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研究生: 陳怡倩
Chen, Yi-Chien
論文名稱: 一些統計方法在學與教的探索
Some Exploring Statistical Methods for Learning and Teaching
指導教授: 路繼先
Lu, C. Joseph
學位類別: 碩士
Master
系所名稱: 管理學院 - 統計學系
Department of Statistics
論文出版年: 2008
畢業學年度: 96
語文別: 英文
論文頁數: 89
中文關鍵詞: 分配機率圖樣本數非加法性模式交互作用誤差變異一致性分配檢定
外文關鍵詞: Distribution test, Homogeneity, Interaction, Nonadditivity, Probability plot, Sample Size
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  • 在統計課程或教科書中, 經常會以較數學的方式來介紹一些統計方法, 這對於學生的學習或是教師的教學往往不太合適. 因為過於數學的方式可能會使得學生在正確理解上較為困難, 或是對於這些統計方法的意義缺乏了解, 淪為只知道其數學公式與運算. 在學習與教學方面, 圖形化技術或是一些簡易的數值方法經常能對此問題提供良好的幫助.

    我們討論了數種統計方法, 以圖形化的方式來連接統計方法與其相關的數值關係, 增進其意涵的正確表達. 並且利用此方式加強這些統計方法在學習與教學上的詮釋與理解, 幫助我們能對於它們有進一步的推論與探索. 再者, 關於這些統計方法所有的圖形和運算, 我們提供了軟體 R 的程式, 希望能夠以此幫助讀者藉由這些程式來自我學習與適當練習, 以求更加了解統計方法的意涵. 在此, 我們的目的是為了促進學習的樂趣與提倡圖形化方法在學習和應用上的利用.

    Very often the introduction and discussion of some statistical methods in statistical courses or text-books
    are too mathematical oriented that is not adequate for students' learning and teachers' teaching. This might cause the difficulty in understanding their meanings correctly or lack of insights of statistical essentials. Graphical techniques or some simply developed
    numeric methods can often be helpful in learning and teaching that shall lead to correctly using these statistical methods.

    We discuss some statistical methods and make graphical approaches in order to match for corresponding numerical version of statistical methods and enhance the meaning in exhibiting of the current ones.
    They also can strengthen the interpretability and understanding of statistical methods in learning and teaching and help in exploring some subtle issues in statistical methods. Furthermore, we provide codes of software R for these graphical approaches and computation in order to help the readers to have insight about methods and training by self-learning and practicing.
    Our aim is on stimulating interests and promoting the learning and using on graphical approaches in application and teaching.

    1 Introduction 3 1.1 Motivation . . . . . . . . . . . . 3 1.2 Overview . . . . . . . . . . . . . . . . . 4 2 Sample Size 6 2.1 Sample Size for Desired Margin of Error .. . 6 2.1.1 Variance Known . . . . . . . . . . 6 2.1.2 Variance Unknown . . . . . . . . . . . 8 2.1.3 Discussion .. . . . . . . . . . . . . . 14 2.2 Required Number of Experiments. . . . . . . 14 2.3 The Effect of Sample Size on C.L.T . . . . . . . 22 2.3.1 The Central Limit Theorem . . . . . . . 22 2.3.2 Symmetric distribution . . . . . . . . . . 23 2.3.3 Asymmetric distribution . . . . . . . 27 2.4 R Codes and Functions . . . . . . . . . . . . 30 3 About Distribution 35 3.1 t2 Distribution . . . . . . . 35 3.2 Shapiro-Francia Normality Test . . . . . . . . . . 39 3.2.1 Shapiro-Wilk and Shapiro-Francia Normality Test . 39 3.2.2 Covariance Matrix . . . . . . . . . . 43 3.3 Poissonness Plot . . . . . . . 47 3.3.1 Confidence Interval of Poissonness Plot . . 49 3.3.2 Over-Dispersion . . . . . . . . . . . . . . . 54 3.4 R Codes and Functions . . . . . . . . . . . . . 57 4 Data Analysis with Few Information 62 4.1 MLE of Life Test Data . . . . . . . . . . . 62 4.2 Confidence Interval When Only Numbers of Failures observed . . 65 4.3 Interaction or Heteroscedasticity?. . . . . 68 4.3.1 Additivity and Nonadditivity Models. . . . 68 4.3.2 Tukey’s One Degree of Freedom for Nonadditivity . . 69 4.3.3 Mandel’s Model . . . . . . . . . . 71 4.3.4 UV Plot . . . . . . . . . . . . 74 4.3.5 Simulation Study . . . . . . . . 78 4.4 R Codes and Functions . . . . . . . . . . . 80 5 Concluding Remarks 85 References 89

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