Homework Project 2

Homework Project 2

Please submit a hard-copy of your assignment to Dr. Yang, as well as an electronic (PDF) to Canvas).

Note: For this homework, use R for calculations. Do not give raw computer output as your main answer to any question; do include R code in an appendix. Do not report numbers to more significant digits than is warranted. It is recommended to use the options:

options(digits=4, show.signif.stars=FALSE)

Remember that providing a clear and reasonable justification of your answers is at least as important as getting the answer right.

Problem 2.1: Mendel’s Experiment:

1. It is well known among statistician that most of Mendel’s data were too good to be true, i.e., the ratio in the Mendel’s results (on page 9 of the lecture slides, or Table 2-1 at https://ncbi.nlm.nih.gov/books/NBK22098/) Links to an external site. were too close to the ideal value 3:1. How do you confirm this suspicion?
2. What is really suspicious about Mendel’s data was his estimation of the ratio of 𝐴𝐴𝐴𝐴 versus 𝐴𝐴𝐴𝐴 in 𝐹𝐹2 (page 11 of the lecture slides). According to his theory, it should be 1:2. Since 𝐴𝐴𝐴𝐴 and 𝐴𝐴𝐴𝐴 had the same phenotype, Mendel had to do further experiment to ascertain them. He made his decision based on the phenotypes of their self-fertilized offspring (𝐹𝐹3). Plants of 𝐴𝐴𝐴𝐴   would produce only phenotype𝐴𝐴, but plants of 𝐴𝐴𝐴𝐴 would produce types 𝐴𝐴 and𝐴𝐴. This is easy to determine for traits related to the seed because one plant could produce a large number of seeds, but for the traits related to the flower and pod, he had to wait until the seed grew into a full-grown plant. This took time and intensive labor. He decided to plant 10 seeds from each of the 100 𝐹𝐹2 plants (that meant 1000 plants) for the 𝐹𝐹3 observations. His data were as follows:

The ratio is indeed very close to 1:2. However, R. A. Fisher pointed out that the theoretical ratio should have been 1:1.696 when Mendel’s law was true. How did Fisher arrive at this ratio?

Problem 2.2: Spencer et (1964, Nature 201: 299-300) showed that there are three allelic variants (A, B and C) of the red cell acid phosphatase The observed frequency of the red cell acid phosphatase types in 178 random selected English adults are reproduced below:

1. What are the gene frequencies estimated from this sample?
2. Why were no CC individuals found?

Problem 2.3: Using the csv dataset (available from the Canvas), conduct transmission-disequilibrium test. The marker (alleles 1 and 2) has been reported to be associated with the disease.

1. Write down the null and alternative
2. Count the total number of heterozygous Count the number heterozygous parents who transmitted allele 1 but not allele 2. Count the number heterozygous parents who transmitted allele 2 but not allele 1. Calculate the TDT (McNemar) statistic and its p-value.
3. Based on a) and b), report the

Problem 2.4: Pick up a paper mentioned in Week 4 Write down the citation of the chosen paper. Focus on the data analysis part.

1. What is the research question of this paper?
2. What are the design of experiment and sample size? Are subjects independent?
3. What are the null and alternative hypotheses?
4. What is the statistic used for addressing the research question? What are the observed statistic and p-value (if available)?
5. What are the conclusions from data analysis?