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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/5949

    Title: 變異數不相等時的單階段變異數分析
    Other Titles: Single-Stage Analysis of Variance under Heteroscedasticity
    Authors: 陳順益
    Contributors: 淡江大學數學學系
    Keywords: 未知且不等之變異數;變異數分析;t分配;F檢定;Unknown and unequal variance;ANOVA;t distribution;F-test
    Date: 1997
    Issue Date: 2009-03-16 12:52:53 (UTC+8)
    Abstract: The procedures of testing the equality of normal means in the conventional analysis of variance (ANOVA) are heavily based on the assumption of the equality of the error variances. Studies have shown that the distribution of the F-test depends heavily on the unknown variances and is not robust under the violation of equal error variances. When the variances are unknown and unequal, Bishop and Dudewicz (1978) developed a design-oriented two-stage procedure for ANOVA, which requires additional samples at the second stage. In this paper we use a single-stage sampling procedure to test the null hypotheses in ANOVA models under heteroscedasticity. The single-stage procedure for ANOVA has an exact distribution and it is a data-analysis-oriented procedure. It does not require additional samples, and can reach a conclusion much earlier, save time and money. Simulation results indicate that the power of the single-stage procedure is better than the two-stage method when the initial sample size is smaller than 6, and performs well when n o is 6 or larger. Table of critical values and a numerical example are given.
    Appears in Collections:[Graduate Institute & Department of Mathematics] Research Paper

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