Statistical Analysis for Education and Psychology Researchers

Figure 5.12: Histogram and normal

probability plot for log transformed

variable ‘CORRD’—percentage

correct difficult reading passage

Notice the distribution for the log transformed data in Figure 5.12 has considerably
improved the shape of the original distribution shown in Figure 5.9. Examining the
transformed data, however, shows that it still departs significantly from normality, Pr<W
0.0001. An alternative transformation suitable for data which is in the form of
percentages or proportions is the arcsine transformation.

Count data, especially proportions or percentages with skewed

distributions

When the variance is a direct function of the mean (σ^2 =P(1−P)) for example with
proportions and percentages, the arcsine transformation should be considered. Generally,
percentage scores tend to cluster around the high or the low end of a range, rather than
the middle. The effect of the arcsine transformation is to move high scores towards the
centre of the distribution. A modified arcsine transformation:

Choosing a statistical test 153