請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44416完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 劉清(Ching Liu) | |
| dc.contributor.author | Wei-De Jan | en |
| dc.contributor.author | 詹維德 | zh_TW |
| dc.date.accessioned | 2021-06-15T02:56:19Z | - |
| dc.date.available | 2010-08-06 | |
| dc.date.copyright | 2009-08-06 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-08-03 | |
| dc.identifier.citation | Andersen, H., Spliid, H., and Larsen, S. (2000). Statistical models for toxicity and safety pharmacology studies. Drug Information Journal, 34,631-643.
Federer, W. T. (1955), Experimental Designs-Theory and Application, New York: Macmillan (republished by Oxford and IBH Publishing Co., New Delhi, India, 1964, 1974) Federer, W. T. (1975), ‘The Misunderstood Split Plot,’ in Applied Statistics, ed. R. P. Gupta, Amsterdam: North-Holland, pp. 1-39. Federer, W. T. (1977), ‘Sampling, Blocking, and Modeling Considerations for Split Plot and Split Plot Designs,’ Biometrical Journal, 19, 181-200. Federer, W. T., Feng, Z. D., and Miles-McDermott, N. J. (1987). ‘Anonotated Computer Output for Split Plot Design :SAS GLM,’ Annotated Computer Output 87-8, Mathematical Sciences Institute. Cornell University,201 caldwell Hall, Ithaca, NY 14853. Federer, W. T., Feng, Z. D., and Miles-McDermott, N. J. (1987a). ‘Anonotated Computer Output for Split Plot Design : GENSTAT,’ Annotated Computer Output 87-4, Mathematical Sciences Institute. Cornell University,201 caldwell Hall, Ithaca, NY 14853. Federer, W. T., Feng, Z. D., and Miles-McDermott, N. J. (1987b). ‘Anonotated Computer Output for Split Plot Design : BMDP 2V,’ Annotated Computer Output 87-5, Mathematical Sciences Institute. Cornell University,201 caldwell Hall, Ithaca, NY 14853. Federer, W. T., and Henderson, H. V. (1979), ‘Covariance Analysis of Designed Experiments x Statistical Packages: An update,’ in Proceedings, Computer Science and Statistics, 12th Annual Symposium on the Interface, pp. 228-235. Federer, W. T., and Freedom, K. (2007). Variations on Split Plot and Split Block Experiment Designs. John Wiley & Sons, Inc. Federer, W. T., and Meredith, M. P. (1992). ‘Covariance Analysis for Split-Plot and Split-Block Designs,’ The American Statistician, 46, 155-162. Hartely, H. O. and Rao, J. N. K. (1967). ‘Maximum-Likelihood Estimation for Mixed Analysis of Variance Model,’ Biometrika, 54, 93-108. Harville, D. A., (1977). ‘Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems,’ Journal of the American Statistical Association, 72, 320-338. Henderson, C. R., (1984). ‘Application of Linear Models in Animal Breeding,’ University of Guelph. Jennrich, R. I. and Schluchter, M. D., (1986). ‘Unblanced Repeated-Measures Models with Structured Covariance Matrices,’ Biometrics, 42, 805-820. Jeremy, A. and Wherly, P. H., (2002). ‘Split-Plot