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PC-SAS program for estimating Huhn's nonparametric stability statistics
No full textA program written in the SAS language for personal computers to estimate Hühn's two nonparametric stability statistics is presented. Nonparametric methods proposed by Hühn in the 1970s are based on the ranks of genotypes in each environment and use the idea of homeostasis as a measure of stability. A stable genotype shows similar rankings across environments. Nonparametric stability statistics provide a viable alternative to existing parametric measures based on absolute data. They require no statistical assumptions about the distribution of the phenotypic values and are easy to use. Addition or deletion of one or a few observations is not as likely to cause great variation in the estimates as would be the case for parametric stability measures. For many applications (e.g., selection in breeding and testing programs), the rank orders of genotypes are the most essential information. The program deals with a two-way table with K genotypes and N environments. The output contains two main features: (i) corrected values and their ranks of genotypes within each environment, and (ii) two nonparametric stability estimates and their test of significance. From the output, one may exmnine the rankings of genotypes in each environment and look for stability differences among genotypes. This program should make practical the more frequent use of nonparametric stability statistics to investigate genotype x environment interactions in agricultural research
Applications of Multivariate Analysis in Agricultural Science
No full text農業科技上常會針對某研究主題同時測量一大堆不同變數（調查性狀）的資料，但我們並非針對個別變數進行統計分析，而是將所有變數合起來共同討論，針對這樣資料的統計分析，就需要用到多變數分析技術。本文試以不涉及統計理論從實用角度出發，針對農業科技研究上常用的多變數分析法，以實例分析說明其意義、應用場合、分析流程及結果解釋，期能有助於農業科技研究之參考。這些多變數分析方法包括主成份分析、對應分析因素分析、集群分析、判別分析、路徑分析及典型相關分析。
Data containing many variables (measured characters) are often collected in agricultural science research. An interpretative analysis of multivariate data considers all the variables simultaneously is required, and entails the use of multivariate statistical analysis. This paper provides a non-statistical, practical overview of the commonly used multivariate methods in agricultural science research, including principal component analysis, correspondence analysis, factor analysis, cluster analysis, discriminant analysis, path analysis, and canonical correlation analysis. The meaning, applicability, analytical procedures, and results interpretation of these methods are presented with cited examples. Our objective is to provide the researcher an intuitive understanding of multivariate analysis and their applications in agriculture
(38(2):208-215)Studies on Nonparametric Method of Phenotypic Stability. I. Comparison Between Nonparametric and Parametric Measures
No full text變異係數（cv）與直線迴歸係數（b）為目前用來評價各基因型之穩定性的方法中最常用且有效的穩定性介量，但是在實際應用上，不但須滿足一些統計前提，同時，在樣本數少時，其估計值亦容易受離值的影響而造成甚大的變異。基此，本研究即就Nassar及Hühn在1987年所提出的以順位觀點為主之非介量統計分析法的理論，配合Yates和Cochran（1938）之5個大麥品種在6種相異環境下的收量試驗資料作為應用上分析的材料，分別就全部資料及刪除高產區或低產區的離值資料進行分析，並與cv及b之評估結果作一比較，以測試該非介量法用以解釋穩定性問題的可靠性與適用性。
其結果顯示：非介量法較少受統計前提之限制，操作簡便，且增添或刪除一個以上的觀測值也不會造成估計值太大的變異，而其所表達的穩定性意義偏重於生物觀點。cv及b兩種穩定性介量之估計值問存在顯著正相關，但其與非介量穩定性測量值之間則無顯著相關。
Coefficient of variation (cv) and linear regression (b) are useful to evalute the phenotypic stability of genotypes over environments. However, a proper use of these two parametric measures requires some statistical assumptions, and their estimates can be unduly influenced by one or two outliers for small samples. A nonparametric method for stability based on the ranks of genotypes in each environment is proposed by Nassar and Hühn (1987). The purpose of this study is to test the reliability and applicabillity of the nonparametric method by comparing the nonparametric with the parametric stability measures. The comparsion is made using data on 5 genotypes (varieties) of barley in 6 environments (sites) from the yield trials of Yates and Cochran (1938), with and without excluding the highest or lowest yielding site.
