Biological Statistics
Homework 6
Due Thursday, Oct. 18

Because we will not finish covering the material on one-way anova until Tuesday, this assignment is due on Thursday, Oct. 18. You should be able to do part of it over the weekend.

For this assignment (and all assignments for the rest of the semester), please do not just print out your spreadsheets. Instead, type up your results into an attractive format, with tables and graphs as necessary. You should be able to copy a graph from Excel or Calc and paste it into a word processing document.

Part I. 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 Excel) for the following analyses:

  1. Using the information in the map, design an orthogonal set of at least three planned comparisons among the watersheds.
  2. Pick one of the watersheds with a large number of samples (Double Pipe Creek, Patuxent River, or Youghiogheny River) and plot three frequency histograms for the data: one for the untransformed data, one for log-transformed data, and one for square-root transformed data. Say which transformation you think makes the data look most normal. (Note: because the data includes zeros, you should use the feature on the histogram web page to add 0.5 to each value before log-transforming.)
  3. Perform Bartlett's test on the variances of the 12 watersheds, for untransformed, log-transformed (with 0.5 added), and square-root transformed data. Report the three P-values.
  4. Based on the histograms and the Bartlett's test, say whether you think the untransformed, log-transformed or square-root transformed data fits the assumptions of the anova best. Say whether you think the data meet the assumptions well enough to do the anova, or whether you should do the Kruskal-Wallis test instead. (For the purposes of this homework, you'll do both; in real life, you should pick one or the other before you see the P-values.)
  5. Perform a single-classification anova on the data, either untransformed, log transformed, or square-root transformed (whichever you thought was best). 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. (Optional for extra fun: if you transformed the data and you want an extra challenge, you can back-transform the means and comparison intervals before graphing.)
  6. 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.)
  7. Perform a Kruskal-Wallis test on the data, and compare the result to the result of the anova. (You normally wouldn't do both the anova and Kruskal-Wallis, this is just for practice.)

Part II. If I said the measurement data you collected for Homework 5 were acceptable, perform all of the steps above (except for the planned comparisons, questions 1 and 6) on your data. If I said your data weren't acceptable, modify them in whatever way I described.

Abundance of blacknose dace (number of fish per 30 meters of stream) in 12 watersheds.

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 Statistics syllabus

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This page was last revised October 12, 2007. Its URL is http://udel.edu/~mcdonald/stathw6.html