Tests of Linear Combinations of Means, Independent Groups (1 of 7)

In a hypothetical experiment, aspirin, Tylenol, and a placebo were tested to see how much pain relief each provides. Pain relief was rated on a five-point scale. Four subjects were tested in each group and their data are shown below:
Aspirin      Tylenol    Placebo
   3            2          2
   5            2          1
   3            4          3
   5            4          2
Before conducting the experiment, the researcher planned to make two comparisons: (1) a comparison of the average of the aspirin and Tylenol groups with the placebo control and (2) a comparison between the aspirin and Tylenol groups. The comparisons can be framed in terms of linear combinations of means: The first comparison is:

In terms of coefficients:

(0.5)(μaspirin) + (0.5)(μTylenol) + (-1)(μplacebo)