Biological Data Analysis: Homework 8

Due Tuesday, October 29

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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