Data Transformations - Agricultural Statistical Data Analysis Using Stata - page 203

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D ata t ranSformationS
The analysis of variance has certain underlying assumptions to make
the analysis valid. This includes that the data were obtained from a
random sample of the population; that the error terms occur randomly,
are normally distributed, and are not correlated. The sample popula-
tions have equal or homogeneous variances. This is often referred to as
homoscedastic variances . This can be a little confusing. If this is an anal-
ysis of variance, how can the variances be the same? The assumption is
that the variance within one group is the same as the variance in other
groups. The means of the groups, however, may differ. In ANOVA
(analysis of variance), the F-tests are based on a ratio—the variation
between the group means divided by the variation within the groups
(pooled across groups). It is when there is a disparity between these
variances that a significant difference is detected. The variances and
treatment means should not be correlated. Finally, the factor levels
are assumed to be additive. That is, the model parameters, treatments,
replications, error, etc. are added together to create the model. This is
often referred to as a linear model or it has linearity.
Not all data will meet these underlying criteria, but often the data
can be transformed so that they do. One underlying assumption is the
errors are normally distributed. This is the classic bell-shaped curve.
There are cases where the data deviate from normality and it may be
corrected by transforming the data. Load the dataset Onion Disease
Transform Data.dta, which is a dataset from an onion variety trial
with data on the number of diseased plants per plot, the number of
seedstems (flowering), and the number of doubled bulbs per plot.
Reasonable steps to approaching the problem of analyzing these
data would be to run the ANOVA and determine if the residuals
(errors) are normally distributed. Enter the following to compute the
ANOVA on the raw data:
anova plantcount var rep
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