臺灣博碩士論文加值系統

　　當完全隨機化設計中存在共變量或伴隨變數時，可以利用共變異數分析來修正共變量對處理比較的影響，以降低實驗的誤差變異。然而，隨機指派處理的方式並無法完全排除共變量的影響，因此，本文考慮在一個共變量存在的一因子配置設計中，透過適當地配置處理指派，來降低共變量所造成的處理間變異，使得處理對比的變異數受共變量影響的程度能夠降到最低，亦即使得處理間差異比較的變異數平均能夠符合A-最佳化準則，並試圖以相鄰交換法與成對交換法來搜尋一個共變量存在時A-最佳化的一因子設計。
　　本文以十二個例子測試相鄰交換法與成對交換法搜尋的效率，結果證明處理經由適當的指派後，的確明顯地降低處理間差異比較之變異數平均，而且每個例子的平均A-效率都達到99%以上。

　　When the completely randomized design in the presence of a covariate or a concomitant variable, ANCOVA can amend the influence of a covariate on treatment comparisons and reduce the experimental error variance. However, random assignment of the treatments cannot eliminate the influence of a covariate completely. Therefore, we consider allocating the assignment of treatments appropriately in the one-way design in the presence of a covariate in order to reduce the variation of the treatment groups due to a covariate, and minimize the variance of the treatment contrasts, in other words, confirming the average of the variance of treatment difference comparisons correspond to the A-optimal criterion. Hence, we attempt to use a neighbour exchange algorithm and a pair-wise exchange algorithm to search for A-optimal one-way layouts in the presence of a covariate.
　　Twelve illustrations are used to test the efficiency of the neighbour exchange algorithm and the pair-wise exchange algorithm. The results reveal that after allocating the assignment of the treatments appropriately, the average of the variance of treatment difference comparisons has been reduced and the average of the A-efficiency in each illustration exceeds 99%.

第一章　緒論
1.1　資料分析
1.2　研究動機與架構
1.3　文獻回顧
第二章　以交換法搜尋A-最佳化的設計
2.1　相鄰交換法
2.2　成對交換法
第三章　交換法搜尋A-最佳化設計的結果
3.1　相鄰交換法的搜尋結果
3.2　成對交換法的搜尋結果
3.3　結果比較
3.4　討論
第四章　結論與未來研究方向
4.1　結論
4.2　未來研究方向
參考文獻
附錄A　相鄰交換法程式
附錄B　成對交換法程式
附錄C　SAS程式
附錄D　十二個例子相關的統計量

[1]Atkinson, A. C. and Donov, A. N. (1992). Optimum Experimental Designs. Oxford University Press.

[2]Armitage, P. and Berry, G. (1987). Statistical Methods in Medical Research, 2nd ed. Oxford: Blackwell Scientific.

[3]Bonate, P. L. (2000). Analysis of Pretest-Posttest Design. Chapman & Hall/CRC.

[4]Christensen, R. (1996). Plane Answers to Complex Questions : the Theory of Linear Models, 2nd ed. Springer.

[5]Cochran, W. G. (1957). Analysis of Covariance: Its Nature and Uses. Biometrics, Vol. 13, No. 3, Special Issue on the Analysis of Covariance, 261-281.

[6]Cox, D. R. (1951). Some Systematic Experimental Designs. Biometrika, Vol. 38 : 312-323.

[7]Cox, D. R. (1952). Some Recent Work on Systematic Experimental Designs. Journal of the Royal Statistical Society, Series B (Methodological), Vol. 14 : 211-219.

[8]Cox, D. R. (1957). The Use of a Concomitant Variable in Selecting an Experimental Design. Biometrika, Vol. 44 : 150-158.

[9]Dean, A. and Voss, D. (1999). Design and Analysis of Experiments. Springer.

[10]Everitt, B. S. and Dunn, G. (2001). Applied Multivariate Data Analysis, 2nd ed. Oxford University Press.

[11]Huitema, B. E. (1980). The Analysis of Covariance and Alternatives. John Wiley & Sons, Inc.

[12]Jacroux, M. and Ray, S. R. (1990). On the Construction of Trend-Free Run Orders of Treatments. Biometrica, Vol. 77 : 187-191.

[13]Jones, B. and Eccleston, J. A. (1980). Exchange and Interchange Procedures to Search for Optimal Designs. Journal of the Royal Statistical Society, Series B, Vol : 238-243.

[14]Kirk, R. E. (1995). Experimental Design: Procedures for the Behavioral Sciences, 3rd ed. Brooks/Cole.

[15]Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P. (1983). Optimization by Simulated Annealing. Science, New Series, Vol. 220 : 671-680.

[16]Kuehl, R. O. (2000). Design of Experiments: Statistical Principles of Research Design and Analysis, 2nd ed. Duxbury Press.

[17]Lin, W. C. and Stufken, J. (1999). On Finding Trend-Free Block Designs. Journal of Statistical Planning and Inference, 78 : 57-70.

[18]Majumdar, D. and Notz, W. I. (1983). Optimal Incomplete Block Designs for Comparing Treatments with a Control. Annals of Statistics, Vol. 11 : 258-266.

[19]Maxwell, S. E., Delaney, H.D. and Manheimer, J. M. (1985). ANOVA of Residuals and ANCOVA: Correcting an illusion by Using Model Comparisons and Graphs. Journal of Educational Statistics, 10 : 197-209.

[20]Montgomery, D. C. (1997). Design and Analysis of Experiments, 4th ed. John Wiley & Sons, Inc.

[21]Rubin, D. B. (1977). Assignment to Treatment Group On the Basis of a Covariate. Journal of Educational Statistics, Vol. 2 : 1-26.

[22]Shah, K. K. and Sinha, B. K. (1989). Lecture Notes in Statistics 54: Theory of Optimal Designs. Springer.

[23]Whitaker, D. and Triggs, C. M. and John, J. A. (1990). Construction of Block Designs using Mathematical Programming. Journal of Royal Statistical Society, Series B, 52 : 497-503.

[24]林清山(1992)。心理與教育統計學。東華書局。

[25]余民寧(2005)。心理與教育統計學。三民書局。