Biological Data Analysis: Homework 2

Due Tuesday, Sept. 15

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.

We didn't get to the exact test of goodness-of-fit in this week's lectures, but I'd like to have you try to do the the first three questions of the homework anyway. Read through the textbook page on the exact test of goodness-of-fit, then try to answer the questions. Don't spend a lot of time on this; I have no idea how easy it will be to learn the test just from the textbook.

I've deleted questions 4 and 5, about power analysis, and I'll move them to assignment number 3.

1. In human males, the left testis hangs lower than the right in 57 to 80% of adult men. You want to know whether the same kind of asymmetry occurs in chimpanzees (Pan troglodytes). You will observe some wild chimpanzees and record which testis hangs lower. (The testes of chimpanzees are so large that they couldn't walk if the testes hung at the same level, so you don't have to worry about ties; each chimp will be either "right" or "left.") You are going to analyze your data with an exact binomial test. Should you do a one-tailed test or a two-tailed test? What are the advantages and disadvantages of a one-tailed test for this experiment?

The advantage of a one-tailed test is that it gives you more power; certain right: left ratios would be significant with a one-tailed test but not with a two-tailed test. But the disadvantage of a one-tailed test is that if there are more chimps with right testis lower than left (which is how it turned out when this study was actually done), the deviation from a 1:1 ratio couldn't be significant.

2. If you observe 30 chimpanzees, how many would have to have the left testis lower in order to have a signficant (P<0.05) result with a one-tailed test? Same question, but for a two-tailed test? Use the exact binomial test spreadsheet, and use trial and error to find the answers.

For a one-tailed test, you need at least 20 left-testis chimps; that gives a one-tailed P-value of 0.049. For a two-tailed test, you need at least 21 left-testis chimps (or 21 right-testis chimps); that gives a two-tailed P-value of 0.043.

3. Using either a one-tailed or two-tailed test (whichever you decided was more appropriate in question 1), how many chimps would have to have the left testis lower in order to have a signficant result if the sample size was 50, or 100, or 500?

One-tailed: 32/50, 59/100, 269/500
Two-tailed: 33/50, 61/100, 273/500

Here are four more practice questions for the final exam. For each experiment, list the variables that are mentioned in the description, and say whether each is a nominal, measurement, or ranked variable. Don't list variables that are not mentioned in the description; for example, don't list "weight of mother" for the first experiment.

6. You want to know whether aspirin taken during pregnancy has an effect on the size of offspring. You ask 1072 new mothers whether they took aspirin during the first three months of their pregnancy. The average weight of newborn babies of mothers who took aspirin is 103 grams less than babies of mothers who didn't take aspirin.

aspirin or not: nominal
weight of baby: measurement

7. You want to know what affects the breakdown of fructose at high temperatures (due to caramelization and Maillard reactions) in apples. You bake 8 Winesap apples, 8 Rome Beauty apples, 8 Jonathan apples, and 8 Granny Smith apples for 90 minutes at 180 C, and you bake another set of 8 apples of each variety for 90 minutes at 200 C. You measure the amount of fructose (in milligrams of fructose per gram of baked apple) in each apple.

type of apple: nominal
baking temperature: nominal (because there are just two values, 180 and 200
milligrams of fructose per gram: measurement

8. You want to know whether certain "home remedies" used for ant control really work. You find 40 houses that are infested with pavement ants (Tetramorium caespitum). In 10 of the houses, you place bay leaves along the baseboards; you sprinkle boric acid along the baseboards of 10 houses, sprinkle diatomaceous earth along the baseboards of 10 others, and leave the last 10 houses untreated. After two weeks, you place sticky traps in each house and count the number of ants caught in a 12-hour period.

treatment (bay leaves, boric acid, diatomaceous earth, control: nominal
number of ants caught: measurement

9. In order to increase rotation speed during a figure skating jump, skaters must be strong enough to pull their arms in towards the center quickly after taking off. Strength tests have shown that skaters may not have the upper body strength necessary to overcome the centrifugal forces and pull their arms in, so you decide to put female figure skaters through a strength training program. Using a high-speed camera, you measure the rotation speed during the first spin of a triple Lutz-double toe loop combination of 9 top skaters, put them through a 12-week strength training program, then measure the rotation speed again.

this one's kind of tricky. One way to look at it would be to treat rotation speed as one measurement variable, name of skater as one nominal variable, and before-vs.-after the 12-week training program as one nominal variable. Another way to think about it would be to treat rotation speed before training as one measurement variable and rotation speed after training as a second measurement variable, with name of skater as a "hidden" nominal variable. I'd prefer the first method, but the second method is not incorrect.

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