ABSTRACT
Interpretation of transformed scores is sometimes difficult. For example, if a log transformation is used then a mean log score of 1.065, see Figure 5.12, is difficult to comprehend. This mean log score should be back-transformed (antilog taken) into the original metric. The antilogarithm (base 10) of the value 1.065 is 11.61. This is now comparable with the original mean of 14.96. The antilogarithm of the mean of the log scores is known as the geometric mean (see Chapter 3, section 3.4). The antilogarithm of the natural log (log to base e) would give the same result. The geometric mean is not equivalent to the metric mean and therefore it is not appropriate to transform the 95 per cent confidence intervals back to the original metric values. This is a drawback of transforming data. It is suggested that when reporting geometric means for transformed data the medians of the original data distributions are also reported. Transformations can also be used to stabilize variances prior to t-or F-tests of means. If variances of different groups are heterogeneous, transforming the distributions can improve the homogeneity of variances and hence make use of a t-or F-test more justified as well as making the analysis more exact. These are called variance stabilizing transformations. In this chapter only an overview of some of the more common data transformations has been presented. The reader is referred to Mosteller and Tukey (1977) for a more detailed account.