Model with Covariate: A Cautionary Table,’ The American Statistician.56,284-289. Laird, N. M. and Ware, J. H., (1982). ‘Random-Effect Models for Longitudinal Data,’ Biometrics, 38, 963-974. Littell, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996). SAS System for Mixed Models, Cary, NC: SAS Institute Inc. Little, R. J. A., (1995). ‘Modeling The Drop-out Mechanism in Repeated Measures Studies,’ Journal of the American Statistical Association, 90, 1112-1121. Meredith, M. P., Miles-McDermott, N. J., and Federer, W. T. (1988). ‘The Analysis of Covariance for Split-Unit and Repeated Measures Experiments Using the GLM Procedure, Part II,’ Proceedings, SAS Users Group International 13th Conference, Cary NC: SAS Institute, Inc., pp. 1059-1064. Miles-McDermott, N. J., Federer, W. T., and Meredith, M. P. (1988). ‘The Analysis of Covariance for Split-Unit and Repeated Measures Experiments, Pare I,’ Proceedings, SAS Users Group International 13th Conference, Cary NC: SAS Institute, Inc., pp. 1053-1058. Patterson, H. D. and Thompson, R., (1971). ‘Recovery of Inter-Block Information When Block Sizes Are Unequal,’ Biometrika, 58, 545-554. Robisnson, G. K., (1991). ‘That BLUP Is A Good Thing: The Estimation of Random Effects,’ Statistical Science, 6,15-51 Searle, SR., (1982). ‘Mixed Model and Unbalanced Data. John Wiley and Sons, Inc., New York. SAS Institude Inc. SAS/STAT 9.1 User’s Guide 2003. Yates, F. (1937). ‘The Design and Analysis of Factorial Experiments,’ Imperial Bureau of Soil Science Technical Communications, 35, 1-95. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44416 | - |
| dc.description.abstract | 當裂區設計在有共變數存在的情況下時，其統計分析十分複雜，統計書籍或是教科書上皆很少有詳細完整說明，所以今天我們藉由探討在農業的試驗或是工業的試驗上，大家比較熟悉比較常利用的三種裂區設計，分別是簡單裂區設計（split-plot design）、二重裂區設計(split-split-plot design)與雙向區集裂區設計（Split-Block Experiment Design），探討這三種裂區設計在有共變數存在時該如何進行統計分析。
本研究重點在於建立利用混合模型理論來對三種裂區設計進行變積分析，並且主要重點是著重在探討各效應經過校正之後的平均值與各效應經過校正後的平均差異之變方，我們將文獻中所提及的各效應經過迴歸係數校正後的平均值與各效應經過校正後的平均差異的變方之計算公式簡稱為代數式，並且將矩陣模型理論之計算各效應經過迴歸係數校正後的平均值與各效應經過校正後的平均差異的變方之計算公式簡稱為矩陣式。 利用一組試驗資料來分別探討矩陣式與代數式的差異，此試驗資料是一組模擬的資料，根據（Jeremy and P.Hoffman ,2002）中的數據加以改變以進行資料模擬。利用代數式的方法來計算會遭遇到許多的問題，像是當設計方法改變成上述三種裂區設計以外的裂區設計，或當共變數增加至兩個或是兩個以上時，代數式的計算公式也會跟著改變，並且代數式的計算公式只能使用在均衡的資料上，要是均衡的資料變成不均衡的資料時，代數式的公式則完全不能利用。 簡單裂區設計、二重裂區設計、雙向裂區設計這三種裂區設計的模式中包括了固定型效應與隨機型效應，所以視為混合模式，本文特地用混合模式理論來進行計算，是因為這三種裂區設計是混合模式特例，利用混合模式理論來進行統計計算，不僅可以用在這三種裂區設計上，連別種的裂區設計或當共變數有兩個以上時皆可以使用，並且不管資料是否均衡皆可以使用矩陣式的計算公式來計算。 | zh_TW |
| dc.description.abstract | The correct statistical analysis of a split-plot design with covariate is complicated and the analysis method is not well documented in statistical literature. This paper studies the general methodology for the analyses of covariance for split-plot, split-split plot and split-block designs which are widely used in agrucultural and industrial experiments.
