Partitioning the Sums of Squares (1 of 7)

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Data from a hypothetical experiment on pain relief described earlier 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.

Treatment Effects
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."
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