In behavioral and educational research, subjects may be randomly sampled from some population and randomly assigned to one of two or more groups (control, treatment level 1, treatment level 2, etc.). A comparison of the groups tells us about the effects of the treatments. These treatment level effects represent differences between subjects.
In a between-subjects design, responses from a given subject appear in only one group.
The variability of scores within each group reflects individual differences and is accounted for by the chance elements in sampling. This sampling variability is thus due to chance.
The variability of means between groups reflects both individual (chance) differences and differences due to the treatment.
Consider the following 4-group experiment:
y.1 -- mean of group 1
y.2 -- mean of group 2
y.3 -- mean of group 3
y.4 -- mean of group 4
y.. -- grand mean
Linear Statistical Models Course
Phil Ender, 12Feb98