Search

In biological and social sciences, it is essential to consider data transformations to normality for detecting structural effects and for better data representation and interpretation. An array of transformations to normality has been derived for data exhibiting skewed, leptokurtic and unimodal shapes, but is less amenable to data exhibiting platykurtic shapes, such as a nearly bimodal distribution. This study proposes and constructs a new family of hyperbolic power transformations for improving normality of raw data with varying degrees of skewness and kurtosis. An advantage this new family has is its effectiveness in transforming platykurtic or bimodal data distributions to normal. A simulation study and a real data example on mathematics achievement test scores are used to illustrate the wide-ranging applications of the proposed family of transformations. As a cautionary note, usefulness and limitations of the proposed method will be discussed for stabilizing the variance of DNA microarray data and for symmetrizing the data distribution towards normality. The empirical applications also illustrate an example of conservative t - and ANOVA F -tests when the assumption of normality is violated. [ABSTRACT FROM AUTHOR]

Abstract: We develop a simple model for the random distribution of a gene product. It is assumed that the only source of variance is due to switching transcription on and off by a random process. Under the condition that the transition rates between on and off are constant we find that the amount of mRNA follows a scaled Beta distribution. Additionally, a simple positive feedback loop is considered. The simplicity of the model allows for an explicit solution also in this setting. These findings in turn allow, e.g., for easy parameter scans. We find that bistable behavior translates into bimodal distributions. These theoretical findings are in line with experimental results. [Copyright &y& Elsevier]

Tail moments in the single cell gel electrophoresis (comet) assay usually do not follow a normal distribution, making the statistical analysis complicated. Researchers have used a wide variety of statistical techniques in an attempt to overcome this problem. In many cases, the tail moments follow a bimodal distribution that can be modeled with a mixture of gamma distributions. This bimodality may be due to cells being in two different stages of the cell cycle at the time of treatment. Maximum likelihood, modified to accommodate censored data, can be used to estimate the five parameters of the gamma mixture distribution for each slide. A weighted analysis of variance on the parameter estimates for the gamma mixtures can be performed to determine differences in DNA damage between treatments. These methods were applied to an experiment on the effect of thymidine kinase in DNA damage and repair. Analysis based on the mixture of gamma distributions was found to be more statistically valid, more powerful, and more informative than analysis based on log-transformed tail moments. [ABSTRACT FROM AUTHOR]