二階段抽樣程序初始樣本數的選取

Initial Sample Size Selection for the Two-Stage Sampling Procedure

許育賓(Yu-Pin Hsu)

指導教授 ： 陳順益

淡江大學/理學院/數學學系碩士班/碩士(2012年)

https://doi.org/10.6846/TKU.2012.00476

摘要

在常態分布母體下，當變異數未知且不相等時，Bishop and Dudewicz(1978)提出二階段抽樣程序方法來檢定母體平均數是否相等。二階段抽樣程序是一種屬於實驗設計的方法，其先決定第一階段的初始樣本數，然後在第二階段收集更多的樣本。本文討倫其初始樣本數和最後總樣本數之間的關係。本文另提供兩個指標T和R來幫助選取初始樣本數。

關鍵字

變異數分析 ； 一階段抽樣程序

並列摘要

When observations are taken from populations that are normally distributed with unknown and possibly unequal variances, Bishop and Dudewicz (1978) proposed a two-stage sampling procedure for the analysis of variance problem under heteroscedasticity. The procedure is a design-oriented process which requires an initial sample at the first stage and additional observations at the second stage. In this article we discuss the relationship between the initial sample size n_0 and the final total sample size. Two indicators T and R are provided to help selecting the initial sample size.

並列關鍵字

analysis of variance ； one-stage sampling procedure

參考文獻

[1] Bishop,T.A. and Dudewicz,E.J.(1978). Exact analysis of variance with unequal variances: Test procedures and tables. Technometrics,20,419-430.

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[4]Brown,M.B. and Forsythe,A.B.(1974). The Small Sample Behavior of Some Statistics Which Test the Equality of Several Means. Technometrics, 16(1),129-132.

[6] Stein, C.M.(1945). A two-sample test for a linear hypothesis whose power is independent of the variance. Annals of Mathematical Statistics,16,243-258.