Two way ANOVA for unbalanced designs
Is there a relationship between bedrock type and lung cancer
rates? Data are collected from 26 counties in Pennsylvania, New
Jersey and New York. Archer (Archives of Environmental
Health, 1987, 42:87-91) found a relationship between lung cancer rates and the underlying bedrock type: counties over Reading Prong granite had more cancer. Since these granites emit radon, a potent carcinogen, it seems plausible that radon from the Reading Prong bedrock causes higher cancer rates.
For the dataset, bedrock.txt, the following variables are measured:
- County
- State
- Lung cancer: White female lung cancer rate per 100,000 per year, 1950-1969
- Bedrock area: Reading Prong areas overlie granite bedrock that has been associated with high indoor radon concentrations. Fringe areas border the Reading Prong, and control areas lie outside it.
- Mean house radon: Cohen (Archives of Environmental
Health, 1988, 43:313-314) reports mean radon concentrations in pCi/L, for living areas of hundreds of individual houses within each county. Categories used here are: low (0-1.5); mid (1.6-2.4); and high (over 2.5). In five counties, Cohen's means are based on fewer than 10 houses.
Fit the following ANOVA models and bring them to class:
- Cancer~Bedrock.Area*Mean.House
- Cancer~Bedrock.Area+Mean.House
- Cancer~Mean.House+Bedrock.Area
- Cancer~Bedrock.Area
- Cancer~Mean.House
- Compare the sums of squares for Mean.House and for Bedrock.Area under each model.
- Review the model selection handout from class, stepping through the model selection process.