| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 92 === Many experiments are implemented to see if there is a significant mean difference in outcome between two treatments. Two independent sample T test and the analysis of variance (ANOVA) are two major methods. However, sometimes the outcome may be apparently affected by the covariate. The way to remove the influence from the covariate is so-called the analysis of covariance (ANCOVA). Comparing with the two methods, T and F, the ANCOVA can increase the Power to the test.
Neter (1999) used the adjusted covariate term as an independent variable in the regression model. Hicks & Turner (1999) adjusted the sum of squares of the ANOVA model by using the form of sum squares of residual from the simple linear regression model. And they are both a kind of analysis of covariance. However, there are some assumptions coming with the ANCOVA.
The purpose of this thesis is to propose a test that will release the assumption in the ANCOVA model. The basic idea comes from the bivariate-normal distribution of the response variable. The least square method and the regression model are used to do our job. Finally, the Monte Carlo simulations are used to evaluate the performance of the desired level and power.
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