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標題: 使用變方分析與羅吉斯回歸分析比例數據資料之比較
Comparison of Using ANOVA and Logistic Regression to Analyze the Proportional Data
作者: Szu-Wei Yang
關鍵字: analysis of variance;logistic regression;proportional data;binary data;arcsine square root transformation;變方分析;羅吉斯回歸;比例數據;二元資料;反正弦平方根轉換
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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.
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