An investigation of simulated data for gene expression values that examines the issues of false positive and false negative results in R program.

(a) Create four samples named A, B, C, and D each consisting of 10 independent random values from the normal distribution with = 1000 and = 200. These data simulate the 10 measured expression levels of a hypothetical gene for 4 equal-sized groups A, B, C, D (e.g., of patients or cell lines) without differences between the groups.

Recalling that usage of the ANOVA oneway test is

oneway.test(values~ind,groupsdataframe,var.equal=TRUE) 

and usage of the Kruskal-Wallace test is

kruskal.test(values~ind,groupsdataframe) 

(b) Use ANOVA and Kruskal-Wallis tests to test your simulated data for any difference of the mean and median between the groups at the p=0.05 level.

(c) Repeat a) and b) 10000 times separately accumulating the p-values from the tests (do not show the output). For the each of the ANOVA and Kruskal-Wallis tests, how many times do you find a significant difference in the means or medians of the four groups? Why are these results to be expected?

(d) Create four samples named A, B, C, and D each consisting of 10 independent random values sampled from a normal distribution with = 200 in all cases, but with A having mean = 1000, B having = 1100, C with = 1050 and D with = 870. Such data simulates 10 measured expression levels of a hypothetical gene for 4 equal-sized groups A, B, C, D with small differences between the groups.

(e) Test 10000 repeats of (d) for significant differences in the means/medians using both ANOVA and Kruskal-Wallis tests. For each type of test, in how many cases is a significant difference not found. Why are these results to be expected?