Data Transformations - Agricultural Statistical Data Analysis Using Stata - page 207

stats | plantc~t transpc
---------+--------------------
skewness | 2.599091 -.1750206
kurtosis | 10.44925 3.341528
mean | 36.70833 3.157877
p50 | 25.5 3.238486
------------------------------
The column headings include stats , plantc~t (abbrev.
plantcount ), and transpc , which represent the measured statis-
tic, plantcount , and transformation of plantcount , respectively.
Note how the skewness and kurtosis changes with the transformation
from plantcount to transpc representing a more normal distri-
bution. p50 represents the median, and notice how it is less than the
mean with the original data (mean = 36.7) indicating a positive skew-
ness and slightly to the right with the transformed value ( transpc )
(mean = 3.2). Remember the kurtosis will be a 3 with a normal distri-
bution and notice how the transformation is much closer to this value.
The log transformation, which we have used here to reduce
skewness and kurtosis for a more normal distribution, also is often
used with data where the variances are not homogeneous or they
are said to be heteroscedastic and the standard deviations are pro-
portional to the means. To see this with the plantcount, data enter
the command
anova plantcount var rep
This will calculate and display the ANOVA table, and immediately
after this is calculated, enter the command
rvfplot
This will graph the residuals versus the fitted values, which should
occur randomly around 0. If the values don't, then this is an indication
that the variances are not homogeneous. Calculate the anova for the
transpc data and then enter the rvfplot command.
Figure 11.1 shows this graph for both the plantcount and
transpc data. Notice how the points are clustered at one end of
the graph with the untransformed data and the points appear more
random after transformation.