Data Transformations - Agricultural Statistical Data Analysis Using Stata - page 210

nonadd seedstems var rep
This calculates Tukey's test for nonadditivity to determine if the
assumption of additivity is violated. The results are
Tukey's test of nonadditivity (Ho: model is additive)
SS nonadd = df = 1
F (1,86) = 7.2406072 Pr > F:.00856253
In this case, we see that the data differ significantly from being addi-
tive. Transform these data with a log transformation and compute
Tukey's test again. Enter the commands
generate transtem = log10 (seedstems+1)
nonadd transtem var rep
This results in the following output:
Tukey's test of nonadditivity (Ho: model is additive)
SS nonadd = df = 1
F (1,86) = 1.3522982 Pr > F:.2480934
The transformed data now meet the criteria of additivity.
The log transformation can be either a base 10 or natural log or any
other log base and the effect will be similar, although a base 10 log
will probably work better with data that are multiplicative. Usually
some constant is added to the value before this transformation is used
particularly if there are any zeros in the dataset or numbers very close
to 0. This prevents such data points from being missing data in the
transformation. Finally, this type of transformation will not work
with negative numbers as these also will be missing data points after
the transformation.
Another type of transformation that is commonly used is the arc-
sine or angular transformation. This type of transformation is often
used with percent data particularly when the percentages occur both
below 30% and above 70%. These types of datasets often exhibit a
binomial distribution rather than a normal distribution and the treat-
ment variances are often less at the extremes of the range than in the
middle. This transformation is y = arcsine(square root(x)) where x is
the original data.