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Logarithms

Transforming the data

One can test whether data are normally distributed, and the test shows that the compensatory and punitive awards in Table 1 are not normally distributed. This lack of normality is common in real-world data involving dollar amounts. Because some useful statistical tests depend on the data being normally distributed, or at least symetrically distributed, it is common to transform the data to obtain a distribution that more closely approximates a normal distribution.

One common transformation is to take the logarithm of the original value. That is, we can replace the value of each punitive award with the logarithm of the punitive award, and replace the value of each compensatory award with the logarithm of the compensatory award.

Table 2 reports the transformed variables, now in logarithms, that appeared in Table 1.

The awards reported in Table 2 are in base 10 logarithms. Therefore, an award of 4.0 corresponds to an award of 10 to the fourth power or 10⁴, or $10,000. An award of 6.0 corresponds to an award of 10⁶, or $1 million.