順序尺度資料間之相關性研究

• Main Author: 廖俊嘉
• Language: 中文
• Published: 國立政治大學
• Subjects: 順序尺度; 皮爾森相關係數; 多序類相關係數; ordinal-scale; Pearson correlation coefficient; Polychoric correlation coefficient
• Online Access: http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22G0903540011%22.

摘要 皮爾森相關係數通常作為描述區間尺度變數間相關性的參考指標，然而在社會科學領域中，由於資料多數以順序尺度的形式呈現，因此藉由傳統的皮爾森相關係數來描述順序尺度資料間的相關性通常會導致某種程度的誤差。儘管如此，以往的文獻多數傾向支持以等距離分數來取代順序尺度資料，並直接計算皮爾森相關係數。藉由模擬實驗的結果，我們發現這樣的作法並非在所有情況下都合理。 此外本研究中也對多序類相關係數進行探討。就表示順序變數間相關性的準確程度而言，多序類相關係數明顯優於利用等距離分數來計算皮爾森相關係數的方法；但若以操作上的便利程度而言，後者仍具有其優勢。 關鍵字：順序尺度、皮爾森相關係數、多序類相關係數。 === Abstract Pearson correlation coefficient is typically used to describe the correlation between two interval-scaled variables. In social science, however, most of the data are represented in ordinal-scale, and hence describing the correlation between two ordinal-scaled variables in terms of Pearson correlation coefficient would inevitably result in certain errors. Though the practice is deemed acceptable and generally supported in literatures, we found, through intensive simulations, that it should be executed with care. Polychoric correlation coefficient was also investigated. In order to describe the correlation between two ordinal-scaled variables, we found, in terms of the degree of accuracy, that Polychoric correlation coefficient is definitely better than Pearson correlation coefficient with equal-distance scores. Pearson correlation coefficient, on the other hands, is much easier to calculate, and should not be totally ignored. Key words：Ordinal-scale、Pearson correlation coefficient、Polychoric correlation coefficient。