**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. **As I was typing this assignment, our cat Gus wanted me to pet him, so he patted me on the arm with his left paw 9 times and his right paw 2 times. Is this significantly different from a 1:1 ratio? Analyze the data using all three of the goodness-of-fit tests we've learned, report the P-values, and write a sentence interpreting any differences among the results.

**exact binomial: P=0.065
chi-square: P=0.035 without Yates correction, P=0.07 with
G-test: P=0.028 without Yates correction, P=0.063 with
Without the Yates correction, the chi-square and G tests give significant (P<0.05) P-values, which are too low. With the Yates correction, the P-values are closer to the exact value given by the exact test, but they are still a little off.**

**2. **Falk and Ayala (1971) collected data on 1187 individuals, recording whether each one clasped their hands with the right thumb on top (R) or the left thumb on top (L). There were 535 R individuals and 652 L individuals. Is this significantly different from a 1:1 ratio of R and L individuals? Analyze the data using all three goodness-of-fit tests, report the P-values, and write a sentence interpreting any differences among the results. Note: download the latest version of the exact binomial spreadsheet for this.

**exact binomial: P=0.00075 (spreadsheet says "N is too big," but it actually can handle these numbers)
chi-square: P=0.00068 without Yates correction, P=0.00076 with
G-test: P=0.00068 without Yates correction, P=0.00075 with
Without the Yates correction, the chi-square and G tests give that are only slightly too low. With the Yates correction, the P-values are very close to the exact value given by the exact test.**

**The Yates correction won't be on the exam. If you only use chi-square and G-tests for really large sample sizes and exact tests for everything else, you'll never have a reason to use the Yates correction, but it's good to be aware of it in case someone else uses it.**

**3. **Under certain conditions, animal cell lines can become "immortalized," meaning they will keep growing and dividing indefinitely in laboratory cultures. Nowak et al. (2004) looked at the effect of the pro-apoptotic protein Bax on immortalization of mouse muscle cells. They made mice without the Bax protein (Bax^{−/−}), established cell lines from them, and compared them to cell lines from mice with the Bax protein (Bax^{+/−} and Bax^{+/+}). After 50 days, all 7 lines of Bax^{−/−} cells were still growing, while only 3 out of 9 of the lines with Bax were growing. Test the data using all three tests of independence, and compare the results of the three tests.

**Fisher's exact test: P=0.011. Chi-square test: P=0.0063. G-test: P=0.0018. The different P-values illustrate that with small sample sizes, the three tests give different results; in this case, the chi-square and G-tests give P-values that are too low.**

**The figure shows how to enter the numbers in the spreadsheet for the chi-square or G-test. The same numbers are used for the Fisher's exact test. Some people used 3 alive and 9 dead for the Bax+ numbers, but the total was 9 for Bax+, so when the question says 3 were alive, it means that 6 were dead.**

**4. **McDonald (1989) collected amphipods (*Platorchestia platensis*) on a beach on Long Island, New York, and determined their genotype at the mannose-6-phosphate isomerase (Mpi) locus. Totalled across several dates, there were 1002 Mpi^{100/100}, 1715 Mpi^{100/90}, and 761 Mpi^{90/90} females; there were 676 Mpi^{100/100}, 1204 Mpi^{100/90}, and 442 Mpi^{90/90} males. Is the difference in genotype proportions between females and males significant? Test the data using the chi-squared and G-tests of independence, and compare the results of the two tests.

**Chi-square: P=0.026. G-test: P=0.026. This illustrates that the chi-square and G-tests, which gave different results with the small numbers in the first question, give about the same result with a large sample size.**

**5. **Plot the data from question 4 on a graph. You must create this graph using a computer; do not draw it by hand.

**6. **Those pictures I've been showing before class this week are from a trip I took 5 years ago, and I can remember each day of the trip in vivid detail. But I can't remember anything about what I was doing two weeks ago. Biological statistics is an important part of your life, of course, but it shouldn't be the only part of your life. Do something fun and adventurous and exciting and interesting this weekend, so fun and so adventurous that you'll remember it 5 years from now. If you have the kind of fun adventure you can tell me about, then tell me about it; if you have the kind of fun you'd like to keep private, then don't tell me about it.

**Thanks for telling me about your wild adventures. For those of you who didn't answer question 6, I'll just assume your adventures were really, really wild. **

**I didn't do anything particularly memorable over the weekend, but last Thursday evening I took some students from my other class on a field trip to the Mispillion River to collect mussels, snails, and oysters. After dinner we went to Big Stone Beach in hopes of seeing phosphorescence; there wasn't any, so we had to settle for watching the moon rise over New Jersey. I'll try to think of a statistics-related field trip to take all of you on.**

Falk, C.T., and F.J. Ayala. 1971. Genetic aspects of arm folding and hand-clasping. Japanese journal of human genetics 15: 241-247.

McDonald, J.H. 1989. Selection component analysis of the Mpi locus in the amphipod *Platorchestia platensis*. Heredity 62: 243-249.

Nowak, J.A., J. Malowitz, M. Girgenrath, C.A. Kostek, A.J. Kravetz, J.A. Dominov, and J.B. Miller. 2004. Immortalization of mouse myogenic cells can occur without loss of p16INK4a, p19ARF, or p53 and is accelerated by inactivation of Bax. BMC Cell Biology 5:1.

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This page was last revised September 17, 2014. Its URL is http://udel.edu/~mcdonald/stathw3.html