ABSTRACT
This chapter is a tale of a purpose, some ideas, some successes, some disappointments, and a need for further workable ideas. The search for factor analytic type structures in dichotomously scored items has presented nasty, exasperating problems for many years. Three publications in 1941 provide early indications as to the nature of these problems. Guilford (1941) published an analysis of Seashore's test of musical talent in which there were factors related to the difficulty of the items. Ferguson's (1941) article on the factorial interpretation of test difficulty gave a theoretic basis for factors related to item difficulty. Guttman (1941) presented his theory for the quantification of a class of attributes which included his components of scalability. Wherry and Gaylord (1944) followed the Guilford and Ferguson articles with a publication relating content, difficulty, and constant error factors to the type of correlation coefficients used. Guilford used tetrachoric correlation coefficients while Ferguson's development was based on the phi coefficient. Carroll (1945) pointed out the need to correct the fourfold tables for the effects of guessing before obtaining tetrachoric correlations and removed much of the effects of item difficulty from the Guilford analysis. Gourlay (1951) published on the difficulty factors arising from the use of tetrachoric correlations. Dingman (1958) also commented on the relation between coefficients of correlation and difficulty factors. Carroll (1961) discussed the nature of data with a relation as to how to choose a correlation coefficient. Carroll (1983) returned to consideration of effects of the probabilities examinees know the answer to an item as well as the effects of chance guessing on the product moment correlations and the tetrachoric correlations between items. He did not consider how to correct the correlations for these influences.
