Data Description

One English test form from a national standardized examination administered in 1999 was examined using Q3 index. The test consists of 5 passages and there are 15 items associated with each passage. The number of examinee who has taken the test is 2551. Since, items are nested in particular passage in the test, we cannot be certain that local independence assumption is held for this data. So the check-up procedure is needed such as calculating Q3 index. IRT item parameters, $a_i$, , and $c_i$, and the examinee parameter, ${\theta}_k$ for 3-PL model of test data were estimated using computer software from [33]. Once the item parameters and the examinee parameter are estimated, can be estimated using equation 6.6. Then Q3 statistic can be calculated. Thus, we have a matrix for the item parameters, $a_i$, , and $c_i$, called PAR, a $2551 \times 1$ matrix for the examinee parameter, ${\theta}_k$, called THT, and a matrix for the answers of each student, called RAW.