The great XKCD did this cartoon a while ago, illustrating the problem. If results with P>0.5 are simplistically treated as proving a hypothesis - and all too often they are - then 1 in 20 hypotheses so proven will actually be false. Similarly, if P<0.05 is taken as disproving a hypotheses then 1 in 20 true hypotheses will be wrongly rejected. P-values don't tell you whether a hypothesis is true or false, they tell you whether a hypothesis is probably true or false. It seems the referenced article is kicking back against the all-too-common naïve interpretation.

The great XKCD did this cartoon a while ago, illustrating the problem. If results with $P\gt0.05$ are simplistically treated as proving a hypothesis - and all too often they are - then 1 in 20 hypotheses so proven will actually be false. Similarly, if $P\lt0.05$ is taken as disproving a hypotheses then 1 in 20 true hypotheses will be wrongly rejected. P-values don't tell you whether a hypothesis is true or false, they tell you whether a hypothesis is probably true or false. It seems the referenced article is kicking back against the all-too-common naïve interpretation.