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系統識別號 U0026-2106201009425900
論文名稱(中文) 一些統計方法在呈現上的探索
論文名稱(英文) Exploring Exhibition of Some Statistical Methods
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 98
學期 2
出版年 99
研究生(中文) 何旻儒
研究生(英文) Min-Ju Ho
學號 r2697403
學位類別 碩士
語文別 中文
論文頁數 59頁
口試委員 指導教授-路繼先
口試委員-高正雄
口試委員-任眉眉
中文關鍵字 假設檢定  迴歸分析  類型誤差  區間曲線 
英文關鍵字 Hypothesis testing  Regression  Type Errors  interval curve 
學科別分類
中文摘要 統計發展的過程中,過去因為計算或者繪圖不容易,所以往往在發展統計方法時,
傾向於簡單好算並便於繪圖; 但現今電腦與軟體計算快速、繪圖容易,
所以我們可以呈現這些方法作更有效率,
並且能夠擴充甚至延伸過去所不便或是無法畫出來的圖形,
借由圖形化我們可以更容易理解與詮釋統計方法,
於此我們將討論一些統計方法利用軟體 args{R} 來改進與呈現,
希望可以對統計方法的學習能有更為簡易與清楚的理解。

就 Jerrel 於 1988 年用 Minitab 於犯型一與型二誤成本問題的文章,
以其圖形呈現的部份為我們想要有所改進的動機。
在以現在的知識,技術,乃至於軟體工具,
重新來檢視這篇文章所涉及的相關問題。 但在過程中,
我們認知到應更具體的去呈現在統計檢定中, 有關型一與型二誤的圖形說明;
卻也發現一些統計教本上有著不明確甚是錯誤的圖示,
這些容易引起學習上的誤導實有必要予以澄清與更正。

在此過程中, 我們發現在目前幾乎所有關於型一與型二誤的解說,
都僅限於常態分配的平均數,亦即位置參數的差異顯示。
然而卻沒有任何關於檢定變異數 (或是尺度參數)
時型一與型二方面任何說明。
因而我們也在此方面提出一些以圖形呈現來協助統計觀念的理解與學習。

再者,於迴歸分析的部分,我們發現有好些統計教本,文章,甚至統計軟體,
會將模型之配適線加上其 95\% 信賴區間曲線加到原始資料之散佈圖上。
使得此種有著原始資料與對配適模型之 95\% 信賴區間曲線的圖,
實是個誤導的圖形,對此我們認為有必要予以澄清與修正而提出一些建議。
英文摘要 The process of statistical development, the calculation and drawing
is not easy in the past, so statistician often preferred easy
calculation in the development of statistical methods. With the
capability of modern computer and softwares: faster computing,
handling of complicated programming, and generating of sophisticated
graphs, we are able to make use of such approach more efficiently,
and have the approach further extended and generalized. Graphical
techniques can strengthen the interpretability and
understanding of statistical methods in learning and teaching.
Furthermore, we provide codes of software args{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.

The motivation by Jerrel(1988) that used software Minitab to
demonstrate about the costs of Type I and Type II errors issues, we
can improve this work by modern knowledge, skills, and software
tools.

In the study, however, we recognize that there to be more specific
presentation in the statistical test, by the Type I and Type II
errors graphical instructions. It also found that there is some
inappropriate graphs in statistics textbooks, these easily lead to
misleading that need to be clarified and corrected.
We also found that almost the Type I and Type II errors instructions
are limited to hypothesis testing for mean. So we also worked out
hypothesis testing for variance.

In regression analysis, we also found in statistics textbooks,
articles, and statistical software that fitted line and its 95 \%
confidence interval, even prediction interval curves will be add to
the scatter plot of original data. It is a misleading graph and we
suggested to clarify and recommended an appropriate way to a add on
fitted model curves instead.
論文目次 1 序言 1
2 假設檢定 2
2.1 成本問題. . . . . . . . . . . . . . . . . . . 2
2.2 指正誤導圖形 . . . . . . . . . . . . . . . . . 7
2.3 平均數檢定. . . . . . . . . . . . . . . . . . 9
2.3.1 假設檢定概念圖形 . . . . . . . . . . . . 9
2.3.2 犯型一、二誤機率圖形 . . . . . . . . . . 12
2.3.3 成本問題衍伸 . . . . . . . . . . . . . . 12
2.4 變異數檢定 . . . . . . . . . . . . . . . . . . 17
2.4.1 假設檢定概念圖形 . . . . . . . . . . . . 17
2.4.2 犯型一、二誤機率圖形 . . . . . . . . . . 20
2.4.3 成本問題衍伸 . . . . . . . . . . . . . . 21
3 迴歸分析 25
3.1 指正誤導圖形 . . . . . . . . . . . . . . . . . 25
3.2 (log-)Location-Scale model . . . . . . . . . 27
3.2.1 (Log-)Normal model . . . . . . . . . .. 29
3.2.2 (Log-)Logistic model . . . . . . . .. . 32
3.2.3 Weibull and SEV models . . . . . . .. . 34
3.3 Exponential model . . . . . . . . . . . . . . 35
3.4 Poisson model . . . . . . . . . . . . . . . . 39
4 結論 42
參考文獻 45
附錄“ 46
參考文獻 Bowerman, B.L., O’Connell, R.T., and Murphree, E.S.(2001), Business Statistics in Practice,
2th Ed., New York: McGraw-Hill.
Coles, S.(2001), An Introduction to Statistical Modeling of Extreme Values, London:
Springer-Verlag.
Dobson, A.J.(1990), An Introduction to Generalized Linear Models, London: Chapman &
Hall.
Jerrell, M.E.(1988), “Computer programs to demonstrate some hypothesis-testing issues,"
The American Statistician, Vol. 42. 80-81.
Meeker,W.Q., and Escobar, L.A.(1998), Statistical Methods for Reliability Data, New York:
John Wiley & Sons.
Moore, D.S., McCabe, G.P., and Craig, B.A.(2009), Introduction to the Practice of Statistics,
6th Ed., New York: W.H.Freeman.
Ruppert, D., Wand, M.P., and Carroll, R.J.(2003), Semiparametric Regression, New York:
Cambridge University Press
Tilman, D., Hill, J., and Lehman, C.(2006), “Carbon-Negative Biofuels from Low-Input
High-Diversity Grassland Biomass," Science, Vol. 314. 1598–1600.
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