The use of statistical process controlcharts for person fit analysis in computerized adaptive testing

In this study a cumulative-sum (CUSUM) procedure from the theory of Statistical Process Control was modified and applied in the context of person-fit analysis in a computerized adaptive testing (CAT) environment. Six person-fit statistics were proposed using the CUSUM procedure, and three of them could be used to investigate the CAT in online test taking. The usefulness of these statistics was explored in a small simulation study. In most CUSUM procedures standard normally distributed statistics are used. Based on this normality, boundaries can be determined to decide when a process is out of control. The statistics proposed in this study, however, are not standard normally distributed, and therefore, in this study, boundaries were determined using simulated data. The study investigated whether the numerical values of the upper and lower threshold were dependent on the latent trait, theta. Results show that the upper and lower bound were rather stable across theta-levels. However, the height of the boundaries was dependent on the particular statistic chosen.