The comparison of the normality tests with small sample size

碩士論文(全文於2009/07/01公開)[[abstract]]大部分的統計分析方法，往往是在常態假設之下所發展出來的，因此運用這些方法從事資料分析之前，我們必須先驗證資料是否符合常態的特性。關於資料之常態分佈性質檢測的議題，過去已有許多研究文獻，本論文僅以六種檢定常態特性的方法檢測資料：Cramér-von-Mises檢定法、Kolmogorov-Smimov檢定法、Anderson-Darling檢定法、Shapiro-Wilk檢定法、相關係數檢定法(The probability plot correlation coefficient test) 以及Jarque-Bera檢定法，檢測資料之常態性。 本論文主要是針對小樣本資料做常態分佈的檢定，在實際應用的資料中，有些實驗的樣本數偏小，因此小樣本的常態性檢定有其必要性，例如微陣列(microarray)實驗。我們利用模擬方式產生各種不同分佈的資料，包括單一參數(卡方、指數及t等分佈)、兩個參數(柯西、Beta、Gamma、均勻等分佈)、與三個參數(三角形)的分佈，並將各種不同分佈的資料透過上述文獻中的常態性檢定方法比較其差異，並簡單敘述在不同屬性資料下應選擇不同的檢定法做檢測。 根據我們的模擬結果可知，除了柯西、t及邏輯斯分佈之外，KS檢定法和Cramér-von-Mises檢定法有較好的檢測效果，並且以Cramér-von-Mises檢定法優於KS檢定法。其餘的四個檢定方法則各有其優劣，在不同分佈下各有其不同的檢定效果。[[abstract]]The most of statistic analysis methods was developed by under normal hypothesis. Before using these methods to analyse data, we should test whether the data have characteristics of normal distribution. In previously research, there are many topics about the normality tests. This paper used six normality test methods checking out the testing data, such as Cramér-von-Mises test, Kolmogorov-Smirnov test, Shapiro-Wilk test, Anderson-Darling test, Jarque-Bera test, and The probability plot correlation coefficient test. This paper focused on small sample size to do normality test. Because of in the real application data, there are some sample sizes close to small. Hence small sample size is an important normality test, such as microarray. We used the simulation method to produce kind of data in different distribution. The single parameter such as Chi-square, Exponential and student's t distribution , and the two parameters such as Cauchy, Beta, Gamma, Uniform distribution, and the three parameters such as Triangular distribution. Finally each different data through the listing references compared the difference, and describe the data in different attribution to choose the different methods. Following our result, the KS test and Cramér-von-Mises test got the best testing outcome excluding the Cauchy, student's t and Logistic distribution, and Cramér-von-Mises test is better than KS test. The other four testing methods have their advantage and drawback in different distribution has the different testing outcome