單變數的卡方檢定會因資料分組而降低檢定力之外,還會因移動起始格子點而影響檢定的結果｡因此有學者提出能夠提高檢定力且不會因為起始格子點而影響檢定結果的方法｡在此篇論文,我們將考慮雙變數均勻分布的檢定問題,會如何受移動格子點影響定結果｡也試著提出新的檢定統計量和卡方檢定來做比較,透過模擬數據可以顯示新的檢定統計量是比卡方檢定更佳｡

The power of univariable chi-square test will be lower, and explained test outcome will be affected by moving beginning and end point of cells. After then, some scholars have proposed various methods to raise power , and they does not affect by moving beginning and end point of cells. In this paper , we will consider the problem that a testing for two dimension’s uniform distribution ,and the outcome how to affect by moving cells. We will also propose new test statistic to compare with chi square ,and use analog data to prove and see that the new test statistic will be more accurate than chi-square.

第一節	 緒論………………………… 1

第二節	 卡方檢定的可靠性
      2-1原始資料與轉換資料的轉換……… 3
      2-2原始資料和轉換資料的相關係數… 4
      2-3卡方檢定可靠性的結論…………… 10

第三節	提出新的統計量
      3-1新統計量的想法及作法…………11
      3-2新統計量所遭遇不適當的問題…12

第四節	模擬數據
      4-1 模擬作法及結論……………… 25
      4-2 模擬資料 ………………………26

附註 : 參考文獻……………………33

1.The advanced theory of statistics (1958) by Maurice G.  Kendall and Alan Stuart. 

2.On the Reiability of the Chi-Square Test by A.J.Violazz (1986) .

3.Wu, J.S., and Deng, W.S.* (2010). Averaged Shifted Chi-square Test, in revision for Journal of Nonparametric Statistics (SCI).

4.The Cambridge Dictionary of Statistics Fourth Edition by B.S.Everitt and A.Skrondal.

5.Tailor-made Test of Goodness Fit By Peter Hall (1983).

6.Introduction to Scientific Programming and Simulation Using R (2009) 

by Owen Jones, Robert Maillardet and Andrew Robinson.

7.Introductory Statistics With R by Peter Dalgaard (2002).