一階段與二階段抽樣程序在不同分布與樣本數的表現

On the Sample Sizes of One-Stage and Two-Stage Sampling Procedures under Heteroscedasticity

蔡泳思(Yung-Szu Tsai)

指導教授 ： 陳順益

淡江大學/理學院/數學學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00401

摘要

在檢定母體平均數是否相等的變異數分析方法中，其基本假設是模型誤差項為獨立的常態分布、和有相等變異數。當變異數未知且不相等時，Bishop and Dudewicz (1978) 導出二階段抽樣程序方法，而 Chen (2001) 提出一階段抽樣程序方法，分別用來檢定是否有相同的母體平均數。本文首先討論一階段與二階段抽樣程序在同樣的總樣本數下，比較不同的起始樣本n0 的表現。此外在模型誤差項為不同分布時，討論兩種抽樣程序的型一誤差與檢定力表現。

關鍵字

變異數分析 ； 二階段抽樣程序 ； 一階段抽樣程序

並列摘要

One of the assumptions of test procedures in the conventional analysis of variance is the equality of error variances. When the variances are unknown and unequal, Bishop and Dudewicz (1978) developed an exact analysis of variance for the means of k independent normal populations by using a two-stage sampling procedure. Chen and Chen (1998) used a one-stage sampling procedure to test hypotheses of equality of means in ANOVA model. In this study, we will first thoroughly explore the optimal choice of the initial sample size, n_0, for both the one-stage and two-stage sampling procedures by simulation study. We also investigate the effect on inference about the means of the one-stage and two-stage procedures when the assumption of normality is violated.

並列關鍵字

analysis of variance ； two-stage sampling procedure ； one-stage sampling procedure

參考文獻

Bishop, T.A., Dudewicz, E.J.(1978). Exact analysis of variance with unequal

Bradley, J.V.(1978). Robustness? British Journal of Mathematical and Statistical

Psychology, 31, 144-152.

Chen, H.J., Lam, K.(1989). Single-stage interval estimation of the largest normal

Chen, S.Y., Chen, H.J.(1998). Single-stage analysis of variance under heteroscedasticity.