基于三种重复方式下超希腊拉丁方设计的方差分析  

Analysis of Variance of Hyper-Graeco-Latin Square Design Based on Three Repetition Modes

作　　者：肖宇佳 熊烽景 李洪毅[1] XIAO Yujia;XIONG Fengjing;LI Hongyi(College of Mathematics and Statistics,Jishou University,Jishou 416000)

机构地区：[1]吉首大学数学与统计学院,吉首416000

出　　处：《系统科学与数学》2024年第4期1147-1158,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(12161040,12361053,11961027);湖南省自然科学基金项目(2023JJ30486);湖南省教育厅重点项目(22A0355)资助课题。

摘　　要：超希腊拉丁方设计可以从多个不同方向控制试验的误差,在医学和工农业生产等领域有着广泛的应用.因此,对超希腊拉丁方设计进行方差分析有着重要意义.文章首先给出了超希腊拉丁方设计的方差分析,并讨论了在三种不同重复方式下的超希腊拉丁方设计的方差分析,最后通过例子验证所获的理论结果.The Hyper-Graeco-Latin square design can control experimental errors from multiple different directions,and is widely used in many fields such as medicine and agricultural production.Therefore,it is of great significance to perform analysis of variance on the Hyper-Graeco-Latin square design.In this paper,the analysis of variance for the Hyper-Graeco-Latin square design is presented,and the analysis of variance for the Hyper-Graeco-Latin square design is discussed under three different repetition modes.Finally,some examples are provided for supporting the theoretical results.

关 键 词：试验设计 拉丁方设计 超希腊拉丁方设计 方差分析 

分 类 号：O212.6[理学—概率论与数理统计]