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.xls. 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. If you use a software program, please show your work. I prefer work to be shown on the computer than by hand. Thanks.

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

Are my answers below correct? Please use statistical software to generate your responses and please provide a step-by-step explanation to verify if my answers are correct.

A) 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?

p-value = 0.5828

Is it necessary that the variances be roughly equivalent to perform ANOVA?

Yes, it is necessary that the variances be roughly equivalent in order to perform ANOVA.

B) What is the p-value of the F test that compares the between groups and within groups variances?

p-value = 0.0000978, or p < .0001

What is the F value?

F value is 7.863

What can you conclude?

Because p < .0001, our results are significant and we can reject the null hypothesis that all variances are equal. There is a significant variance between the three groups.

C) What is the Bonferroni-corrected p-value (from software) for each of the following pairwise comparisons? Please use statistical software to generate your responses. Please indicate which answers below are correct. If they are all incorrect, please show the right answers.Thanks.

1.6/1.6 to 1.6/0.7: -1.000 (or 1.0)

1.6/1.6 to 0.7/0/7: -0.0065 (or 0.018)

1.6/0.7 to 0.7/0.7: -0.0015 (or 0.004)

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

The genotype 0.7/0.7 is different from the other genotypes in terms of age of onset.