An APL program for minimum-error Guttman scaling

Computer programs which perform minimum-error Guttman scaling are not widely available. The most accessible program to perform any type of Guttman scaling is the SPSS (Nie, Hull, Jenkins, Steinbrenner, & Bent, 1975) program, which uses the Goodenough (1944) procedure for counting errors. Unfortunately, according to McConaghy (1976), the statistical tests used to evaluate the scales produced by SPSS are based on the minimum-error rather than the Goodenough procedure. This discrepancy produces an overly conservative statistical test. A program written to perform minimum-error Guttman scaling uses an error-counting technique and statistical tests that are consistent with each other. The program permits ambiguous score patterns that have minimum Guttman errors at two or more "true" score values to be treated in any of four different ways. These treatments include random selection among the possible score values, selection of the middle score, and selection of the highest or the lowest of the possible scores. The variety of alternatives illustrates the continuing nature of the controversy which still surrounds the scaling procedure (Dotson & Summers, 1970; Henry, 1952; Wimberley, 1976). Computer and Language. The program is written in the APL language for use at a computer terminal. The language and the program combine to permit a high degree of interaction between the user and the computer. The algorithms can be translated into FORTRAN, but would result in a program more than five times as long ae the APL program. The program will function on any computer with an APL system. Input, A matrix containing the data to be analyzed must be prepared before the program is executed. Each row of the matrix represents a case; each column represents the responses to an item forming the scale. Responses must be coded in binary form, with 1 indicating than an item was passed and 0 indicating that an item was failed. Other input is requested during the execution of the program: specification of processing, statistics and output options, and the insertion of a title for each analysis. Computational Procedure. The entire matrix (or any subset of columns selected by the user) is rearranged according to the number of cases passing each item. The response pattern of each case is then compared to a matrix of perfect-scale types. The number of Guttman errors associated with the comparison to each perfect scale is stored in an error vector. Unambiguous cases are assigned the score corresponding to the perfect-scale type which resulted in the fewest Guttman errors. Ambiguous cases are handled in one of four ways, depending on the user's preference. Statistics are computed after each case is assigned a "true" Guttman score. (See Appendix A for an example of perfect data; Appendix B shows random data.) Output. The following information may be printed at the terminal or stored on an APL file for later printing on a high-speed line printer: (1) number of cases passing each item, (2) coefficient of reproducibility, (3) minimum marginal reproducibility, (4) percent improvement, (5) coefficient of scalability, (6) descriptive statistics and frequency distributions for "true" scores and for case-bycase Guttman errors, and (7) complete listing of scale score, number of errors, and response pattern for all cases. Restrictions. The input data matrix should be limited to no more than 10,000 elements (e.g., 500 cases and 20 items). Availability. Copies of this paper and a source listing with complete documentation may be obtained without charge from Marshall H. Segall, Interdisciplinary Social Science Program, Syracuse University, Syracuse, New York 13210.