Common items play an important role in item response theory (IRT) true score equating under the common-item nonequivalent groups design. Biased item parameter estimates due to common item outliers can lead to large errors in equated scores. Current methods used to screen for common item outliers mainly focus on the detection and elimination of those items, which may lead to inadequate content representation for the common items. To reduce the impact of inconsistency in item parameter estimates while maintaining content representativeness, the authors propose two robust scale transformation methods based on two weighting methods: the Area-Weighted method and the Least Absolute Values (LAV) method. Results from two simulation studies indicate that these robust scale transformation methods performed as well as the Stocking-Lord method in the absence of common item outliers and, more importantly, outperformed the Stocking-Lord method when a single outlying common item was simulated.

Item parameter estimates of a common item on a new test form may change abnormally due to reasons such as item overexposure or change of curriculum. A common item, whose change does not fit the pattern implied by the normally behaved common items, is defined as an outlier. Although improving equating accuracy, detecting and eliminating of outliers may cause a content imbalance among common items. Robust scale transformation methods have recently been proposed to solve this problem when only one outlier is present in the data, although it is not uncommon to see multiple outliers in practice. In this simulation study, the authors examined the robust scale transformation methods under conditions where there were multiple outlying common items. Results indicated that the robust scale transformation methods could reduce the influences of multiple outliers on scale transformation and equating. The robust methods performed similarly to a traditional outlier detection and elimination method in terms of reducing the influence of outliers while keeping adequate content balance.

Common test items play an important role in equating alternate test forms under the common item nonequivalent groups design. When the item response theory (IRT) method is applied in equating, inconsistent item parameter estimates among common items can lead to large bias in equated scores. It is prudent to evaluate inconsistency in parameter estimates of common items before conducting IRT equating. The evaluation of inconsistency in parameter estimates is typically achieved through detecting outliers in the common item set. In this study, a linear regression method is proposed as a detection method. The newly proposed method was compared with a traditional method in various conditions. The results of this study confirmed the necessity of detecting and removing outlying common items. The results also show that the newly proposed method performed better than did the traditional method in most conditions.

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