The Distribution of Indexes of Person Fit within the Computerized Adaptive Testing Environment

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Abstract
The extent to which a trait estimate (6) represents the underlying latent trait of interest can be estimated by using indexes of person fit. Several statistical methods for indexing person fit have been proposed to identify nonmodel-fitting response vectors, including the lz (Drasgow, Levine, & Williams, 1985) and ECI4z (Tatsuoka, 1984) indexes (see Nering, 1996). These two person-fit indexes have generally been found to follow a standard normal distribution for conventionally administered tests (Birenbaum, 1985, 1986; Drasgow, Levine, & McLaughlin, 1987, 1991). The present investigation found that within the context of computerized adaptive testing (CAT) these indexes tended not to follow a standard normal distribution. As the item pool became less discriminating, as the CAT termination criterion became less stringent and as the number of items in the pool decreased, the distributions of lz and ECI4z approached a standard normal distribution. It was determined that under these conditions the kz and ECI4z distributions approached standard normal distributions because more items were being administered. However, even when over 50 items were administered in a CAT the indexes of person fit were distributed in a fashion that was different from what was expected.