Statistical Analysis for Education and Psychology Researchers

Figure 5.13: Histogram and normal

probability plot for arcsine

transformed variable ‘CORRD’—

percentage correct difficult reading

passage

It is evident from Figures 5.13 and 5.14 that the modified arcsine transformations have
improved both original distributions. There are however particular problems of
interpretion with this transformation and in certain circumstances (when the null
hypothesis is false) statistical power is reduced (see Chapter 8 section 8.11 for further
discussion).

Negatively skewed distributions or when the variance is proportional to

the mean

With count data the variance is often proportional to the mean rather than the standard
deviation and this often results in a negatively skewed distribution. A modified square
root transformation should be considered for negatively skewed distributions. When
values are small, i.e., less than 5, then it is suggested that 0.5 is added to all values prior
to transformation of the data. The form of the transformation is:

(^) Modified
square root
transforma
tion—5.5
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