# Biological Data Analysis: Homework 2

## Due Thursday, Sept. 20

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. Get five coins and put them in a container with a lid, so that you can flip all five coins at once by shaking the container and then letting the coins fall to the bottom. If you flip the five coins, and the probability of one coin being "tails" is 0.50, what is the probability of getting "tails" on all five coins?

2. Now you are going to do an experiment to see whether thinking about tails makes tails more likely to appear. You will think about tails, shake your coin container, and see how many tails you get. What is the biological null hypothesis? The biological alternative hypothesis? The statistical null hypothesis? The statistical alternative hypothesis?

3. Now do the experiment. Think about tails, flip your five coins, and record how many tails (0 to 5) you got.

4. If you got five tails in question 3, skip question 4 and just answer question 5. If you didn't get five tails, maybe you just weren't doing the experiment right. So keep repeating the experiment, only do things a little differently every time. You might flip the coins with your right hand, then your left hand; sitting down or standing up; with your eyes open or shut; while thinkg about the tails of coins, the tails of animals, or the word "tails"; etc. Every time you do the experiment, write down the number of tails you get. Keep going until you get five tails, then stop and go to question 5. Turn in a table of your results, with rows labelled "1" through however many flips it took, and the number of tails on each flip. Also write down the conditions for the trial that gave you five tails ("standing up with your eyes shut while flipping with your left hand and thinking about horse tails," for example).

Do not cheat; keep flipping your five coins until you get five heads. A real scientist never makes up data!

5. Based on the results of just your last experiment (the one that gave you five tails when you flipped them under a particular combination of conditions), what would a stupid or evil biologist conclude?

6. You're not stupid or evil (I hope), so what do you conclude?

7. Download the balance data set, which has the data everyone in the class collected for homework 1. Pick two of the nominal variables that have two values (sex, arm on top, thumb on top, stood on left or right foot, left or right handed). Write down the statistical null hypothesis in terms of the two variables. Then analyze just the data on eight people that you collected, using each of the three tests of independence that you've learned. Give your raw data (the numbers of each of the four combinations of your two variables) and the P-values for the three tests in a nice little table (do NOT just copy over the spreadsheets).

8. Do the same three tests of independence on the same two variables as in question 7, only use the entire data set from everyone in the class. Present the raw data and P-values in another nice little table.

9. Write a few sentences about how similar the three P-values are in question 7 to each other, how similar the three P-values are in question 8 to each other, whether you got significance in any of the tests, and if so, what you think that means biologically.