Taneichi(1993)提出一個新的適合度檢定統計量J<sup>2</sup>，具有近似卡方分配的性質。然而在小樣本的情形下，計算機模擬結果顯示，它的估計顯著水準大於期望顯著水準。所以本論文的重點之一，就是對J<sup>2</sup>進行改進，根據不同的準則，來選取一個適當的常數a。我們建議對每一觀測次數加一常數0.32，作為我們修正後的統計量，這個統計量我們記為J<sub>1</sub><sup>2</sup>。
另一探討的重點是在比較皮爾生卡方統計量X<sup>2</sup>，概似比例統計量G<sup>2</sup>，Cressie & Read統計量 I(2/3)，J<sup>2</sup>和J<sub>1</sub><sup>2</sup>之性質，我們想要了解在小樣本的情形之下，何者較接近於卡方分配，何者具有較強的檢定力。研究結果顯示，X<sup>2</sup>和I(2/3)較接近卡方分配，但J<sub>1</sub><sup>2</sup>又較G<sup>2</sup>及J<sup>2</sup>好；至於檢定力，我們發現沒有一個統計量在文中所探討的對立假設的情況下，同時都具有最大的檢定力。這些現象都可以用觀測次數對期望次數比值間的關係來解釋。 / Taneichi(1993) introduces a new goodness-of-fit statisticJ<sup>2</sup>, which has an asymptotic chi-squared distribution. However, the results of simulation indicate that the levels of significance are in general bigger than the nominal levels, which prompts us to device a version of J<sup>2</sup> statistic which would perform better under small sample size situations. We suggest adding 0.32 to each observed value and find that the adjustment indeed works rearonably well. This version of J^2 statistic is denoted as J(1)^2.
Although Pearson chi-square statistic X<sup>2</sup>, likelihood ratio statistic G<sup>2</sup>, Cresse-Read statistic I(2/3), J^2 and J(1) ^2 all have asymptotic chi-squared distributions, their small sample behaviors are not expected to be the same. Comparisons based on simulation studies are then made. The conclusions are as follows : (1) In terms of levels of significance, X<sup>2</sup> and I(2/3) behave more like a chi-squared distribution. Though J(1) ^2 does not perform as good as X<sup>2</sup> and I(2/3), it does outperform G<sup>2</sup> and J<sup>2</sup>. (2) In terms of powers, it does not seem that any of the test statistics has a clear advantage over the others.
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002003901 |
| Creators | 吳裕陽, Wu, Yuh Yang |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 中文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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