Biological Data Analysis: Homework 5

Due Tuesday, Oct. 13

You must type this and all other homework assignments. Do not e-mail the assignment to me; turn it in early (at 322 Wolf) for a foreseeable absence, or turn it in late after an unexpected absence from class.

1. Do a one-way anova on the data you collected for Homework 4. State a biological question, the biological null hypothesis, and the statistical null hypothesis. Test the homogeneity of means, using both my spreadsheet and SAS, and report the mean squares, degrees of freedom, F-statistic, P-value, and results of the Tukey-Kramer procedure. Plot a graph showing the means and the Gabriel comparison intervals. For SAS, show your program and the output. Modify the graph you did for Homework 4 to show Gabriel comparison intervals in stead of 95 percent confidence intervals, and report the results of the Tukey-Kramer test.

[Don't test the assumptions of the anova, just do it even if the data seem non-normal or heteroscedastic. You'll test the assumptions in the next assignment.]

2. What do your results tell you about your biological question?

3. At the bottom of this page are abundance data for the blacknose dace at multiple locations in 12 watersheds in Maryland. The data are extracted from a much larger data set, the Maryland Biological Stream Survey. In this survey, 30-m long stretches of streams were "electrofished"--electrodes were put in the water and a current passed through, stunning all the fish and causing them to float to the surface, where they were collected and identified. Use these data (you should be able to copy them from this web page and paste them into a spreadsheet) for the following analyses:

• Using the information in the map, design an orthogonal set of at least three planned comparisons among the watersheds. Explain in a sentence or two the reason you would want to plan those particular comparisons.
• Perform a one-way anova on the data. Report the mean squares, degrees of freedom, F-statistic, P-value, and results of the Tukey-Kramer procedure. Plot a graph showing the means and the Gabriel comparison intervals.
• Perform your planned comparisons, and report the P-value for each. (Note that you normally wouldn't perform both planned comparisons and unplanned comparisons, nor would you use both the Gabriel and Tukey-Kramer methods for unplanned comparisons. You're doing all three just for practice.)

Abundance of blacknose dace (number of fish per 30 meters of stream) in 12 watersheds. Multiple 30-m stretches of stream are shown for each watershed.

Anacostia River
112
67
29
367
43
188
92
105
12
0
6
131
7
0
1
0
119
181

Back River
40
15
125
151
0
6
2
213
259
1404
214
0

Deer Creek
182
119
112
124
228
75
23
146
162
446
0
148
250
149
430
194
347
302

Double Pipe Creek
45
389
1
133
17
0
486
124
1
89
0
0
12
202
39
47
0
136
42
233
126
0
0
42
4
63
244
3

Fifteen Mile Creek
15
299
61
143
25
216
56
42
1
0
47
0
200
0
82
2
114

Gwynns Falls
0
1
0
0
0
0
29
62
0
0
105
0
2
0
12
1

Jones Falls
35
37
40
41
121
5
53
0
111
0

Little Gunpowder Falls
197
47
85
91
4
93
22
9

Patapsco River Lower North Branch
159
0
1
54
102
0
351
20
7
32
152
202
0
73
69
65
129

Patuxent River (Lower)
20
71
16
39
24
93
131
130
154
103
0
0
1
78
0
27
31
0
50
10
38
78
249
255
60
2
54
198

Rock Creek
102
53
102
93
76
39
12
55
98

Youghiogheny River
41
6
97
5
2
1
45
1
0
286
11
29
0
1069
44
69
185
2
25
0
4
0
125
123
12
225
27
0
6
0
142
100
0
0
0
85
267
9
21
14
141
323
129
0

Return to the Biological Data Analysis syllabus

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This page was last revised August 4, 2009. Its URL is http://udel.edu/~mcdonald/stathw5.html