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

Box-Cox transformation of firm size data in statistical analysis