As an example, consider a hypothetical experiment in which aspirin, Tylenol, and a placebo are tested to see how much pain relief each provides. The amount of pain relief is rated on a five-point scale. Four subjects are tested in each group. The data are shown below:

The problem is to calculate the 95% confidence interval on the difference between the average of the aspirin and Tylenol groups and the placebo. That parameter being estimated is:Aspirin Tylenol Placebo 3 2 2 5 2 1 3 4 3 5 4 2

where μ

The first step is to find the coefficients (a's) so that

Σa

where aspirin is Condition 1, Tylenol is Condition 2, and placebo is Condition 3. The solution is: a