I mention Benford because someone noted that of my original sample the videos from the Twitter post , none of the distributions actually reject Benford at p 0 . 05 . Of course this was due to small sample size , and the aggregate of the videos easily rejects Benford , but I wanted to check it regardless . It ' s true that it doesn ' t fail at every possible level , and my wording could be improved there fails at each of the reasonable levels mentioned . Thank you . As for visualization , that was my intent with the dice example even though it wasn ' t pictorial , I still consider it a visualization . My goal was to create an association in the readers ' minds between rolling a die and drawing from 1 of 6 possible values in the tens digit . I wanted them to get that the latter is as random as the former and then to show that this isn ' t disproven by the ptest on the aggregate data . Honestly , you have more faith in my readers than I do if you expect them to read the footnotes . I wouldn ' t be surprised if half or more saw that the post was long and tried to immediately skip to the tldr . I hadn ' t considered the idea of just reporting the pvalues asis , but it makes a lot of sense in this context . I ' ll keep that in mind . Would you agree then that the difference of orders of magnitude between the one pvalue and the rest is the noteworthy part , and not the fact that the former is below some arbitrary thresholds while the latter are above them ?