機差變方非均質時綜合試驗資料分析的一個新方法

A New Approach to the Analysis of Combined Experimental Data When the Error Variances Are Not Homogeneous

陳嘉瑩(Chia-Ying Chen) ； 胡凱康(Kae-Kang Hwu) ； 楊素絲(Sue-S Yang) ； 彭雲明(Yun-Ming Pong)

《作物、環境與生物資訊》 2卷4期 (2005/12) Pp. 315-335

https://doi.org/10.30061/CEB.200512.0007

摘要

長久以來，綜合試驗資料均以傳統的綜合變方分析的方式來分析，這個分析的前提－機差均方需具有均質性－是大多數資料無法滿足的條件。若是在前提違背的情形下仍以傳統變方分析模式進行統計分析，則可能導致第一型錯誤率的大幅偏離名目值。我們提出新的觀點，目的在於放寬均質性的要求，改為設法描述異質性的結構，主要是設法將所有的機差均方歸類為少數幾層，使得每層內的均方值較接近，層數的多少是依據AIC的值來判斷。俟機差的變方結構確定後，以混合模式的方式分析綜合試驗資料，整個統計分析的計算可以利用SAS套裝軟體的proc mixed來達成。一個小型的模擬研究也說明了新的方法對控制第一型誤差率上的控制有大幅的改善。

關鍵字

綜合試驗資料 ； 機差均質性 ； 綜合變方分析 ； 第一型錯誤率 ； 混合模式

並列摘要

Conventional combined analysis of variance has been employed to analyze combined field trial data for a long time. One of the assumptions of this method is about the homogeneity of error variances. However, field trial data collected by agronomists and breeders seldom meet this requirement. Since there is no alternatives while this assumption is violated and the scientists are usually forced to ignore the assumption and proceed to do the conventional combined analysis. This might end up an inflation or shrinkage of type Ⅰ error rate. Instead of sticking to the unreasonable assumption, we propose a procedure for finding effective error variance structure. One out of a handful possible error variance structures will be pick as working error variance structure which has the smallest AIC value. Once the structure is determined a mixed effects model with this error structure is used to fit the data. The computation of the proposed method can be executed by SAS proc mixed. A small scale simulation study shows that the proposed method has a significant improvement over the conventional one on the control of type Ⅰ error rate.

並列關鍵字

Combined experimental data ； Homogeneity of error variances ； Combined analysis of variance ； Type Ⅰ error rate ； Mixed effects models