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| Title: | 順序尺度資料間之相關性研究 |
| Authors: | 廖俊嘉 |
| Contributors: | 江振東
廖俊嘉 |
| Keywords: | 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 |
| Date: | 2002 |
| Issue Date: | 2009-09-17 18:47:35 (UTC+8) |
| Abstract: | 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。 |
| Reference: | 參考文獻
Babakus,E. 1985. The sensitivity of maximum likelihood factor analysis given violations of interval scale and multivariate normality. Unpublished PhD dissertation. The University of Alabama.
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Brown,M.B. & Bendetti,J.K. 1977. On the mean and variance of the tetrachoric correlation coefficient. Psychometrika 42:347-355.
Joreskog,K.G. 1994. On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika 59:381-389.
Kirk,D.B. 1973. On the numerical approximation of the bivariate normal (tetrachoric) correlation coefficient. Psychometrika 38:259-268.
Labovitz,S. 1967. Some observations on measurement and statistics. Social Forces 46:151-160.
Labovitz,S. 1970. The assignment of numbers to rank order categories. American Sociological Review 35:515-524.
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Mayer,L.S. 1970. Comment on the assignment of numbers to rank order categories. American Sociological Review 35:916-917.
O’Brien,R.M. 1979. The use of pearson’s R with ordinal data. American Sociological Review 44:851-857.
Olsson,U. 1979. Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika 44:443-460.
Tallis,G.M. 1962. The maximum likelihood estimation of correlation form contingency tables. Biometrics 18:342-353.
Vargo,L.G. 1971. Comment on the assignment of numbers to rank order categories. American Sociological Review 35:517-518. |
| Description: | 碩士
國立政治大學
統計研究所
90354001
91 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0903540011 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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