A numerical study of the accuracy of some approximations for the chi-square distribution to normality

A numerical comparison of the performance of three power transformations of chi-square random variable to normality is presented for three selected values of the degrees of freedom (5, 10 and 100). The transformations considered are the following: the Fisher’s square root transformation (F), the third root transformation of Wilson and Hilferty (WH) and the Canal’s power-linear transformation (L). Performance was assessed in terms of z-scores. Among the methods, the L transformation demonstrated the best approximation to normality, followed by the WH transformation. The findings highlight the potential advantages of the L transformation, particularly for cases with smaller degrees of freedom.