This study was to investigate a practicability of rule space theory. Three research research questions were hypothesized. First, the classfications of item response patterns in rule spaces would result in the same error rates as those in the fields composed of the first two principal components which were computed from the item response patterns which were used in the classifications in rule spaces. Second, the classifiers would equally behave over the varying number of slips. Third, misclassification rates would be the same among the rule groups within a dataset.
A Mont-Carlo study was processed in four steps. First, using MCGENPC developed by Tatsuoka & Bailie(1988). two equivalent sets of 1800 40-item response patterns. a total of 3600. were simulated for each number of slips. which were varied 1 through 5 and expected numbers. One set was consisted of 9 rule groups. each of which contained 200 item response patterns. Those 9 groups were specially selected to form three triplets. one in the center area of ability continuum, and the other two in both extremes fo the continuum. Second, from each set of item response patterns, rule space variables and prinipal component scores were computed separately. These datesets then fomulated to enable to test the hypotheses on the effects of rule/principal-component field, the number of slips, and group memberships on the error rates. Third, a series of discriminant analyses were processed, which resulted in four types of error rates. two apparant error rates and two error rates from separate samples from each equivalent dataset. Fourth, hypotheses were tested.
Ahead of presenting the classification results, equivalence of the mathched datasets was tested. T-test of the mean differences and F-tests of the variance differences evidenced the equivalences of locations and shapes, respectively.
Findings enabled to reject all of the null hypotheses. First, the classfications in rule spaces were more erroneous when the number of slips were less than 5. But, the use of rule space provided more consistent and less errornous results when the number of slips were set to the theoretically expected ones. Second, as number of slips increased. error rates rised. Third, misclassifications happenned more frequently between the groups located closer.
Based on the results, three points were discussed. First, the comparison between the classifications in rule-space and in principal-component space was basically to research a effectiveness of rule-space model. It was clarified that even a positive result for principal component space could not replace the rule space for cognitive diagnostic measure. Second, number of slips might well be studied for its redefinition. Finally, a practical research deserves for a possibililty of a broader grouping of similar rules and of redefinition of the number of slips.