Nonparametric measures requires less statistical assumptions, and are easy to use. Furthermore, addition or deletion of one or a few observations is not as likely to cause great variations in the estimates as would be the case for parametric stability measures. The nonprarmetric measures correspond to a biological concept of stability. The results indicated significant positive correlation between the cv and b, and showed no correlation between nonparametric and parametric stability measures
(45(4):336-351)Subset Method for Assessing Varietal Stability in Unbalanced Regional Trial Data
No full text本省區域試驗一般採用的穩定性介量多以最受廣泛使用的直線迴歸分析法為主。該法僅適用於每一基因型與環境組合都有資料之場合，因此一旦含有缺區，便無法正確估得環境指標，並進行穩定性分析；過去一般處理缺區的方式，係將含缺區的品系或環境全部刪除，使其呈均衡資料後，再進行穩定性分析，如此在缺區數多時勢必會造成品系或環境數減少，反而降低了評估結果的準確度。對此，本研究利用子集合分析法以擴大穩定性分析之應用範圍至不均衡的區域試驗資料。子集合分析可處理含交感模式之不均衡資料，在觀念上相當簡單直接，係就所分割成的兩個不同子集合均衡資料各進行穩定性分析，並利用兩子集合重疊部份，對共存環境下之品系進行穩定性選拔。惟該法在使用上必須注意，所有品系的共存環境數不得太少。Linear regression analysis is the most common and useful method to assess the varietal stability in a regional trial. However, a major practical limition to date, stability analysis have been a requirement of no missing data, that is, data for every genotype and environment combination or treatment have been necessary. The precison of stability analysis can be unduly influenced by removing all the data of the genotypes or environments which contain missing plot, because of the reduction in number of genotypes and environments. This study proposed a subset method for analyzing stability of unbalanced data in regional trials. Subset analyses for unbalanced data with interaction model were simple and straightforward. The set of unbalanced data was divided into two subsets of balanced data, then one used the stability analysis for these subsets. The analyses of overlapping subsets of the data revealed available information to selecting superior genotypes with common environments. This subset method for stability analysis of unbalanced regional trial data performed well when there were many common environments for genotypes
(49(2):36-48)A Demonstration of Outlier Detection on Stability Analysis of Crop Regional Trial
No full text本省作物區域試驗一般採用的穩定性介量多以最受廣泛使用的直線迴歸分析法為主。由於傳統迴歸分析是以最小平方法(LS)來估計迴歸係數，對離群值（或異常值）之存在非常敏感，離群值之存在會造成迴歸係數估計不良，也會造成直線迴歸分析殘差均方異質，從而可能影響穩定性分析之準確度。現行用以診斷離群值的統計方法甚多，可區分為兩大類別：傳統的迴歸診斷及最新發展的穩健迴歸。然而，它們卻從未被引用到作物區域試驗資料之穩定性分析。為尋求適當可行的方法，對作物區域試驗資料作一鑑定與判斷，以找出有影響力的離群值，本研究利用Yates and Cochran (1938) 之大麥資料作為材料，進行各種離群值診斷法在穩定性分析的應用分析。結果得知，以LS殘差為基礎的傳統迴歸診斷法並不適合作為離群值診斷工具，而利用穩健迴歸可有效地辨識出資料的型式及偵測出離群值。Linear regression analysis is commonly used to assess the relative stability of varieties grown at different regions in Taiwan. However, the conventional least squares (LS) regression is susceptible to the occurrence of outliers (or unusual observations), which may have a deleterious effect on estimates of regression coefficients and on homogeneity of residual mean squares from the regression. Thus, outliers may have a significant impact on the precision of stability analysis. Many diagnostic statistics have been designed to detect outliers. They are classified into two approaches: classical regression diagnostics and recently developed robust regression. However, they are never applied in stability analysis of regional trial data. To investigate their applicability, demonstration of several diagnostics for the outlier detection using the barley data of Yates and Cochran (1938) was performed. The results revealed that the residuals from LS fits are not useful as outlier diagnostics, whereas the robust regression is useful in screening data sets and identifying outliers
(40(3):255-261)Dynamic Studies on Concurrence with Growth Time in Linear Regression Analysis of Genotype-Environment Interactions
No full text直線迴歸模式能有效地估計數量性狀對環境的適應能力。然而，利用交感效應隨環境指標所求得的〝穩定性〞，係一種相對性的概念，隨參試材料與環境因子的種類、數目之不同，其估值也改變，因此，直線迴歸模式實為一種描述性的穩定性模式，而無法用之於預測工作，同時也造成表型平均值與穩定性係數之間往往存在正相關關係。此種相關的情況，即所有迴歸線通過一共點。在符合直線迴歸模式且基因型與環境效應均為逢機型之前提下，由逢機樣本估得之共點乃提供了一預測上極有用的指標。另一方面，植物性狀的穩定性常因生長及發育的不同而異，故所估得之共點介量也會隨生長時間而有變化。因此針對此問題，本研究將以實驗植物Arabidopsis thaliana為材料，建立共點介量與生長時間的特定關係，以探明共點性隨著生長發育之變化趨勢，俾能誘導出一測定穩定性的預測模式。
結果得知：各生長時間下除了第1週外，共點性均存在，所估計的共點皆落在生產正常範圍內，故採用迴歸係數估值作為穩定性之選拔準則有效，然其所選出的高產且穩定基因型會因生長時間之不同而改變。由本研究Arabidopsis thaliana的資料配合結果，顯示共點係數ct與時間t之間呈一種指數生長曲線關係，其值在生長初期最大而隨時間經過則變小，此可用以預測同族群其他未受試之基因型及環境，但預測的可靠性僅侷限於該特定時間內。Linear regression model is useful to evaluate the adaptation of a quantitative character to the change of environments. However, the stability in the regression model is a relative measure depending on the genotypes and environments included in the test. Therefore, the regression model for G×E interaction is a descriptive model based on the data being analysed, but not a predictive model. This results in positive correlations between the phenotypic mean and regression coefficient. The correlations to occur is that all regression lines for all genotypes pass throught a common point, that is the regression should be concurrent. The concurrent point can be used to predict the performance of untried genotype when grown in a hypothetical environment, if both genotype and environment are considered as random samples from larger populations. Moreover, the stability of a quantitative character of a plant often varies with time at different stage of growth and development. This results in the diversity of concurrence for different periods. Thus, this project is to study the tendency of concurrence with growth time, and establish a forecasting model in plant stability by inducing the close relationship between concurrence and growth time into the linear model. The experiments will be conduced to test reliability and applicability of the above-mentioned empirical model by using Arabidopsis thaliana plants as materials.
