Randomization analysis of dental data characterized by skew and variance heterogeneity

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Abstract
Many distributions of dental variables exhibit positive skew and variance heterogeneity. Although the use of parametric tests on data with these disturbances usually does not pose a problem with respect to alpha error level, transformation of data sometimes increases power. Occasionally one or both of these expectations do not hold and it becomes problematic as to whether data should be transformed and which analyses should be considered valid. Simulated dental trials were conducted on independent samples (n = 25 per group) drawn from exponential distributions with the same or different population means, t-tests on raw, log, and square root transformed data; the Mann-Whitney-Wilcoxon ranking test; and a randomization test, all exhibited satisfactory levels of alpha error but the randomization test exhibited the greatest power followed closely by the t-test on raw scores. The present results demonstrate that the log transformation does not increase power for all forms of positively skewed data. Randomization tests, not being subject to normality and variance homogeneity assumptions, may yield greater confidence in validity in these cases. Some implications for analytical strategy are discussed.