A study of the validity of D-values for samples of different sizes and normal and non-normal errors

"The p-value is broadly used for testing statistical significance in a variety of settings. It is well known that statistical significance is easily achieved with a large enough sample. Additionally, the p-value can only be used to make conclusions for the means of the groups rather than on the individual level. This may be important for studies in the comparison of medical interventions where the goal is to assess improvements made to the health of individuals rather than groups. A complement to the p-value is the D-value. The D-value is an empirical version of the theoretical value of δ=ϕ((μ_y-μ_x)/(σ√2)) where ϕ(∙) is the cumulative distribution function of the normal distribution. Note that the D-value does not depend on sample size and provides an effect size on a probability scale for the individual rather than the group. Sample size still affects the sampling distribution in the D-value. We will be investigating this question by using the bootstrap method. First we will use resampling to compute an approximation of the sampling distribution of D. From the sampling distribution of D we can compute the D-value. The simulation will be expanded to include non-Normal of D errors for a One Way ANOVA. Finally we will compare the results of the D-values for non-normal errors for different sample sizes.