Use the Hedenfalk, breast cancer gene expression dataset. The files...

Use the Hedenfalk, breast cancer gene expression dataset. The files are GeneExp.txt and Samples.txt

Part a
For each gene, implement and apply a permutation test to compare the difference in means between BRCA1 samples and BRCA2 samples. The null hypothesis here is that the difference in means is 0. Use a two- sample t-statistic for the permutation test. Don’t forget that the test is two-sided. There are 15/7 = 6435 possible shufflings, so for the purposes of this homework it may be impractical to enumerate all the possible combinations. We suggest that you do 500 to 2,000 permutations per gene, depending on your computing capacity. Plot a histogram of your p-values. Hint: dplyr’s do() function may be helpful if you have your data in a tidy format.

Part b
For each gene, test the difference in means between BRCA1 and BRCA2 samples using a parametric t-test. Then, plot the p-values computed by each method against each other to compare the results of the two testing approaches. What does the plot suggest about the t-test assumptions? Some hints for making an effective plot: you will want to draw the y = x line to represent exact concordance between the results and it may be helpful to fix the plot aspect ratio.