Sensitivity of Linkings between AP Multiple-Choice Scores and Composite Scores to Geographical Region: An Illustration of Checking for Population Invariance.

This application study investigates whether the multiple-choice to composite linking functions that determine Advanced Placement Program exam grades remain invariant over subgroups defined by region. Three years of test data from an AP exam are used to study invariance across regions. The study focuses on two questions: (a) How invariant are grade thresholds across regions? and (b) Do the small sample sizes for some regional groups present particular problems for assessing thresholds invariance? The equatability index proposed by Dorans and Holland (2000) is employed to evaluate the invariance of the linking functions, and cross-classification is used to evaluate the invariance of the composite cut scores. Overall, the linkings across regions seem to hold up reasonably well. Nevertheless, more exams need to be examined.