Most responses to educational and psychological test items may be represented in binary form. However, such dichotomously scored items present special problems when an analysis of correlational interrelationships among the items is attempted. Two general methods of analyzing binary data are proposed by Horst to partial out the effects of differences in item difficulties: (1) a least square simplex data matrix solution, and (2) a least square simplex covariance matrix solution. Of these, the first was selected for study using (1) a regression approach, (2) a raw data approach, and (3) the computational algorithm for the raw data matrix approach. The results indicate that Horst's modification clearly induces an effect that contaminates the common factor structure of the variables. Further, the findings also indicate that image, alpha, and principal components analysis of correlation matrices obtained from binary data matrices are all satisfactory methods of analysis without the modification. This may be an important finding since it tends to confirm earlier empirical findings concerning the varying difficulties of binary items. (CK)