Statistical Analysis for Education and Psychology Researchers

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.

Summary

This chapter has presented the issues to consider when choosing a statistical test for the
most common research situations in education and psychology. These considerations can
be viewed as an extension of IDA prior to inferential analysis. Appraisal of the research
design and likely data structure as well as choice of statistical test(s) and consideration of
statistical power should be born in mind when planning a study or when evaluating a
reported study. The point of determining statistical power for a given research plan is that
should power be deemed insufficient, that is generally <80%, then the research plan can
be revised prior to implementation.
After IDA, data will have been screened and out of range, missing values and outliers
will have been detected and dealt with. A plausible underlying data distribution will also
have been identified, such as binomial/categorical, ordered data or normal data. The next
step will be to check skewness and kurtosis either inferentially or by using a normal
probability plot. The later approach has the advantage of highlighting any outliers.
A preliminary choice of a statistical test can then proceed based on the research
design, specific research questions addressed and the type of data distribution and
inference for the variables of interest. The statistical decision chart, Figure 5.1, can be
used at this point. Consideration should also be given to the statistical power of any
proposed inferential analyses as well as any advantages or disadvantages of transforming
any non normal data distributions. The final choice of statistical test will rest upon
consideration of test specific assumptions, such as homogeneity of variance for a t-test.
These specific assumptions can be checked in the relevant chapter that deals with the
particular statistical test under consideration.

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