頁籤選單縮合
題名 | 二階段全距檢定法=Two-Stage Range Test of the Equality of Means Under Heteroscedasticity |
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作者 | 陳順益; 吳秀芬; 張惠芳; | 書刊名 | 中國統計學報 |
卷期 | 36:4 1998.12[民87.12] |
頁次 | 頁339-359 |
分類號 | 319.5 |
關鍵詞 | 檢定法; 變異數分析; t變數之全距; 最保守均數結構; Power of a test; ANOVA; Range of t distribution; Least favorable configuration; |
語文 | 中文(Chinese) |
中文摘要 | 一般使用變異數分析(analysis of variance)檢定平均數是否相等,基本假設是 誤差項為獨立常態分配且變異數相等。但如誤差項變異數不相等,尤其是每一組的樣本個 數不一致時,使用F統計量來推論母體平均數,則對結果有嚴重影響。在多組獨立樣本的實 驗資料中,當各組變異數不相等時,Bishop和Dudewicz(1978)導出二階段變異數分析法, 來處理不等變異數之變異數分析問題。Wilcox(1983)研究獨立Student's t隨機變數之全距 ,提供臨界值表格,應用於多重比較的問題,但未探討檢定力及未提供檢定力表格。本文 提出一個比二階段變異數分析法簡單易懂的二階段全距檢定法,導出其檢定統計量,並提 供完整檢定力表格,表格中涵蓋檢定力範圍從0.01至0.99,適用絕大部分情況。二階段全 距檢定的統計量有精確統計分配,所以其實際顯著水準即為其名目水準。模擬比較二階段 全距檢定法和二階段變異數分析法的檢定力,兩者表現相當,無甚明顯差別。本文同時舉 出實例,說明二階段全距檢定法的應用。本文簡單易懂的全距檢定法及其完備的統計表格 ,具有實際應用價值。 |
英文摘要 | The procedures of testing the equality of normal means in the conentional analysis of variance (ANOVA) are heavily based on the assumption of the equality of the error variances. Studies have shown that the F-test is not robust under the violation of equal error variances. When the variances are unknown and unequal, Bishop and Dudewicz(1978) developed a two-stage procedure for ANOVA, which gives exact tests with power and level independent of the un- known variances. In this paper we propose a two-stage range test procedure to test the null hypotheses in ANOVA models under heteroscedasticity. Simulation results indicate that the power of the new range test procedure is as good as that of the two-stage ANOVA method. The two-stage range test is much simpler and is easy to interpret. A numberical example and complete statistical tables for implementation are given. |
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