Box-Cox transformation of firm size data in statistical analysis

Ting Ting Chen and Tetsuya Takaishi

Papers from arXiv.org

Abstract: Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions.

Date: 2015-11
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Published in Journal of Physics: Conference Series 490 (2014) 012182

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1511.07821

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