The ability parameter of persons/examinees estimates can be obtained using the Joint Maximum Likelihood (JML) estimation in Item Response Theory (IRT). However, JML estimates can be biased in some cases. Although the Bootstrap method has been considered for JML, existing studies remain far from satisfactory concerning the ability parameter estimation. This research evaluates the performances of JML and Bootstrap estimates of the ability parameter in terms of Standard Error Measurement (SEM) in the 2-Parameter Logistic (2-PL) model conducting a detailed Monte Carlo simulation study. According to the results, the average SEM estimates of the Bootstrap method are less than the average SEM estimates of JML in terms of the ability parameter.
Analysis of association between ordinal categorical variables has been widely studied especially in social sciences and medicine. It is known that ordinal scale has several advantages over nominal scale for researchers. Mantel-Haenszel (MH) chi-square statistic, which is known as the appropriate statistics to identify the association between ordinal categorical variables, takes into consideration the linear trend. In this study, integer, midrank, exponential, Van der Waerden, and joint scores were compared with a Monte Carlo simulation study to evaluate power of MH chi-square statistics. Although integer score has been used so far in literature, it is seen that Van der Waerden score is also preferable according to results.
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