Andy Garland Timm writes:
My package for working with Type S/M errors in hypothesis testing, ‘retrodesign’, is now up on CRAN. It builds on the code provided by Gelman and Carlin (2014) with functions for calculating type S/M errors across a variety of effect sizes as suggested for design analysis in the paper, a function for visualizing the errors, and implements Lu et al.’s (2018) closed form solution for type M error, which is a nice speed boost. You can find the vignette online here, which goes into more detail about its functionality. Next on my to-do list for the package are tools for working with these errors in regression more easily.
If you want a visual for people, this little example of type S/M error with simulated N(.5,1) data could be good (Is including images often still a thing bloggers care about?):
Here, the dotted line is the true effect size, and the full lines are where the statistic becomes statistically significantly different from 0, given our standard error of 1. The grayed out points aren’t statistically significant, the squares are type M errors, and the triangles are type S errors.