A method of scalogram analysis using summary statistics

Post-Training Performance Criterion Development and Application. The Development of Unidimensional Scales for the Dimensions Derived From a Multidimensional Scale Analysis of the Job of the Naval Aviation Electronics Technician

“…Following the procedure of the earlier scaling studies, the method of Guttman analysis described by Green (1956) was employed. In this method an index of consistency, I, is used to replace the several requirements for scalability proposed by Guttman.…”

GSCALE: Scalogram analysis for dichotomously scored items

“…Although some have advocated methods of scalogram analysis which maximize the fit between the sample data and the scalogram model (cf. Chevan, 1972;White & Saltz, 1957), Green (1956) has pointed out that, when Guttman's model holds, the items must be ranked by difficulty (or popularity) and that little is usually gained by seeking optimal solutions. GSCALE is therefore most appropriately used when a set of items is initially being screened for scalability.…”

“…Each such response is considered a scale error and R =1 -E/NK, where N is the number of subjects, K is the number of items, and E is the total number of scale errors for all subjects. A more detailed description of the error counting procedure is given by Green (1956).…”

“…Exact calculation of chance reproducibility requires generation of 2 K possible response patterns, calculation of the number of scale errors associated with each pattern, and estimation of the number of subjects showing each response pattern when the items are mutually independent. However, a useful approximation has been developed by Green (1956), and Chilton (1969) has shown that Green's coefficient, RI, gives highly accurate estimates for K~10. Although the accuracy of Green's estimate for longer tests has not been determined, RI, in conjunction with the confidence interval for R, will permit an approximate test of the null hypothesis of item independence.…”

“…Although the accuracy of Green's estimate for longer tests has not been determined, RI, in conjunction with the confidence interval for R, will permit an approximate test of the null hypothesis of item independence. Since the upper limit of R is 1, Green (1956) suggested calculation of an index of consistency [I = (R -RI)/(1 -Rd] , which equals 1 when the items are perfectly scalable and which has an expected value of owhen the items are independent. Green suggested that items be considered scalable if I ;;, .5.…”