吾人常利用傳統的皮爾森（Pearson ）卡方統計量來做適合度檢定及獨立性檢定之用 ，但此皆基於無限群體之樣本是以歸還簡單隨機抽樣而得者，然而於實務上，往往以 有限群體為對象，並採用較為複雜之抽樣方法，例如幾乎都牽涉到分層抽樣及集體抽 樣或分層多段抽樣，若此時仍用皮爾森卡方統計量，經許多學者之證實發現會導致錯 誤之結論，故本文之目的即在研究適合度檢定式及獨立性檢定式之漸近分布，以及抽 樣調查設計對其之影響，並說明對這些檢定式做些許校正之後之結果。 本文共分六章，第一章說明本文之研究動機及目的。第二章則研究適合度檢定式X2之 漸近分布，及抽樣調查設計對其之影響，並對X2做修正。第三章研究兩個變數之獨立 性檢定式的漸近分布，以及抽樣調查設計對其之影響，並對此檢定式做一些修正。第 四章研究多個變數之獨立性檢定式的漸近分布，及抽樣調查設計對其之影響，並對此 檢定式做少許修正。第五章則研究特殊集體抽樣模型下之適合度及獨立性檢定式。第 六章則為本文之結論。

工業的發達與否代表一個國家國力的強弱，故欲使我國達已開發國家之林，提昇整個工業或產業的升級，已經是刻不容緩的事。近年來，政府致力於發展新的高科技產業，同時，對於傳統工業也以獎勵或鼓勵技術升級的方式，以提昇整體產業競爭力。其中包含了所謂"傳統工業技術升級計畫"。 　　所以，本文欲藉助對數線型模式，針對"傳統工業技術升級計畫"，來建構及解釋一些模式，並提出建議，以期傳統工業升級計畫，能更符合每個產業的要求。 / Modernization of Industry represents the powerfulness of a country. It'surgent to upgrade the inndustry, so that our country become a developed country.The government has been making every effort on new hi-tech industries lately, at the same time, the government also provide different incentives to upgradethe tradional industries. This way would increase the competitiveness of ourone of the incentives is that the government provided the so called "Conventionalindustries upgrading program" 　　In this paper, we use loglinear models to analyze the data given by those companies that participated "Conventional industries upgrading program". Based on the models, we shall make some suggestions and conclusions.

Taneichi(1993)提出一個新的適合度檢定統計量J²，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J²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J₁²。 　　另一探討的重點是在比較皮爾生卡方統計量X²，概似比例統計量G²，Cressie & Read統計量 I(2/3)，J²和J₁²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，X²和I(2/3)較接近卡方分配，但J₁²又較G²及J²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 statisticJ², 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 J² 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 X², likelihood ratio statistic G², 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, X² and I(2/3) behave more like a chi-squared distribution. Though J(1) ^2 does not perform as good as X² and I(2/3), it does outperform G² and J². (2) In terms of powers, it does not seem that any of the test statistics has a clear advantage over the others.