Examining the comparability of individual skill scores obtained through cognitive diagnostic models with parallel forms

Diagnostic assessment identifies students' strengths and weaknesses, and learning needs. Cognitive Diagnostic Models (CDM) provide feedback on objectives or skills identified as attributes within the framework of measurement aims. Test equating refers to the process of combining scores from different test forms on the same scale, indicating that these scores can be used interchangeable and convey the same meaning. The aim of this study is to investigate the feasibility of obtaining comparable skill scores between tests through traditional test equating practices by converting mastery level probability values obtained through mixed hierarchically structured GDINA model analyses of test forms created within the framework of Cognitive Diagnostic Models (CDMs). In this context, three 20-item multiple-choice diagnostic tests constructed to measure six algebraic thinking abilities were administered to a total of 2600 high school students, and the response patterns obtained were used. Mastery level probabilities obtained through mixed hierarchically structured GDINA model analyses that fit the response patterns were converted into ability scores. Equating ability scores between tests was examined through various methods, including mean, linear, equipercentile, and kernel equating, by restricting the equating to generalized arithmetic, quantitative reasoning, and functional thinking abilities, within the frameworks of equivalent groups, non-equivalent groups with anchor test, and non-equivalent groups with covariates designs. Statistical information such as equated score differences, equating errors, and bias were shared. According to the findings of the study, it is observed that equating can be performed in groups showing no significant differences in group moments and having similar score distribution patterns.