A 1989 study by Parl et al. (Breast Cancer Res Tr; 14:57-64) showed an association between a polymorphism in the estrogen receptor gene and the age of onset of breast cancer. The data is in the data set polymorphism.dta. There are three genotypes: 1.6/1.6, 1.6/0.7 and 0.7/0.7. The numbers refer to the size of a PvuII restriction fragment in kilobases.

1. Perform ANOVA to compare the three genotypes with age of onset as the response. What is the p-value for Bartlett's test for equal variances?__________________ Is it necessary that the variances be roughly equivalent to perform ANOVA?
2. What is the p-value of the F test that compares the between groups and within groups variances? ____________________. What is the F value? ___________What can you conclude?
3. What is the Bonferroni-corrected p-value (from software) for each of the following pairwise comparisons?

1.6/1.6 to 1.6/0.7: ____________________

1.6/1.6 to 0.7/0/7: ____________________

1.6/0.7 to 0.7/0.7: ____________________

1. What genotype (if any) is different from the others in terms of age of onset?

1. A follow-up study in 1992 by Yaich et al. (Cancer Res 52:77-82) examined patients at Nashville Memorial Hospital. Your data set (polymorphism.dta) contains data from Vanderbilt University Hospital in the same city. Based on your data set, fill in the following table:

Genotype Mean age of onset (Vanderbilt) Mean age of onset (Nashville) 1.6/1.6  FILL IN 59.2 1.6/0.7  FILL IN 59.5 0.7/0.7  FILL IN 63.1 

1. Follow-up studies since the 1992 study have confirmed the lack of association between genotype & age of onset of breast cancer. Would you say that the lack of association and the Nashville data agree with the ANOVA result from your data set? If not, statistically speaking (not medically or environmentally), explain what type of error was made and how that is possible.

SHOW WORK USING R STUDIO.

age genotype 43 1.6 /1.6 47 1.6 /1.6 55 1.6 /1.6 57 1.6 /1.6 61 1.6 /1.6 63 1.6 /1.6 63 1.6 /1.6 69 1.6 /1.6 70 1.6 /1.6 72 1.6 /1.6 72 1.6 /1.6 75 1.6 /1.6 79 1.6 /1.6 79 1.6 /1.6 38 1.6 /0.7 43 1.6 /0.7 43 1.6 /0.7 45 1.6 /0.7 49 1.6 /0.7 53 1.6 /0.7 54 1.6 /0.7 54 1.6 /0.7 54 1.6 /0.7 59 1.6 /0.7 59 1.6 /0.7 62 1.6 /0.7 65 1.6 /0.7 65 1.6 /0.7 67 1.6 /0.7 68 1.6 /0.7 68 1.6 /0.7 70 1.6 /0.7 71 1.6 /0.7 73 1.6 /0.7 73 1.6 /0.7 73 1.6 /0.7 75 1.6 /0.7 76 1.6 /0.7 78 1.6 /0.7 79 1.6 /0.7 83 1.6 /0.7 83 1.6 /0.7 87 1.6 /0.7 33 0.7/0.7 36 0.7/0.7 39 0.7/0.7 44 0.7/0.7 45 0.7/0.7 45 0.7/0.7 46 0.7/0.7 46 0.7/0.7 51 0.7/0.7 52 0.7/0.7 55 0.7/0.7 57 0.7/0.7 60 0.7/0.7 62 0.7/0.7 63 0.7/0.7 72 0.7/0.7