The main focus of this study is to construct a mixed model method for the various split-plot designs, to discuss the treatment means adjusted for the covariate, and to calculate the standard errors of the differences between two adjusted treatment means. Existing formulae for the above computations in the statistical literature are called 'algebraic formulae' and the formulae derived from the mixed model method are called 'matrix formulae' in this paper. The results from the algebraic formulae are then compared with those from the matix formulae for the hypothetic balanced data. The matric results all coincide with the algebric results. The disadvantage of algebraic method is that the whole set of formulae needs to be extensively modified when the design or the number of covariates changes. Beside, the algebraic formulae can only be used for balanced data (data without missing value). The mixed model method by matrix formulae is free from all the aforementioned difficulties encountered by the algebraic method. Both hypothetical balanced and unbalanced data were used in this study to demonstrate the versatility of the mixed model method. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T02:56:19Z (GMT). No. of bitstreams: 1 ntu-98-R95621202-1.pdf: 720859 bytes, checksum: 261ad284eb188d9ddcc572f0b33644ec (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 表目錄.......................................I
圖目錄.......................................III 摘要.........................................IV 英文摘要.....................................VI 前言.........................................1 第二章 前人研究..............................5 第三章 研究方法..............................10 第一節 裂區設計在有共變數下之變積分析......11 第二節 不同裂區設計在有共變數下之架構......14 I. 簡單裂區設計（Split-Plot Designs)...14 II. 二重裂區設計（Split-Split-Plot Design）......16 III. 雙向裂區區集設計（Split-Block Design）.......18 第三節 各種裂區設計之代數式計算法..........20 I. 簡單裂區設計........................20 II. 二重裂區設計........................22 III. 雙向裂區區集設計....................27 第四節 各種裂區設計之矩陣式計算法..........29 I. 混合模式（Mixed Model）.............30 II. 固定型效應之矩陣標記（Matrix notation of fixed effect)......................................32 III. 混合模式的公式(Formulation of the Mixed Model) ....................................32 IV. 估計隨機效應之變方（G）與機差項之變方（R）.....34 V. 估計固定效應（β）與隨機效應（γ）(Estimating β and γ) ....................................35 VI. 統計性質(Statistical Properties)....35 VII. 統計檢定與推論（Inference and Test Statistics） ....................................36 第四章 結果與討論............................38 第一節 在有共變數下之簡單裂區設計..........39 I. 資料均衡之簡單裂區設計..............39 (A) 資料分析............................39 (B) 結果與討論..........................42 II. 資料不均衡之簡單裂區設計............44 (A) 資料分析............................45 (B) 結果與討論..........................47 第二節 在有共變數下之二重裂區設計..........50 I. 資料均衡之二重裂區設計..............50 (A) 資料分析............................50 (B) 結果與討論..........................53 II. 資料不均衡之二重裂區設計............57 (A) 資料分析............................58 (B) 結果與討論..........................60 第三節 在有共變數下之雙向區集裂區設計........65 I. 資料均衡之雙向區集裂區設計..........65 (A) 資料分析............................65 (B) 結果與討論..........................68 II. 資料不均衡之雙向區集裂區設計........70 (A) 資料分析............................71 (B) 結果與討論..........................73 參考書籍與文獻...............................121 | |
| dc.language.iso | zh-TW | |
| dc.subject | 簡單裂區設計 | zh_TW |
| dc.subject | 二重裂區設計 | zh_TW |
| dc.subject | 雙向區集裂區設計 | zh_TW |
| dc.subject | 變積分析 | zh_TW |
| dc.subject | 迴歸係數 | zh_TW |
| dc.subject | 混合模型理論 | zh_TW |
| dc.subject | 共變數 | zh_TW |
| dc.subject | covariate | en |
| dc.subject | mixed model theory | en |
| dc.subject | ANCOVA | en |
| dc.subject | split-block design | en |
| dc.subject | split-split-plot design | en |
| dc.subject | split-plot design | en |
| dc.subject | regression coefficient | en |
| dc.title | 不同類型裂區設計之變積分析 | zh_TW |
| dc.title | Analysis of covariance for different types of split-plot designs | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 謝英雄(In-Shong Hsia),謝邦昌(Ben-Chang Shia) | |
| dc.subject.keyword | 簡單裂區設計,二重裂區設計,雙向區集裂區設計,變積分析,混合模型理論,迴歸係數,共變數, | zh_TW |
| dc.subject.keyword | split-plot design,split-split-plot design,split-block design,ANCOVA,mixed model theory,regression coefficient,covariate, | en |
| dc.relation.page | 123 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-08-03 | |
| dc.contributor.author-college | 生物資源暨農學院 | zh_TW |
| dc.contributor.author-dept | 農藝學研究所 | zh_TW |
| 顯示於系所單位： | 農藝學系 | |
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