Discuss practical importance of results based on interval estimates and p-value functions, not only on point estimates and null p-values

It has long been argued that we need to consider much more than an observed point estimate and a p-value to understand statistical results. One of the most persistent misconceptions about p-values is that they are necessarily calculated assuming a null hypothesis of no effect is true. Instead, p-values can and should be calculated for multiple hypothesized values for the effect size. For example, a p-value function allows us to visualize results continuously by examining how the p-value varies as we move across possible effect sizes. For more focused discussions, a 95% confidence interval shows the subset of possible effect sizes that have p-values larger than 0.05 as calculated from the same data and the same background statistical assumptions. In this sense a confidence interval can be taken as showing the effect sizes that are most compatible with the data, given the assumptions, and thus may be better termed a compatibility interval. The question that should then be asked is whether any or all of the effect sizes within the interval are substantial enough to be of practical importance.