淡江大學機構典藏:Item 987654321/41699
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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/41699


    Title: Single-stage analysis of variance underheteroscedasticity
    Authors: 陳順益;Chen, Shun-yi;Chen, H. J.
    Contributors: 淡江大學數學學系
    Keywords: Unknown and unequal variances;t distribution;one-way layout;two-way layout
    Date: 1998-08-01
    Issue Date: 2010-01-28
    Publisher: Taylor & Francis
    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.
    Relation: Communications in Statistics: Simulation and Computation 27(3), pp.641-666
    DOI: 10.1080/03610919808813501
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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