K-모집단 동질성검정에서 피어슨검정의 오차성분 분석에 관한 연구

Abstract

Traditional Pearson chi-squared test is not appropriate for the data collected by the complex sample design. When one uses the traditional Pearson chi-squared test to the complex sample categorical data, it may give wrong test results, and the error may occur not only due to the biased variance estimators but also due to the biased point estimators of cell proportions. In this study, the design based consistent Wald test statistics was derived for k-population homogeneity test, and the traditional Pearson chi-squared test statistics was partitioned into three parts according to the causes of error; the error due to the bias of variance estimator, the error due to the bias of cell proportion estimator, and the unseparated error due to the both bias of variance estimator and bias of cell proportion estimator. An analysis was conducted for empirical results of the relative size of each error component to the Pearson chi-squared test statistics. The second year data from the fourth Korean national health and nutrition examination survey (KNHANES, IV-2) was used for the analysis. The empirical results show that the relative size of error from the bias of variance estimator was relatively larger than the size of error from the bias of cell proportion estimator, but its degrees were different variable by variable.