In ANOVA and DOE, a balanced design has an equal number of observations for all possible combinations of factor levels. An unbalanced design has an unequal number of observations.
|
You have exactly one observation for all possible combinations of the factor levels for factors A, B, and C: (0, 0, 0); (1, 0, 0); (0, 1, 0); (0, 0, 1); (0, 1, 1); (1, 1, 0); (1, 0, 1); and (1, 1, 1).
| ||||||||||||||||||||||||||||||
|
Here, you are missing the (1, 0, 0) factor level combination and you have two observations of the (0, 1, 0) combination. Either one of these conditions, by itself, makes this design unbalanced. | ||||||||||||||||||||||||||||||
Analysis of a balanced design is generally straightforward because you can use the differences among the raw factor level means for your estimates of the main and interaction effects. If your design is not balanced, either by plan or by accidental loss of data, differences in the raw factor level means may reflect the unbalanced observations rather than changes in factor levels. For unbalanced designs, you can use fitted (or least squares) means to predict the results a balanced design would have produced.