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

Several person-fit statistics have been proposed to detect item score patterns that do not fit an item response theory model. To classify response patterns as misfitting, the distribution of a person-fit statistic is needed. The theoretical null distributions of several fit statistics have been derived 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 distribution of the lz statistic across trait. 0levels for CAT and P&P tests was investigated. The distribution of the l*z statistic proposed by Snijders (in press) was also investigated. Results indicated that the distribution of both lz and l*z differed from the theoretical distribution in CAT. The second study examined the distributions of lzand l*z using simulation. These simulated distributions, when based on O [UNKNOWN], were found to be problematic in CAT. In the third study, the detection rates of l*z and lz were compared. The rates for both statistics were found to be similar in most cases