ANOVA for one-way balanced design with variance heterogeneity

• Main Authors: Yi-ching Wang, 王怡晴
• Other Authors: Jung-pin Wu
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/76261666853973555800

碩士 === 逢甲大學 === 統計與精算所 === 95 === Analysis of variance is the most frequently used method to test the mean difference.The F test of analysis of variance assumes the constant variances for the involved populations.But on the practice, variance is usually unknown and may not be equal.Based on the experiencses, in biomedical experiment, when the assumptionis not reasonable, the simplicity of the F test might not justify the consequence. In this study, we do not assume variance homogeneity. According to expected value of mean square of treatment and mean square of error, we supposed the same test statistic and proved it would not be F distribution. So we used bootstrap to simulate distribution of test statistic and estimated p value. Then we simulated size and power by Monte Carlo .Finally, the instance discussed one-way ANOVA with variance heterogeneity.