An article in Nature Genetics (2003, Vol. 34, pp. 85–90) “Treatment-Specific Changes in Gene Expression Discriminate in vivo Drug Response in Human Leukemia Cells” studied gene expression as a function of different treatments for leukemia. Three treatment groups are as follows:

mercaptopurine (MP) only; low-dose methotrexate (LDMTX) and MP; and high-dose methotrexate (HDMTX) and MP. Each group contained ten subjects. The responses from a specific gene are shown in the table below.

(a) Is there evidence to support the claim that the treatment means differ?

(b) Check the normality assumption. Can we assume these samples are from normal populations?

(c) Take the logarithm of the raw data. Is there evidence to support the claim that the treatment means differ for the transformed data?

(d) Analyze the residuals from the transformed data and comment on model adequacy.

Treatments Observations MP ONLY 334.5 31.6 701 41.2 61.2 69.6 67.5 66.6 120.7 881.9 MP + HDMTX 919.4 404.2 1024.8 54.1 62.8 671.6 882.1 354.2 321.9 91.1 MP + LDMTX 108.4 26.1 240.8 191.1 69.7 242.8 62.7 396.9 23.6 290.4