The bivariate relationship between a continuous predictor and a continuous outcome is conventionally reported as a correlation coefficient and displayed with a scatter plot. Correlations and scatter plots are often difficult to accurately interpret in a probabilistic manner. Common language effect size indicators are occasionally used to aid in interpreting effect sizes. The bivariate probability of superiority is the common language effect size alternative to the correlation coefficient, it is defined as the probability of someone scoring higher (or lower) in an outcome when also scoring higher in some predictor. However, the probability of scoring higher in the outcome changes depending on the magnitude of the difference in X. Here we introduce a probability of outcome superiority curve (POSCs) which captures the conditional probability of superiority given a difference in the predictor. The application of these curves is most useful when applied to decision-making situations such as applicant selection. For example, a POSC computes the probability that person A has a higher outcome (e.g. job performance) than person B given a specified difference in the predictor variable (e.g., cognitive ability).
install.packages('devtools')
devtools::install_github("MatthewBJane/posc")