Earticle

초록

영어

Categorical data collected based on complex sample design is not proper for the standard Pearson multinomial-based chi-squared test because the observations are not independent and identically distributed. This study investigates effects of bias of point estimator of population proportion and its variance estimator to the standard Pearson chi-squared test statistics when the sample is collected based on complex sampling scheme. This study examines the effect under two population homogeneity test. The standard Pearson test statistic can be partitioned into two parts; the first part is the weighted sum of ?? with eigenvalues of design matrix as their weights, and the additional second part which is added due to the biases of the point estimator and its variance estimator. Our empirical analysis shows that even though the bias of point estimator is small, Pearson test statistic is very much inflated due to underestimate the variance of point estimator. In the connection of design-based variance estimator and its design matrix, the bigger the average of eigenvalues of design matrix is, the larger relative size of which the first component part to Pearson test statistic is taking.

목차

Abstract
 1. Introduction
 2. Homogeneity Test
  2.1. Pearson Chi-squared Test
  2.2. Wald Test
  2.3. Bias of Pearson Test
 3. Empirical Analysis
  3.1. Empirical Data
  3.2. Empirical Analysis
 4. Conclusion
 References

키워드

저자

• Sunyeong Heo [ Department of statistics, Changwon National University ] Corresponding author

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  통합자연과학논문집(구 조선자연과학논문집) [Journal of Integrative Natural Science]

• 간기

  계간

• pISSN

  2005-1042

• 수록기간

  2008~2025

• 등재여부

  KCI 등재

• 십진분류

  KDC 405 DDC 505