Partitioning the Sums of Squares (1 of 7)
Data from a hypothetical experiment on pain relief described
are reproduced below.
Aspirin Tylenol Placebo
3 2 2
5 2 1
3 4 3
5 4 2
The experiment consists of one factor
(Drug condition) which has three levels
(Aspirin, Tylenol, and Placebo). There are four subjects in each of
the three groups making a total of N = 12 subjects. The scores for
these 12 subjects obviously differ from each other: They range from
two to five. There are two sources of these differences among scores
(1) treatment effects and (2) error.
It is possible that some of the differences among the 12 scores
obtained in the experiment are due to the fact that different
subjects were given different drugs. If the drugs differ in their
effectiveness, then subjects receiving the more effective drugs will
have the higher pain-relief scores. The more different the
effectiveness of the drugs, the greater will be the differences among
the scores. Since the different drugs represent different ways the
subjects were "treated," differences due to differences in drug
effectiveness are said to be due to "treatment effects."