Chapter 10: Comparing Two Groups
Bivariate Analysis: Methods for comparing two groups are special cases of bivariate statistical methods – Two variables exist:
Response variable – outcome variable on which comparisons are made
Explanatory variable – binary variable that specifies the groups
Statistical methods analyze how the outcome on the response variable depends on or is explained by the value of the explanatory variable
Independent Samples: Most comparisons of groups use independent samples from the groups, The observations in one sample are independent of those in the other sample
Example: Randomized experiments that randomly allocate subjects to two treatments Example: An observational study that separates subjects into groups according to their value for an explanatory variable
Dependent samples: Dependent samples result when the data are matched pairs – each subject in one sample is matched with a subject in the other sample

Example: set of married couples, the men being in one sample and the women in the other.
Example: Each subject is observed at two times, so the two samples have the same subject
Categorical response variable:
For a categorical response variable
- Inferences compare groups in terms of their population proportions in a particular category
- We can compare the groups by the difference in their population proportions: (p1 – p2)
Example: Experiment: Subjects were 22,071 male physicians
Every other day for five years, study participants took either an aspirin or a placebo
The physicians were randomly assigned to the aspirin or to the placebo group
The study was double-blind: the physicians did not know which pill they were taking, nor did those who evaluated the results
What is the response variable?
The response variable is whether the subject had a heart attack, with categories ‘yes’ or ‘no’. What are the groups