usually to obtain scores which have improved normality and homogeneity of variance
characteristics. However, the reader should be aware that transformation of data to
change the variance of a distribution or restore normality will also affect the shape of the
distribution. For example, homogeneity of variance may be achieved but a distribution
may then be skewed. Another consequence resulting from data transformation is the
possibility of induced non-linearity. With reference to the arcsine transformation there is
no general agreement as to when this transformation is appropriate (Milligan, 1987), and
when the null hypothesis is false the transformation can reduce the power of a statistical
test.
A third strategy, seldom mentioned, is to perform the analysis but then to make
nominal adjustments to the statistical significance and power of a test, see Horton (1978)
for discussion of this alternative.
Concluding RemarksGenerally ask yourself the following questions when interpreting results: Does this make
sense? Is it what I might have expected? Is there an alternative interpretation or
explanation? Statistical significance should be distinguished from educational or clinical
significance. If a clinical or educational effect is reported consider the magnitude of the
effect, the ‘effect size’ and the statistical power. Consider also whether reported results
are exploratory or confirmatory and if survey data is reported, pay particular attention to
non-sampling errors when interpreting findings. Statistical analysis should be used to
gain insight into data and not as an end itself or to lend respectability to a poorly designed
study. Too much or over-sophisticated statistical analysis should be avoided, as one
statistician is reported to have commented, any data set will confess if you interrogate it
long enough.
Inferences involving continuous data 343