individuals for health, cultural, or personal reasons. A study by David Holben assessed the selenium content of meat from free-roaming white-tailed deer (venison - VEN) and gray squirrel (squirrel - SQU) obtained from a low selenium region of the United States. These selenium content values were also compared to those of beef produced within (RRB) and outside the same region (NRB). We want to know if the selenium levels are dierent among the four meat groups. The data is found in selenium.csv. We want to answer the following questions. I. Does meat from larger animals have a higher selenium concentration than small? II. Does meat the animals raised in region dier than those raised outside the region? III. Does meat from beef dier from non-domesticated animals? To answer the above questions, do the following:
a) First, conduct analysis of variance on this data set. Don't forget to make an appropriate plot and check necessary assumptions. Specically identify the null and alternative hypothesis statements for the contrasts that we are testing.
b) Using Bonferroni's Method, nd the contrast estimates, along with their 95% condence intervals and the adjusted p-values for the above research questions. This can be done using a single contrast matrix in R. Display the results, and provide plots of the condence intervals.
c) Use your intervals from b) to formally answer the original research questions I, II, and III.
d) Finally, use Tukey's method to conduct a post-hoc analysis of all of the pairwise contrast estimates, their 95% condence intervals. Display the results, and provide a plot of the condence intervals. Comment on any interesting results that you see.
Please show R functions!
Selenium
Meat
26.72
VEN
28.58
VEN
29.71
VEN
26.95
VEN
10.97
VEN
21.97
VEN
14.35
VEN
32.21
VEN
19.19
VEN
30.92
VEN
10.42
VEN
35.49
VEN
36.84
VEN
25.03
VEN
33.59
VEN
33.74
VEN
18.02
VEN
22.27
VEN
26.1
VEN
20.89
VEN
29.44
VEN
14.86
VEN
16.47
VEN
25.19
VEN
37.45
VEN
45.08
VEN
25.22
VEN
22.11
VEN
33.01
VEN
31.2
VEN
26.5
VEN
32.77
VEN
8.7
VEN
25.9
VEN
29.8
VEN
37.63
VEN
21.69
VEN
21.49
VEN
18.11
VEN
31.5
VEN
27.36
VEN
21.33
VEN
37.42
SQU
56.46
SQU
51.91
SQU
62.73
SQU
4.55
SQU
39.17
SQU
38.44
SQU
40.92
SQU
58.93
SQU
61.88
SQU
49.54
SQU
64.35
SQU
82.49
SQU
38.54
SQU
39.53
SQU
37.57
SQU
25.71
SQU
23.97
SQU
13.82
SQU
42.21
SQU
35.88
SQU
10.54
SQU
27.97
SQU
41.89
SQU
23.94
SQU
49.81
SQU
30.71
SQU
50
SQU
87.5
SQU
68.99
SQU
11.23
RRB
29.63
RRB
20.42
RRB
10.12
RRB
39.91
RRB
32.66
RRB
38.38
RRB
36.21
RRB
16.39
RRB
27.44
RRB
17.29
RRB
56.2
RRB
28.94
RRB
20.11
RRB
25.35
RRB
21.77
RRB
31.62
RRB
32.63
RRB
30.31
RRB
46.16
RRB
56.61
RRB
24.47
RRB
29.39
RRB
40.71
RRB
18.52
RRB
27.8
RRB
19.49
RRB
15.82
RRB
27.74
RRB
22.35
RRB
34.78
RRB
35.09
RRB
32.6
RRB
37.03
RRB
27
RRB
44.2
RRB
13.09
RRB
33.03
RRB
9.69
RRB
32.45
RRB
37.38
RRB
34.91
RRB
27.99
RRB
22.36
RRB
22.68
RRB
26.52
RRB
46.01
RRB
38.04
RRB
30.88
RRB
30.04
RRB
25.91
RRB
18.54
RRB
25.51
RRB
44.33
NRB
76.86
NRB
4.45
NRB
55.01
NRB
58.21
NRB
74.72
NRB
11.84
NRB
139.09
NRB
69.01
NRB
94.61
NRB
48.35
NRB
37.65
NRB
66.36
NRB
72.48
NRB
87.09
NRB
26.34
NRB
71.24
NRB
90.38
NRB
50.86
NRB
Selenium
Meat
26.72
VEN
28.58
VEN
29.71
VEN
26.95
VEN
10.97
VEN
21.97
VEN
14.35
VEN
32.21
VEN
19.19
VEN
30.92
VEN
10.42
VEN
35.49
VEN
36.84
VEN
25.03
VEN
33.59
VEN
33.74
VEN
18.02
VEN
22.27
VEN
26.1
VEN
20.89
VEN
29.44
VEN
14.86
VEN
16.47
VEN
25.19
VEN
37.45
VEN
45.08
VEN
25.22
VEN
22.11
VEN
33.01
VEN
31.2
VEN
26.5
VEN
32.77
VEN
8.7
VEN
25.9
VEN
29.8
VEN
37.63
VEN
21.69
VEN
21.49
VEN
18.11
VEN
31.5
VEN
27.36
VEN
21.33
VEN
37.42
SQU
56.46
SQU
51.91
SQU
62.73
SQU
4.55
SQU
39.17
SQU
38.44
SQU
40.92
SQU
58.93
SQU
61.88
SQU
49.54
SQU
64.35
SQU
82.49
SQU
38.54
SQU
39.53
SQU
37.57
SQU
25.71
SQU
23.97
SQU
13.82
SQU
42.21
SQU
35.88
SQU
10.54
SQU
27.97
SQU
41.89
SQU
23.94
SQU
49.81
SQU
30.71
SQU
50
SQU
87.5
SQU
68.99
SQU
11.23
RRB
29.63
RRB
20.42
RRB
10.12
RRB
39.91
RRB
32.66
RRB
38.38
RRB
36.21
RRB
16.39
RRB
27.44
RRB
17.29
RRB
56.2
RRB
28.94
RRB
20.11
RRB
25.35
RRB
21.77
RRB
31.62
RRB
32.63
RRB
30.31
RRB
46.16
RRB
56.61
RRB
24.47
RRB
29.39
RRB
40.71
RRB
18.52
RRB
27.8
RRB
19.49
RRB
15.82
RRB
27.74
RRB
22.35
RRB
34.78
RRB
35.09
RRB
32.6
RRB
37.03
RRB
27
RRB
44.2
RRB
13.09
RRB
33.03
RRB
9.69
RRB
32.45
RRB
37.38
RRB
34.91
RRB
27.99
RRB
22.36
RRB
22.68
RRB
26.52
RRB
46.01
RRB
38.04
RRB
30.88
RRB
30.04
RRB
25.91
RRB
18.54
RRB
25.51
RRB
44.33
NRB
76.86
NRB
4.45
NRB
55.01
NRB
58.21
NRB
74.72
NRB
11.84
NRB
139.09
NRB
69.01
NRB
94.61
NRB
48.35
NRB
37.65
NRB
66.36
NRB
72.48
NRB
87.09
NRB
26.34
NRB
71.24
NRB
90.38
NRB
50.86
NRB
Explanation / Answer
From the given data,
Correct answer: P-value = 0.026685
ANOVA Table Source Sum of square df MS F-ratio F-critical P-value Treatment 30 3 10 3.33333333 2.790008 0.026684645 Error 150 50 3 Total 180 53