在生物統計或生態統計研究中，衡量兩組多維度資料集相關性是重要課題，統計方法中衡量兩資料集相關性除了典型相關係數分析（canonical correlation analysis）外，本研究探討其他方法，包括Mantel檢定（Mantel test）、RV係數（RV coefficient）、PROTEST（Procrustean randomization test）、距離共變異數檢定（distance covariance test），並且比較這幾種方法在不同的資料形態下優劣。Mantel檢定以及距離共變異數檢定需要透過距離來衡量資料集的相關性，本文除了使用Mantel檢定以及距離共變異數檢定常見的歐氏距離（Euclidean distance）外，也加入馬氏距離（Mahalanobis distance）和皮爾森相關係數距離（Pearson correlation distance），比較不同距離方法是否影響檢定效果。透過電腦模擬一般多元常態分配資料以及模擬非常態分配資料，針對每個模型分配改變資料的樣本數、資料的維度、資料變數的變異數，並且依據每種檢定的檢定力（power）和檢定力圖（power curve），來比較各檢定的效果，最後利用美國黃鶯（American wood warbler）音符結構與鳥鳴聲、小白鼠基因與體內脂肪酸兩實證資料集觀察各檢定的檢定結果。

In biological statistics or ecological statistics research, assessing the correlation between two multidimensional datasets is an important topic. In addition to canonical correlation analysis, this study explores other methods for measuring the correlation between two datasets. These methods include the Mantel test, RV coefficient, PROTEST (Procrustean randomization test), and distance covariance test. The study compares the performance of these methods under different data structures. The Mantel test and distance covariance test require the use of distance measures to quantify the similarity between datasets. In this study, besides the commonly used Euclidean distance, Mahalanobis distance and Pearson correlation distance are also employed to examine whether different distance measures affect the test results. Computer simulations are conducted using multivariate normal distribution data and non-normal distribution data. The sample size, dimensionality of the data, and variance of the data variables are varied for each simulated model. The effectiveness of each test is compared based on the test power and power curves. Finally, the empirical datasets of American wood warbler song structures and gene expression with hepatic fatty acids in mice are used to observe the test results of each method.

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