The null distribution of person-fit statistics for conventional and adaptive tests

Several person-fit statistics have been proposed to detect item score patte rns that do not fit an item response theory model. To classify response pat terns as misfitting, the distribution of a person-fit statistic is needed. The theoretical null distributions of several fit statistics have been deri ved for paper-and-pencil (P&P) tests. However, it is unknown whether these distributions also hold for computerized adaptive tests (CAT). A three-part simulation study was conducted. In the first study, the theoretical distri bution of the l(z) statistic across trait (theta) levels for CAT and P&P te sts was investigated. The distribution of the l(z)* statistic proposed by S nijders (in press) was also investigated. Results indicated that the distri bution of both l(z) and l(z)* differed from the theoretical distribution in CAT. The second study examined. the distributions of l(z)* and If using si mulation. These simulated distributions, when based on <(theta)over cap>, w ere found to be problematic in CAT. In the third study, the detection rates of l(z)* and l(z) were compared. The rates for both statistics were found to be similar in most cases.