steeply so that high ranked scores correspond to larger than expected (the straight line)
standardized scores.
To see whether the normal probability plot is reasonable, (i.e., no gross errors) you
should check that when the standardized expected value on the x axis equals zero, the
corresponding ranked value on the y axis should be an approximate estimate of the
median. For example, in Figure 5.10 the standardized score of zero corresponds to a score
on the variable CORRE of about 14, the value of the median.
What can be Done when Data is not Normal?If you face the problem of non normal data there are four possible strategies.
1 Check that there are no extreme outliers indicated by individual data points in a normal
probability plot that depart significantly from both the straight line and other data
points. If outliers are extreme remove them and check again for normality.
2 Consider using distribution free nonparametric statistical procedures.
3 Consider transforming your data.
4 Consider alternative non normal continuous distributions (these are beyond the scope of
this text and you should consult a statistician for help).
Strategy 1) may improve a distribution and should always be considered. It is an essential
part of IDA. However, you should consider the implications of removing outliers in your
results section and in any interpretation. Strategy 2) is useful when data can be ranked.
Examples of nonparametric statistical procedures are given in later chapters. Strategy 3)
is helpful on occasions if data is skewed. Data transformations will minimize the effect of
outliers but extreme observations should be dealt with as in strategy 1). Transformations
should also not be applied directly to the data when there are a large number of zeros in
the data. A constant such as 0.5 should be added to all data values prior to transformation
(this is because values of zero cannot be multiplied and therefore do not work well in
transformations, for example, logarithms are only defined for non-zero positive
numbers). Strategy 4) is beyond the scope of this book. See also the end of Chapter 8 for
further discussion.
Data TransformationsThe benefits from normative data transformations for extreme skewness or kurtosis are
worth considering but transformations should not be used on a routine basis because
statistical procedures such as F and t-tests are generally robust and interpretation of
transformed values can be problematic. Transformations should therefore be the
exception rather than the rule and are generally performed with the intention of: i)
making skewed distributions more symmetric and closer to a normal distribution ii) to
obtain homogeneity of variance in ‘scores’, and iii) to achieve a more meaningful scale of
measurement. This does not always work and transformed data should be checked using
normal probability plots to see whether there is any improvement in normality.
Statistical analysis for education and psychology researchers 150