ABSTRACT
The three data types discussed so far (i.e., contingency tables, multiple-choice data and sorting data) can be subjected, without modifications, to the method of reciprocal averages. This is so because data elements are nonnegative, and the sum of a row (a column) represents the number of responses in that row (column). Once negative elements are involved, however, the sum of the elements of a row no longer tells us how many responses are involved in that row. This is exactly the problem with paired comparison data, and two other types to be discussed in the ensuing chapters. Although it may not be well known, the extension of the method to data matrices containing negative elements was successfully formulated into a practical method by Guttman more than 40 years ago, in 1946. His extension was not obvious because he dealt with the difference between two matrices of nonnegative elements.
