Biological Data Analysis: Homework 7

Due Tuesday, Oct. 22

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.

This is the corrected homework

1. Calculate the residuals for the data you collected for one-way anova. Remember that the residual in this case is the difference between an observation and the mean of its group. For example, if you measure the lengths of leaves on trees A, B, C, D, E, and F, the residual for leaf 1 on tree A would be the length of leaf 1 minus the mean length for tree A.

Next, put all the residuals in one column and draw a histogram of them, using the spreadsheet linked from the href="">normality page. Remember that to copy and paste the numerical results of a formula, you should copy, then choose "Paste Special..." from the Edit menu. Then select the "Values" checkbox, so only the numerical values will be pasted.

Turn in the histogram of your untransformed residuals (just the graph, not the whole spreadsheet).

2. Log-transform your data set (the original data, not the residuals). Then calculate the mean of the log-transformed data for each group, and the residuals of the log-transformed data. Draw a histogram of the residuals of the log-transformed data.

3. Which looks more normal--your untransformed data, or your log-transformed data? Do you think it looks normal enough for an anova?

4. Using either my spreadsheet or SAS (you don't have to do both), do a one-way anova on your log-transformed data. Report the F-statistic and the P-value. Also report the F-statistic and P-value for your untransformed data (that you analyzed in the previous assignment). How do the results compare?

5. Download the spreadsheet for Bartlett's test linked from the homoscedasticity page. We didn't talk about it in class; all you need to know is that Bartlett's test has a smaller P-value when there's greater heteroscedasticity. Enter your one-way anova data (the raw data, not the residuals). Turn in the standard deviations for your groups and the P-value for the Bartlett's test. The spreadsheet gives you the option of log-transforming your data; do each, and turn in the standard deviations and P-value for the Bartlett's test for your log transformed data.

6. Did it look like your untranformed data had a lot of heteroscedasticity? Did the log transformation make it better?

7. Two technicians, "Brad" and "Janet" (these are real data, but I've changed their names), have measured the uptake of a fluorescently labelled protein in rat kidneys. They want to know whether their techniques for anesthetizing the rats, cutting them open, and injecting the fluorescently labelled protein are the same. They also want to know whether it's worthwhile to use multiple rats, and whether it's worthwhile to make multiple measurements from each rat. 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. The data are at the bottom of this page. Analyze the data using a nested anova. Report the F-statistics and P-values for each null hypothesis. You must use my spreadsheet, and you must also analyze the data using SAS. If you get the same P-values in SAS as you did with the spreadsheet (note that SAS may round to a smaller number of decimals), you only need to print the SAS output (from the .lst file). If you get a different result, also print the .log file and your SAS program (your .sas file).

7. interpret the results of question 6--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 October 18, 2013. Its URL is