Jim Matthews wrote:
As well as biostatistics issues such as understanding the difference between Risk Ratio and Odds Ratio, a common discussion point with researchers I talk to is when and how to report p values and what do they mean. Improved education and understanding of this topic would go a long way.
Aside from noting that the 1 in 19 interpretation for p=0.05 has scant connection to judging the extent to which an alternative of interest is more likely than the null, there seem a plethora of alternatives, with little in the way of common agreement on a substitute. Myself, in a case where one outcome appears a priori about as likely as the other I say to think of p=0.05 as corresponding to a relative probability of maybe 2 in favor of the alternative, with a non-point interval null so that one is not testing for the inconsequential. This issue of the choice of null increases in importance at the sample size increases.
The R package BayesFactor, which works with a Cauchy prior (t with 1df) and uses a numerical integration approach to avoid MCMC or suchlike sampling, seems to me a reasonable first step on the way a Bayesian approach. If p lies between 0.005 and 0.05, the Bayes Factors that one gets from BayesFactor seem a reasonable place to go for an indication of what the p-value might mean. If p<0.005 with a meaninful non-null prior, one is usually safe in thinking that there is a real meaningful difference.
There've been a number of replication/reproducibility studies that provide empirical evidence on what p-values mean in the context of published laboratory studies. The evidence that they provide should feature strongly in the educational process.