多種檢定均勻性方法的檢定力研究

A variety of test methods for testing homogeneity forces

陳瑩曦(Ying-Hsi Chen)

指導教授 ： 伍志祥

淡江大學/理學院/中等學校教師在職進修數學教學碩士學位班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.00150

摘要

在眾多適合度檢定的方法中，最常被提及的皮爾遜卡方檢定(Pearson chi-square test)會因為分割起始點(cell point)的選取，造成檢定結果的差異。起始點的選取，可以等價於用0當起始點但使用轉換的資料來做卡方檢定。資料轉換對其他的檢定方法的檢定力影響，是沒被討論的議題，本論文以模擬研究來討論常見的檢定方法的檢定力會如何受影響。
另外本研究還提出皮爾遜卡方檢定的裁剪統計量，我們把區間[0,1]等分割，使其分割格子數與樣本數一樣多，再計算對每一個格子擁有的樣本頻率值的移動平均值，用這些頻率移動平均值來做卡方檢定。從模擬研究中可以發現其檢定力比較穩定，不太會受資料轉換的影響。若與高階間距為基礎所建立的檢定來比較兩者的檢定力，可以發現各有擅長。不似傳統卡方檢定其相對於以間距為基礎所建立的檢定方法，有明顯且有較差的表現。

關鍵字

卡方適合度檢定 ； 頻率移動平均卡方檢定 ； Greenwood檢定

並列摘要

Among the many methods of goodness-of-fit test, the most frequently mentioned is the traditional Pearson chi-square statistics. But chi-square test because of segmentation starting(cell point) the selection , resulting in differences in test results. Select a starting point(cell point), you can use 0 as the starting point is equivalent to using the conversion of data to do chi-square test. Data Conversion to other test methods impact test force is not being discussed topics of this thesis to discuss common analog test methods test force might be impacted
In addition the study also suggested crop Pearson chi-square test statistic, we interval [0,1] so divided so lattice division number of samples as many, and then calculate for the lattice for each sample has a moving average frequency value, moving average of these frequencies to do with chi-square test. Can be found from the simulation study of its test force is relatively stable and less affected by the impact of data conversion. If the spacing is based on the established order of the test to compare the test force can be found their own good. Unlike conventional chi-square test with respect to space-based verification method established, there are clear and there is poor performance.

並列關鍵字

chi-square goodness-of-fit test statistics ； moving average frequency chi-square statistics ； Greenwood test

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