C&B Notes

Overvaluing P Value

Within the research community, an uncritical focus on P values coupled with a lack of deeper thinking about correlation/causation has led to a number of published findings that are either non-replicable or, even worse, nonsensical.  Many of the psychological misjudgments that plague investors also manifest themselves in scientists.

It turned out that the problem was not in the data or in Motyl’s analyses.  It lay in the surprisingly slippery nature of the P value, which is neither as reliable nor as objective as most scientists assume.  “P values are not doing their job, because they can’t,” says Stephen Ziliak, an economist at Roosevelt University in Chicago, Illinois, and a frequent critic of the way statistics are used.  For many scientists, this is especially worrying in light of the reproducibility concerns.  In 2005, epidemiologist John Ioannidis of Stanford University in California suggested that most published findings are false; since then, a string of high-profile replication problems has forced scientists to rethink how they evaluate results.

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The irony is that when UK statistician Ronald Fisher introduced the P value in the 1920s, he did not mean it to be a definitive test. He intended it simply as an informal way to judge whether evidence was significant in the old-fashioned sense: worthy of a second look.  The idea was to run an experiment, then see if the results were consistent with what random chance might produce.  Researchers would first set up a ‘null hypothesis’ that they wanted to disprove, such as there being no correlation or no difference between two groups.  Next, they would play the devil’s advocate and, assuming that this null hypothesis was in fact true, calculate the chances of getting results at least as extreme as what was actually observed.  This probability was the P value.  The smaller it was, suggested Fisher, the greater the likelihood that the straw-man null hypothesis was false…

One result is an abundance of confusion about what the P value means.  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 tumor — 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.  According to one widely used calculation, 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.  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.

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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.”  Such practices have the effect of turning discoveries from exploratory studies — which should be treated with scepticism — into what look like sound confirmations but vanish on replication.  Simonsohn’s simulations have shown that changes in a few data-analysis decisions can increase the false-positive rate in a single study to 60%. P-hacking is especially likely, he says, in today’s environment of studies that chase small effects hidden in noisy data.  It is tough to pin down how widespread the problem is, but Simonsohn has the sense that it is serious.  In an analysis, he found evidence that many published psychology papers report P values that cluster suspiciously around 0.05, just as would be expected if researchers fished for significant P values until they found one.