부산대학교 도서관

The General Tobacco Hazards Prevention Act Test was conducted by the Changhua county health bureau. This test was an internet-based test designated to the high school students. The students who joined the Test were randomly assigned to different groups and received different questions. Since some respondents did not completed the assigned questions, this resulted in having missing data in each questions group. In the presence of missing data, it is difficult to compare the probabilities of the correct response between different questions within the same group. Generally, when the missing data is not well treated, it may cause the invalid inference. We used the nonparametric multiple imputation method proposed by Wang and Chen (2009) to impute the missing data and to estimate the accuracy of the average probabilities of the correct response. We used the McNemar test to analyze the probabilities of the correct response between two different questions answered by the same student. The use of Rubin’s formula underestimated the variance which has to be used as the denominator of McNemar test statistic. Hence, the Bootstrap method was used to correct that estimated the variance which is in the denominator in McNemar test, as well as the other variance used in the numerator. The simulation study was conducted to investigate the performance of proposed estimation of average probabilities of the correct response, and the modified McNemar test. The results of simulation study showed that the proposed approach could produce higher accuracy of estimation average probabilities of the correct answer, compared with just using the original data. Consequently, the modified McNemar test by the correction of Bootstrap had higher power of test than the results of the independent sample proportion test. This study used an example of the data collected from The General Tobacco Hazards Prevention Act Test in 2015 in order to explore the proposed methods.