二水平正交饱和设计的统计分析: 零效应搜索法

华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (1): 51-59.

二水平正交饱和设计的统计分析: 零效应搜索法

张晓琴^1,2, 张应山¹, 茆诗松¹

1. 华东师范大学统计系, 上海 200062; 2. 山西大学数学科学学院, 太原 030006;

收稿日期:2006-12-01 修回日期:2007-04-27 出版日期:2008-01-25 发布日期:2008-01-25
通讯作者: 张晓琴

Statistical analysis of 2-level orthogonal saturated designs:the procedure of searching zero effects(Chinese)

ZHANG Xiao-qin^1,2, ZHANG Ying-shan¹, MAO Shi-song¹

1. Department of Statistics, East China Normal University, Shanghai 200062, China; 2. School of Mathematical Sciences, Shanxi University Taiyuan, 030006, China;

Received:2006-12-01 Revised:2007-04-27 Online:2008-01-25 Published:2008-01-25
Contact: ZHANG Xiao-qin

摘要/Abstract

摘要： 分析正交饱和设计的困难在于,由于没有剩余的自由度用于误差方差的估计, 所以一般的方差分析方法不再适用. 基于次序统计量期望的一个相关性质, 本文提出了一种确定零效应个数的方法----零效应搜索法.这样就能够给出误差方差的估计,进而确定模型的显著因子或显著效应.

关键词: 正交饱和设计, 次序统计量, 零效应, 显著效应, 正交饱和设计, 次序统计量, 零效应, 显著效应

Abstract: The difficulty of analyzing orthogonal saturated designs is that there are no degrees of freedom to estimate the error variance, so that the ordinary ANOVA is no more available. The paper proposes a new method to identify the number of the effect parameters which is equal to zero, namely the Procedure of Searching Zero Effects. This proposed method is based on the mean of the order statistics. Consequently, the error variance is estimated and the active effects are identified.

Key words: order statistics, zero effects, active effects, orthogonal saturated designs, order statistics, zero effects, active effects

中图分类号:

O212.1

张晓琴;张应山;茆诗松. 二水平正交饱和设计的统计分析: 零效应搜索法[J]. 华东师范大学学报(自然科学版), 2008, 2008(1): 51-59.

ZHANG Xiao-qin;ZHANG Ying-shan;MAO Shi-song. Statistical analysis of 2-level orthogonal saturated designs:the procedure of searching zero effects(Chinese)[J]. Journal of East China Normal University(Natural Sc, 2008, 2008(1): 51-59.