The classic coefficient of variation (CV) is the ratio of the standard deviation to the mean and can be used to compare normally distributed data with respect to their variability, this measure has been widely used in many fields. In the Social Sciences, the CV is used to evaluate demographic heterogeneity and social aggregates such as race, sex, education and others. Data of this nature are usually not normally distributed, and the distributional characteristics can vary widely. In this sense, more accurate and robust estimator variations of the classic CV are needed to give a more realistic picture of the behavior of collected data. In this work, we empirically evaluate five measures of relative variability, including the classic CV, of finite sample sizes via Monte Carlo simulations. Our purpose is to give an insight into the behavior of these estimators, as their performance has not previously been systematically investigated. To represent different behaviors of the data, we considered some statistical distributions—which are frequently used to model data across various research fields. To enable comparisons, we consider parameters of these distributions that lead to a similar range of values for the CV. Our results indicate that CV estimators based on robust statistics of scale and location are more accurate and give the highest measure of efficiency. Finally, we study the stability of a robust CV estimator in psychological and genetic data and compare the results with the traditional CV.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable.

We propose a new methodology to estimate λ, the parameter of the Box-Cox transformation, as well as an alternative method to determine plausible values for it. The former is accomplished by defining a grid of values for λ and further perform a normality test on the λ -transformed data. The optimum value of λ, say λ * , is such that the p-value from the normality test is the highest. The set of plausible values is determined using the inverse probability method after plotting the p-values against the values of λ on the grid. Our methodology is illustrated with two real-world data sets. Furthermore, a simulation study suggests that our method improves the symmetry, kurtosis and, hence, the normality of data, making it a feasible alternative to the traditional Box-Cox transformation.

Reaction time (RT) is one of the most common types of measure used in experimental psychology. Its distribution is not normal (Gaussian) but resembles a convolution of normal and exponential distributions (Ex-Gaussian). One of the major assumptions in parametric tests (such as ANOVAs) is that variables are normally distributed. Hence, it is acknowledged by many that the normality assumption is not met. This paper presents different procedures to normalise data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption. Using simulation studies, various outlier elimination and transformation procedures were tested against the level of normality they provide. The results suggest that the transformation methods are better than elimination methods in normalising positively skewed data and the more skewed the distribution then the transformation methods are more effective in normalising such data. Specifically, transformation with parameter lambda -1 leads to the best results.