Balanced and unbalanced designs in ANOVA models

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.

Balanced Design

You have exactly one observation for all possible combinations of the factor levels for factors A, B, and C: (0, 0, 0); (0, 0, 1); (0, 1, 0); (0, 1, 1); (1, 0, 0); (1, 0, 1); (1, 1, 0); and (1, 1, 1).

C1	C2	C3
A	B	C
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

Unbalanced Design

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.

C1	C2	C3
A	B	C
0	0	0
0	1	0
0	1	0
0	0	1
0	1	1
1	1	0
1	0	1
1	1	1

Analysis of a balanced design is usually straightforward because you can use the differences between 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 show the unbalanced observations instead of changes in factor levels. For unbalanced designs, you can use fitted means to predict the results a balanced design would have produced.

Determine whether your data are balanced

Your design must be balanced to use Balanced ANOVA. For a small data set, you can look in the worksheet and easily see if the data are balanced.

To determine whether your data are balanced with large data sets, create a cross tabulation table. To create this table, choose Stat > Tables > Cross Tabulation and Chi-Square. Examine the cells in the resulting output. A cell is the intersection of a row and a column. If a cell's count is not equal to the counts of all other cells, you have unbalanced data.