There are two groups of patients, say, young and old, and we want to determine whether these two groups of patients react differently to our treatment. Let $X$ be a continuous dependent variable, say, blood pressure which will be measured twice for every patient: once before the treatment and once after. An average change of $X$ after the treatment will be calculated for the first and second group, say, values $A_1$ and $A_2$, respectively.
- How can we check whether there is a statistically significant difference between $A_1$ and $A_2$?
- How can we conduct power analysis to estimate the size of the groups if we know only the measurement error of $X$ and the expected difference between $A_1$ and $A_2$?
- Questions 1 and 2 is for the scenario when we measure not absolute, but relative changes in variable $X$.