Improving Your Data Transformations: Applying the Box-Cox Transformation

• Published in: Practical assessment, research & evaluation Vol. 15; no. 12; pp. 12 - 20
• Main Author: Osborne, Jason W
• Format: Journal Article
• Language: English
• Published: College Park Dr 2010; Practical Assessment, Research and Evaluation, Inc
• Subjects: Correlation; Data; Effect Size; Mathematical Concepts; Nonparametric Statistics; Regression (Statistics); Social Sciences; Transformations (Mathematics)
• ISSN: 1531-7714; 1531-7714

Many of us in the social sciences deal with data that do not conform to assumptions of normality and/or homoscedasticity/homogeneity of variance. Some research has shown that parametric tests (e.g., multiple regression, ANOVA) can be robust to modest violations of these assumptions. Yet the reality is that almost all analyses (even nonparametric tests) benefit from improved the normality of variables, particularly where substantial non-normality is present. While many are familiar with select traditional transformations (e.g., square root, log, inverse) for improving normality, the Box-Cox transformation (Box & Cox, 1964) represents a family of power transformations that incorporates and extends the traditional options to help researchers easily find the optimal normalizing transformation for each variable. As such, Box-Cox represents a potential best practice where normalizing data or equalizing variance is desired. This paper briefly presents an overview of traditional normalizing transformations and how Box-Cox incorporates, extends, and improves on these traditional approaches to normalizing data. Examples of applications are presented, and details of how to automate and use this technique in SPSS and SAS are included. (Contains 7 figures and 3 footnotes.)