The likelihood ratio plot

 

The relationships between posterior odds, likelihood ratios and prior odds can be difficult to communicate. Further, the effect of the uncertainties in these quantities, especially on the posterior odds, is greatly underappreciated. This article proposes a plot that displays the relationship between the likelihood ratio and prior odds, and the resulting posterior odds, that incorporates uncertainties. The plot is easy to construct and is very useful in communicating, to both scientists and nonscientists, the weight of evidence in multiple settings, especially in judicial settings where ``transposing the conditionals’’ (misinterpreting the likelihood ratio as the posterior odds) frequently occurs. Illustrations of the plot, constructed using a cited, freely available R package, demonstrate its advantages.