使用變方分析與羅吉斯回歸分析比例數據資料之比較

Abstract

類別資料常存在於農業科學中，例如：植物病害、種子發芽、不同處理對產量高低及植株性狀影響等。對於類別資料的分析，常會將原始服從二項分布的資料轉換成比例數據進行分析，其分析方法通常是使用變方分析，但也可以使用羅吉斯回歸來進行相關的分析。為了比較變方分析與羅吉斯回歸，此兩種分析方式在二元資料所轉換的比例數據上分析之適用性，此論文進行不同情形資料數據的模擬，包括在不同樣本數、不同比例差距以及不同比例位置的情況下，進行變方分析與羅吉斯回歸分析，並以假設檢定方法之p-value去探討其檢定力，使用盒鬚圖及折線圖來呈現其結果，由此來判別在何種情況下，使用何種方法進行分析較為適當。結果顯示樣本數不論大小，比例不論接近0.1、接近0.5，變方分析與羅吉斯回歸兩種分析方法在型一誤差發生的機率α定為0.05時，型一誤差皆沒有增加；不論比例差距大小，比例越接近0.1時，羅吉斯回歸之檢定力較變方分析高，但比例越接近0.5時，雖羅吉斯回歸之檢定力與變方分析差異不明顯，但其檢定力同樣較變方分析高，因此在二元資料轉換為比例數據上的分析，使用羅吉斯回歸分析較為適當。

Categorical data analysis is commonly applied to agricultural science, such as plant disease, seed germination, effect on yields between treatments, or impact on plant traits and so on. For the analysis of categorical data, if the original data can be looked upon as a sample from a binomial distribution, it is usually transformed into proportional data before doing analysis. The frequently used way of analyzing the kind of data is analysis of variance. Logistic regression is also used in analyzing proportional data transformed from binary data. In order to compare the applicability of analysis between analysis of variance and logistic regression on the proportional data transformed from binary data, this study uses simulated data which includes different number of samples, differences of proportion, and values of proportion to compare the results for two analytic methods. The two analytic methods was compared by the power of hypothesis testing. P-value of boxplot and line chart are displayed to demonstrate the result. Finally, the results show that whether the number of samples are large, or whether the proportions are closer to 0.1 or 0.5; type I error will not be increased when using both analysis of variance and logistic regression. It also shows that whether the differences of proportion are large, or the proportions are closer to 0.1; the power tends to be higher when using logistic regression than analysis of variance. However, when proportions are closer to 0.5, the difference of power between logistic regression and ANOVA is not obvious. For the case, power still tends to be higher when using logistic regression than analysis of variance. Hence, logistic regression is more appropriate than analysis of variance in analyzing the proportional data transformed from binary data.