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.

Data set link: https://docs.google.com/spreadsheets/d/14E_L0lv2eFaldsOItUrdDaF93P_S21w2gx2xIl6ru64/edit#gid=1381509714

Please check answers and provide step-by-step solutions when using statistical software. Also, please don't copy and paste from other sources. Thanks.

A. 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 64.6 59.2

1.6/0.7 64.4 59.5

0.7/0.7 50.4 63.1

B. Follow-up studies since the 1992 study have confirmed the lack of association between genotype and 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.

The above hypotheses will be tested utilizing an F-ratio for a One-way ANOVA.

F = 0.027

p = 0.8773, p > 0.05

Conclusion: We fail to reject the null hypothesis.

Conclusion: Because p > .05, we fail to reject the null hypothesis because the results are not significant. This signifies that the means are equal. There is a lack of association from the Nashville data that agrees with the ANOVA results from the data set. The Nashville data set does not agree with ANOVA results due to the Type II error caused by a small sample size.