Testing for bimodality in frequency distributions of data suggesting polymorphisms of drug metabolism--hypothesis testing

Abstract

1. The theory of methods of hypothesis testing in relation to the detection of bimodality in density distributions is discussed. 2. Practical problems arising from these methods are outlined. 3. The power of three methods of hypothesis testing was compared using simulated data from bimodal distributions with varying separation between components. None of the methods could determine bimodality until the separation between components was 2 standard deviation units and could only do so reliably (greater than 90%) when the separation was as great as 4-6 standard deviation units. 4. The robustness of a parametric and a non-parametric method of hypothesis testing was compared using simulated unimodal distributions known to deviate markedly from normality. Both methods had a high frequency of falsely indicating bimodality with distributions where the components had markedly differing variances. 5. A further test of robustness using power transformation of data from a normal distribution showed that the algorithms could accurately determine unimodality only when the skew of the distribution was in the range 0-1.45.