Data Transformations - Agricultural Statistical Data Analysis Using Stata - page 206

In this table, the identity chi-square is the same as from the previous
command and represents the untransformed data. Several transfor-
mations are calculated and several are undefined. The log transforma-
tion has a chi-square value of 1.73 and a probability of 0.420, which
indicates this transformation is normally distributed and would be a
good one to use in analyzing the data. The ladder command also can
include the option generate , which generates a new variable with
the transformation that has the smallest chi-square value. It should be
noted that not all data can be transformed to normality and, in such
cases, other statistical techniques should be considered.
Generate a new variable of plantcount using the natural log
transformation
generate transpc = log (plantcount)
In this particular case, there is not much difference when an ANOVA
is done with the original data compared to the transformed data;
however, when the CV (coefficient of variance) is examined and the
detectable differences between means are examined, there are consid-
erable differences. The CV with the original data was 89% compared
to 26% with the transformed data.
Skewness is a measure of an entire distribution that is most notable
in the tails of a normal distribution, and kurtosis measures the shape
of the normal curve or peakedness. A negative skewness indicates the
tail is longer on the left of the distribution with the median lying to
the right of the mean, whereas a positive skewness has a longer tail
on the right with the median lying to the left of the mean. Kurtosis,
which measures peakedness, has a value of 3 for a normal distribution.
As this value goes down, the flatter the distribution is, and, conversely,
as it goes up, the narrower the distribution. Stata can calculate these
values with a couple of different commands. One method is to use the
summarize command with the detail option. Another option is
to use the tabstat command. Enter the following command:
tabstat plantcount transpc, statistics(skewness
kurtosis mean median)
This results in the following output: