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. Here are some data on the abundance of the tesselated darter, Etheostoma olmstedi, in streams in Maryland. The data are presented as number of fish per 75 meter section of stream. For each stream, data from two sections are given: one section adjacent to a pasture, and the other section not adjacent to a pasture. You want to know whether streams adjacent to pastures have the same density of tesselated darters as streams not adjacent to pastures. Which test would be most appropriate: a Student's t-test; a paired t-test; Wilcoxon's signed ranks test; or a sign test? Write a few sentences giving your reasons for choosing that test.
stream pasture other Andover Branch 0 31 Basin Run 52 21 Big Pipe Creek 2 0 Bynum Run 30 14 Carroll Branch 19 19 Delaware Run 10 0 East Br. Patapsco River 3 2 Gillis Falls 7 1 Gunpowder Falls 1 1 Israel Creek 22 30 Jones Falls 10 8 Little Deer Creek 21 60 Mason Branch 74 111 Middle Run 21 2 Northeast Creek 79 78 Patapsco River 54 4 Piney Run 4 2 Pomonkey Creek 2 0 Prettyboy Branch 2 0 Principio Creek 22 58 Red Lion Branch 55 23 Tuscarora Creek 1 0 Winters Run 75 116
2. Now analyze the data using all four tests: Student's t-test; a paired t-test; Wilcoxon's signed ranks test; and a sign test. You may use spreadsheets, web sites, or SAS. Give the P-values in a nice little table, and write a couple of sentences comparing the results of the tests.
3. Make a graph that summarizes the data in what you think is the most effective way.
4. Two technicians, Brad and Janet, are developing a new technique to measure the uptake of proteins by liver cells (these are real data; the names of the technicians have been changed). They inject a fluorescently labelled protein into one rat, wait one minute, then they each take 12 samples of liver cells from the rat. Using confocal microscopy, they measure the amount of fluorescent protein taken up by the cells in each sample. They take more samples after 60 minutes. You want to know whether the two technicians are getting similar results, or whether one technician gets higher or lower measurements than the other. You also want to know whether there's a difference between the readings at one and 60 minutes. Analyze these data using a two-way anova (you'll have to use SAS or maybe a web page for this) and interpret the results--what would you recommend to Brad and Janet?
Tech Time Protein Brad 1min 0.9490 Brad 1min 1.1265 Brad 1min 1.0468 Brad 1min 0.9341 Brad 1min 1.2349 Brad 1min 1.2827 Brad 1min 0.9586 Brad 1min 1.1753 Brad 1min 0.9724 Brad 1min 1.1382 Brad 1min 0.9511 Brad 1min 1.2837 Brad 60min 1.1248 Brad 60min 1.3274 Brad 60min 1.1669 Brad 60min 1.3987 Brad 60min 1.3338 Brad 60min 1.4191 Brad 60min 1.5732 Brad 60min 1.6369 Brad 60min 1.2153 Brad 60min 1.7057 Brad 60min 1.4904 Brad 60min 1.2777 Janet 1min 1.0524 Janet 1min 1.1819 Janet 1min 1.2548 Janet 1min 1.0275 Janet 1min 1.3676 Janet 1min 1.2186 Janet 1min 1.4215 Janet 1min 1.3880 Janet 1min 1.1413 Janet 1min 1.0530 Janet 1min 0.9133 Janet 1min 0.9174 Janet 60min 1.2257 Janet 60min 1.2559 Janet 60min 1.1268 Janet 60min 1.6080 Janet 60min 1.7720 Janet 60min 1.5759 Janet 60min 1.5887 Janet 60min 1.3341 Janet 60min 1.2031 Janet 60min 1.4293 Janet 60min 1.2388 Janet 60min 1.5600
5. The preceeding experiment was done on a single rat; now Brad and Janet want to know whether their techniques for anesthetizing the rats, cutting them open, and injecting the fluorescently labelled protein are the same. Brad operates on three rats, then after 60 minutes, measures the protein in 10 samples from each rat. Janet does the same on three rats of her own. Analyze the data using a nested anova (using a spreadsheet, web page, or SAS), and interpret the results--what would you recommend to Brad and Janet?
Tech Rat Protein Janet 1 1.119 Janet 1 1.2996 Janet 1 1.5407 Janet 1 1.5084 Janet 1 1.6181 Janet 1 1.5962 Janet 1 1.2617 Janet 1 1.2288 Janet 1 1.3471 Janet 1 1.0206 Janet 2 1.045 Janet 2 1.1418 Janet 2 1.2569 Janet 2 0.6191 Janet 2 1.4823 Janet 2 0.8991 Janet 2 0.8365 Janet 2 1.2898 Janet 2 1.1821 Janet 2 0.9177 Janet 3 0.9873 Janet 3 0.9873 Janet 3 0.8714 Janet 3 0.9452 Janet 3 1.1186 Janet 3 1.2909 Janet 3 1.1502 Janet 3 1.1635 Janet 3 1.151 Janet 3 0.9367 Brad 5 1.3883 Brad 5 1.104 Brad 5 1.1581 Brad 5 1.319 Brad 5 1.1803 Brad 5 0.8738 Brad 5 1.387 Brad 5 1.301 Brad 5 1.3925 Brad 5 1.0832 Brad 6 1.3952 Brad 6 0.9714 Brad 6 1.3972 Brad 6 1.5369 Brad 6 1.3727 Brad 6 1.2909 Brad 6 1.1874 Brad 6 1.1374 Brad 6 1.0647 Brad 6 0.9486 Brad 7 1.2574 Brad 7 1.0295 Brad 7 1.1941 Brad 7 1.0759 Brad 7 1.3249 Brad 7 0.9494 Brad 7 1.1041 Brad 7 1.1575 Brad 7 1.294 Brad 7 1.4543
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This page was last revised August 5, 2009. Its URL is http://udel.edu/~mcdonald/stathw7.html