Statistics for Categorical Data: Odds Ratios and Chi-Square

This assignment focuses on categorical data. Two of the statistics most often used to test hypotheses about categorical data are odds ratios (ORs) and the chi-square. The disease-OR refers to the odds in favor of disease in the exposed group divided by the odds in favor of the unexposed group. Chi-square statistics measure the difference between the observed counts and the corresponding expected counts. The expected counts are hypothetical counts that would occur if the null hypothesis were true.

Part 1: ORs

A study conducted by Lopez-Carnllo, Avila, and Dubrow (1994) investigated health hazards associated with the consumption of food local to a particular geographic area, in this case chili peppers particular to Mexico. It was a population-based case-control study in Mexico City on the relationship between chili pepper consumption and gastric cancer risk. Subjects for the study consisted of 213 incident cases and 697 controls randomly selected from the general population. Interviews produced the following information regarding chili consumption:

Table 1: Chili Pepper Consumption and Gastric Cancer Risk

Part 2: Chi-Square

Bain, Willett, Hennekens, Rosner, Belanger, and Speizer (1981) conducted a study of the association between current postmenopausal hormone use and risk of nonfatal myocardial infarction (MI), in which 88 women reporting a diagnosis of MI and 1,873 healthy control subjects were identified from a large population of married female registered nurses aged thirty to fifty-five years. To test the hypothesis that there is no association between use of postmenopausal hormones and risk of MI, chi-square statistics need to be calculated.
The data are presented as follows:

Table 2: Association between Postmenopausal Hormone Use and Risk of Nonfatal MI

Reference:

Bain, C., Willett, W., Hennekens, C. H., Rosner, B., Belanger, C., & Speizer, F. E. (1981). Use of postmenopausal hormones and risk of myocardial infarction. Circulation, 64(4 42-46.