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)(μ
aspirin) + (0.5)(μ
Tylenol) + (-1)(μ
placebo)