Nature provides an overview of concerns about how much scientists rely on p-values “which is neither as reliable nor as objective as most scientists assume”:

One result is an abundance of confusion about what the P value means⁴. Consider Motyl’s study about political extremists. Most scientists would look at his original P value of 0.01 and say that there was just a 1% chance of his result being a false alarm. But they would be wrong. The P value cannot say this: all it can do is summarize the data assuming a specific null hypothesis. It cannot work backwards and make statements about the underlying reality. That requires another piece of information: the odds that a real effect was there in the first place. To ignore this would be like waking up with a headache and concluding that you have a rare brain tumour — possible, but so unlikely that it requires a lot more evidence to supersede an everyday explanation such as an allergic reaction. The more implausible the hypothesis — telepathy, aliens, homeopathy — the greater the chance that an exciting finding is a false alarm, no matter what the P value is…

These are sticky concepts, but some statisticians have tried to provide general rule-of-thumb conversions (see ‘Probable cause’). According to one widely used calculation⁵, a P value of 0.01 corresponds to a false-alarm probability of at least 11%, depending on the underlying probability that there is a true effect; a P value of 0.05 raises that chance to at least 29%. So Motyl’s finding had a greater than one in ten chance of being a false alarm. Likewise, the probability of replicating his original result was not 99%, as most would assume, but something closer to 73% — or only 50%, if he wanted another ‘very significant’ result^{6, 7}. In other words, his inability to replicate the result was about as surprising as if he had called heads on a coin toss and it had come up tails…

Critics also bemoan the way that P values can encourage muddled thinking. A prime example is their tendency to deflect attention from the actual size of an effect. Last year, for example, a study of more than 19,000 people showed⁸ that those who meet their spouses online are less likely to divorce (p < 0.002) and more likely to have high marital satisfaction (p < 0.001) than those who meet offline (see Nature http://doi.org/rcg; 2013). That might have sounded impressive, but the effects were actually tiny: meeting online nudged the divorce rate from 7.67% down to 5.96%, and barely budged happiness from 5.48 to 5.64 on a 7-point scale. To pounce on tiny P values and ignore the larger question is to fall prey to the “seductive certainty of significance”, says Geoff Cumming, an emeritus psychologist at La Trobe University in Melbourne, Australia. But significance is no indicator of practical relevance, he says: “We should be asking, ‘How much of an effect is there?’, not ‘Is there an effect?’”

Perhaps the worst fallacy is the kind of self-deception for which psychologist Uri Simonsohn of the University of Pennsylvania and his colleagues have popularized the term P-hacking; it is also known as data-dredging, snooping, fishing, significance-chasing and double-dipping. “P-hacking,” says Simonsohn, “is trying multiple things until you get the desired result” — even unconsciously. It may be the first statistical term to rate a definition in the online Urban Dictionary, where the usage examples are telling: “That finding seems to have been obtained through p-hacking, the authors dropped one of the conditions so that the overall p-value would be less than .05”, and “She is a p-hacker, she always monitors data while it is being collected.”

As the article then goes on to note, alternatives haven’t quite caught on. It seems the most basic defense is one that statisticians should adopt anyhow: always recognizing the chance that their statistics could be wrong. It also highlights the need for replicating studies with different datasets to confirm results.

At a relatively basic level, if p-levels are so problematic, how does this change the basic statistics courses so many undergraduates take?