The Efficiency and Sample Size Calculations of Analysis of Covariance

• Main Authors: Huang, Yu-Chia, 黃玉佳
• Other Authors: Shieh, Gwo-Wen
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/81140631835410195303

碩士 === 國立交通大學 === 管理科學系所 === 102 === ANCOVA is a statistical method which is often used in educational and psychological　research. Today, it has been widely used in various fields of academics, but it is still easily misused. Some scholars mistakenly think that adding a covariate can reduce unexplained error variance, but the standard error of covariate-adjusted mean difference is not always smaller than that of the unadjusted mean difference. Actually, ANCOVA does not uniformly yield a smaller standard error or a shorter confidence interval for the treatment means comparison than does ANOVA. Such a misunderstanding may result in insufficient sample size, making the results of ANCOVA less accurate than the results of ANOVA. Therefore, Liu uses efficiency indicators to calculate sample size in order to ensure that using covariate can reduce variability and increase the accuracy of the research. In other words, Liu uses efficiency indicators to assure that ANCOVA is more efficient than ANOVA. In this study, all possible combinations of parameters are to calculate the sample size, and also examine the sample size formula whether it can achieve the desired guaranteed probability by the actual guaranteed probability.