The results show that the concurrence occurred at various plant growth stages except the first week. With a close relationship between concurrent parameter and growth time, a combined concureent model was then introduced. It appeared to be an exponential curve based on the data of Arabidopsis thaliana, thus it can be used to predict the performance of an untried genotype when grown in a hypothetical environment at different growth time, if both genotype and environment are considered as random samples from larger populations
(38(3):335-345)Concurrent Model: the Extension of Linear Regression AnaIysis of Genotype-Environment Interactions
No full text共點模式在各試因均為逢機樣本之前提下，可對同一族羣其他未受試基因型在未受試環境下的反應表現進行預測。該模式係以共點之觀念引入評價適應性的迴歸模式中，而將交感成分同時隨基因型效應及環境效應作迴歸分析。其共點介量的預測效果與生物學上之解釋，在本文中均予詳加探討。
最後，並配之以Arabidopsis thaliana植物鮮重資料作為實例分析，以說明共點模式在基因型與環境交感效應之研究上的應用價值。
Concurrent model can be used to predict the performance of an untried genotype when grown in a hypothetical environment if both genotype and environment are considered as random samples from larger populations. This involves a development of the regression analysis used in assessment of adaptation, and allows for the regression of interaction components onto both genotypic and environmental effects. The usefulness of the single joint regression for prediction is outlined, and the biological interpretation of concurrent is given.
The applicability of the emprical models to the data on plant fresh weight of Arabidopsis thaliana is illustrated by means of example
Correct Usage of Experimental Designs
No full text電腦統計套裝軟體之普及化，對學術研究工作提供了方便、快速又計算準確的統計分析，然而根據多年來從事農業統計及試驗設計諮詢服務之工作經驗中發現，越是常用而簡單的統計方法，其被誤用及濫用的現象也最頻繁。為避免重蹈覆轍，農業研究工作者應該瞭解如何正確地使用試驗設計，才能對試驗結果進行適當之統計分析。對此，將針對以下重點加以說明：一、試驗設計的基本觀念與原則；二、農業上重要的試驗設計方法；三、合併數個試驗（例如合併年度、地區、季節等）的分析方法；四、連續不同時間重複測量（例如不同時期行多次收穫）的試驗；五、處理間的個別比較。
The use of computer software for statistical analysis is rapidly increasing in scientific research. During many years of statistical consultation in agricultural research, I found that misuses and abuses of the design and analysis of experiments still frequently occurred, even though the most common and simple analysis. For this reason, it is necessary to have knowledge of correct usage of experimental designs. This talk concentrates on five parts: 1. Basic concepts and principles of experimental design; 2. Important designs in agricultural experiments; 3. Combined analysis of experiments over years, locations or seasons; 4. Repeated measurement over time; 5. Comparisons between treatments
(43(3):283-292)A SAS Program for Regression Analysis of Stability
No full text利用直線迴歸分析法來解釋植物穩定性的問題，是本省目前最常用而有效的方法。本文以個人電腦之SAS軟體中最基本的STAT功能系統，編寫出一個穩定性迴歸分析程式，並以一數例說明其進行分析的流程及結果，以幫助農業研究工作者進行區域試驗資料之穩定性迴歸分析。程式之輸出結果內容包含有綜合變方分析、各品系在不同環境下之產量平均值、環境指標估值、迴歸分析之統計值摘要表、穩定性係數對品系平均產量之圖示結果。Linear regression method is widely used to investigate the plant stability in Taiwan. A program written in SAS/STAT software is to presented for regressinon analysis of stability. This program runs on personal computers. The procedure is also illustrated through an example. It is useful to agricultural researchers who are analyzing the varietal performance in regional trials by regression approach. Output contains combined analysis of variance, mean yield of each variety under different environments, environmental index, summary statistics of regression analysis, plotting of stability index to varietal mean
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