You are studying the giant kelp Macrocystis pyrifera in Monterey Bay, located off the Pacific coast of California. As part of your study you measure frond length to see if it differs across your study area. You have selected 5 sites, which we'll just call sites A-E. Within each site, you randomly place a 1 m2 quadrat sampler at 2 locations and measure the frond length (in cm) of eight randomly selected kelp fronds in each quadrat. The frond length data you obtain are below, where Q1 and Q2 indicate the data from quadrat 1 and quadrat 2, respectively.
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Which type of ANOVA should you use to analyze these data, and why should you choose this type of ANOVA?
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Analyze your data, being sure to interpret your results and explain your reasons for declaring them significant or not significant.
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Use either Levene's test or Bartlett's test to determine whether your data exhibit homogeneity of variances. Again, be sure to interpret your test results.
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Site A
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Site B
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Site C
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Site D
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Site E
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|
Q1
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Q2
|
Q1
|
Q2
|
Q1
|
Q2
|
Q1
|
Q2
|
Q1
|
Q2
|
|
50.2
|
59.5
|
44.0
|
59.3
|
47.6
|
41.9
|
36.5
|
27.5
|
28.4
|
39.3
|
|
42.7
|
50.0
|
54.2
|
56.8
|
42.0
|
39.9
|
36.1
|
30.3
|
32.8
|
34.5
|
|
55.8
|
61.5
|
55.6
|
51.2
|
47.5
|
44.3
|
35.5
|
26.4
|
42.5
|
37.7
|
|
53.5
|
55.9
|
54.7
|
56.2
|
48.1
|
39.4
|
35.7
|
31.0
|
37.3
|
37.0
|
|
55.9
|
59.7
|
47.8
|
51.8
|
43.3
|
39.6
|
33.9
|
39.0
|
37.8
|
36.7
|
|
53.6
|
54.0
|
51.5
|
59.4
|
47.0
|
44.7
|
40.5
|
34.0
|
30.8
|
34.2
|
|
52.3
|
52.8
|
55.7
|
58.7
|
48.1
|
39.5
|
35.1
|
33.3
|
37.7
|
33.0
|
|
57.4
|
53.5
|
49.7
|
59.5
|
46.6
|
37.4
|
28.5
|
36.5
|
39.2
|
29.5
|