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. Every year, volunteers count the number of breeding horseshoe crabs on beaches on Delaware Bay. Data from this survey are shown below. You want to know whether the number of breeding horseshoe crabs was different between 2011 and 2012. Which test do you think would be most appropriate: a Student's t-test; a paired t-test; or Wilcoxon's signed ranks test? Write a few sentences giving your reasons for choosing that test.
Beach 2011 2012 BennettsPier 35282 21814 BigStone 359350 83500 Broadkill 45705 13290 CapeHenlopen 49005 30150 Fortescue 68978 125190 Fowler 8700 4620 Gandys 18780 88926 Higbees 13622 1205 Highs 24936 29800 Kimbles 17620 53640 KittsHummock 117360 68400 NorburysLanding 102425 74552 NorthBowers 59566 36790 NorthCapeMay 32610 4350 Pickering 137250 110550 PiercesPoint 38003 43435 Primehook 101300 20580 Reeds 62179 81503 Slaughter 203070 53940 SoutBowers 135309 87055 SouthCSL 150656 112266 TedHarvey 115090 90670 Townbank 44022 21942 Villas 56260 32140 Woodland 125 1260
2. Now analyze the data using all three tests: Student's t-test; a paired t-test; and Wilcoxon's signed ranks 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.
(Note: if you use spreadsheets, please learn how to copy and paste data from this web page into your spreadsheets, then use the "Data: Text to Columns" command to put the numbers into separate columns. Instructions are on the web page on using spreadsheets for statistics. If I hear that you've painstakingly retyped everything from this assignment into your spreadsheet, one number at a time, I'll feel very sad.)
3. Make a graph that summarizes the data from question 2 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 for this). Show your SAS program and your SAS output; you only need to print the SAS log file if you think you have a problem. Give your interpretation of the results--what would you recommend to Brad and Janet about how they measure protein uptake in the future?
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
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This page was last revised October 25, 2013. Its URL is http://udel.edu/~mcdonald/stathw8.html