相關係數的相似性檢定

Equivalence Tests For Correlation Coefficient

孫郁喬(Yu-Qiao Sun)

指導教授 ： 謝國文

國立交通大學/管理學院/管理科學系所/碩士(2020年)

摘要

相關係數是所有學科應用中最常使用的關聯度強度衡量，用以表示兩變數之線性相關程度，廣泛用於各個實證社會科學研究領域，本文以Pearson的相關係數r與Fisher’s Z轉換法近似並比較。關於相似性的分析過去常用假設檢定，虛無假設為兩者是否相等，假設檢定若拒絕虛無假設，即表示兩者之間不存在顯著差異，在以往兩者不存在顯著差異即表示兩者相似，故本文對於兩者是否相似深入探討，推導出以假設檢定為雛形之相似性檢定。對該檢定之檢定力與樣本數分析，透過完整的方法論應證，補充Goertzen & Cribbie(2010)Counsell & Cribbi(2015)缺乏之方法論論述與探討。

關鍵字

相關係數 ； 相似性檢定

並列摘要

Correlation coefficient is the most commonly used measure of correlation strength in all academic area. It is used to express the linear correlation of two variables. It is widely used in various empirical social science research fields. This paper uses Pearson's correlation coefficient r and Fisher's Z conversion method to approximate and Compare. The hypothesis testing is not fit to assess equivalence. If the hypothesis test rejects the null hypothesis, it means that there is no significant difference between the two parameters, which means that the two parameter are equivalent. Therefore, this article discusses in depth two parameter are equivalent, and derives a equivalence test based on the hypothesis test. The analysis of the verification power and the number of samples of the verification is verified through a complete methodology, supplementing the methodological discussion and discussion lacking in Goertzen & Cribbie (2010) Counsell & Cribbi (2015).

並列關鍵字

Correlation coefficient ； Equivalence test

參考文獻

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Counsell, A., & Cribbie, R. A. (2015). Equivalence tests for comparing correlation and regression coefficients. British Journal of Mathematical and Statistical Psychology, 68(2), 292-309.

De Winter, J. C., Gosling, S. D., & Potter, J. (2016). Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data. Psychological methods, 21(3), 273.