ABSTRACT
We recall from Chapter 8 that a data set consisting of the values of some response, Y, is said to be balanced if the range of any one subscript of Y does not depend on the values of the other subscripts. If this condition is not satisfied by the data set, then it is said to be unbalanced. Thus, we may have unequal numbers of observations in the subclasses of the data, with possibly some subclasses containing no observations at all. In the latter case, we say that we have empty subclasses or empty cells. For example, in Table 9.1 which gives the prices of a variety of food items sold in large supermarkets (see Example 9.1), we have a total of 48 cells each containing three observations (prices recorded for a total of three months). If, for example, for supermarket 2 in area 1, the price of food item 2 was recorded only twice, then we end up with a data set that violates the condition stated earlier. It is also possible that no information at all was recorded regarding the price of such an item in that supermarket. In this case, the cell (1, 2, 2) corresponding to area 1, supermarket 2, and food item 2 will be empty.
