intervals for risk differences based on asymptotic approximation. Risk difference intervals containing 0 will tell us that the risk is not significantly different for the two row categories. A completely negative interval would say that the second row category has a significantly higher risk of being in that column category. A completely positive interval would say that the first row category is at greater risk of being in that column category. SAS will give us the risk estimates and intervals for each column (so estimates and intervals for being in a particular calcium concentration group given the mortality groups as our tables were set up). Switching the rows and columns will allow us to estimate the other risks and differences. Exercises Sandflies data For the sandflies data set we could do the same type of analysis. • Obtain row and column percentages. • Comment on significance of association. • Do there appear to be any differences within rows or columns? • Obtain confidence intervals for row and column risks and comment on significant differences. Acacia Ants data For this data set (the ants data set from the text), we want to know if there is a greater risk of ants invading one species of acacia tree. We have two species of trees and counts for trees of each species that were invaded by ants.
•Obtain a contingency table including expected counts. Does independence seem reasonable based on the counts? If not, what type of relationship might we expect based on the counts? •Test for association to check your intuition from the previous part. •Obtain risk estimates to see if there are significant differences. Oral Cancer data This example is a table where we have more than 2 rows and more than 2 columns. We will use the code for defining the lesionsdata set given in Chapter 3 of the text. Note that Fisher’s exact test is only generated by default for 2x2 tables. We need to use the exact(or fisher) option if we want that result for larger tables. In this data we have geographic regions of India (3 regions) and types of oral cancer (9 types). •Get a contingency table with just frequencies. •Do counts suggest association? •Obtain measures and test results for association. •Do measures suggest association? •Do tests reject a hypothesis of independence? •Which results should be trust and why?
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- Spring '08
- Pearson's chi-square test, Fisher's exact test