Standard setting with dichotomous and constructed response items: some Rasch model approaches

Using real data comprising responses to both dichotomously scored and constructed response items, this paper shows how Rasch modeling may be used to facilitate standard-setting. The modeling uses Andrich's Extended Logistic Model, which is incorporated into the RUMM software package. After a review of the fundamental equations of the model, an application to Bookmark standard setting is given, showing how to calculate the bookmark difficulty location (BDL) for both dichomotous items and tests containing a mixture of item types. An example showing how the bookmark is set is also discussed. The Rasch model is then applied in various ways to the Angoff standard-setting methods. In the first Angoff approach, the judges' item ratings are compared to Rasch model expected scores, allowing the judges to find items where their ratings differ significantly from the Rasch model values. In the second Angoff approach, the distribution of item ratings are converted to a distribution of possible cutscores, from which a final cutscore may be selected. In the third Angoff approach, the Rasch model provides a comprehensive information set to the judges. For every total score on the test, the model provides a column of item ratings (expected scores) for the ability associated with the total score. The judges consider each column of item ratings as a whole and select the column that best fits the expected pattern of responses of a marginal candidate. The total score corresponding to the selected column is then the performance band cutscore.