This article "The Odds, Continually Updated" from NY Times happened to catch my attention. To be short, it states that
[Bayesian statistics] is proving especially useful in approaching complex problems, including searches like the one the Coast Guard used in 2013 to find the missing fisherman, John Aldridge (though not, so far, in the hunt for Malaysia Airlines Flight 370)........, Bayesian statistics are rippling through everything from physics to cancer research, ecology to psychology...
In the article, there are also some criticisms about the frequentist's p-value, for example:
Results are usually considered “statistically significant” if the p-value is less than 5 percent. But there is a danger in this tradition, said Andrew Gelman, a statistics professor at Columbia. Even if scientists always did the calculations correctly — and they don’t, he argues — accepting everything with a p-value of 5 percent means that one in 20 “statistically significant” results are nothing but random noise.
Besides above, perhaps the most famous paper criticizing p-value is this one - "Scientific method: Statistical errors" by Regina Nuzzo from Nature, in which a lot of scientific issues raised by p-value approach has been discussed, like reproducibility concerns, p-value hacking, etc.
P values, the 'gold standard' of statistical validity, are not as reliable as many scientists assume. ...... 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. ...... “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.”
Another thing is an interesting plot as following from here, with the comment about the plot:
No matter how small your effect may be, you can always do the hard work of gathering data in order to pass the threshold of p < .05. As long as the effect you're studying isn't non-existent, p-values just measure how much effort you've put into collecting data.
With all above, my questions are:
What does Andrew Gelman's argument, in the second block quote, mean precisely? Why did he interpret 5-percent p-value as "one in 20 statistically significant results are noting but random noise"? I am not convinced since to me p-value is used to make inference on one single study. His point seems related to multiple testing.
Update: Check Andrew Gelman's blog about this: No, I didn't say that! (Credits to @Scortchi, @whuber).
Given the criticisms about p-value, and also given there are a lot of information criteria, like AIC, BIC, Mallow's $C_p$ for evaluating the significance of a model (hence variables), should we not use p-value for variable selection at all but use those model selection criteria?
- Are there any good practical guidances of using p-value for statistical analysis which could lead to more reliable research results?
Would Bayesian modeling framework a better way to pursue, as some statistician advocate? Specifically, would Bayesian approach be more likely to resolve false finding or manipulating the data issues? I am not convinced here as well since the prior is very subjective in Bayesian approach. Are there any practical and well-known studies that show Bayesian approach is better than frequentist's p-value, or at least in some particular cases?
Update: I would be particularly interested in whether there are cases that Bayesian approach is more reliable than frequentist's p-value approach. By "reliable", I mean the Bayesian approach is less likely to manipulate data for desired results. Any suggestions?
Just noticed the news, and thought it would be good to put it here for discussion.
A controversial statistical test has finally met its end, at least in one journal. Earlier this month, the editors of Basic and Applied Social Psychology (BASP) announced that the journal would no longer publish papers containing P values because the statistics were too often used to support lower-quality research.
Along with a recent paper, "The fickle P value generates irreproducible results" from Nature, about P value.
Back in March, the American Statistical Association (ASA) released statements on statistical significance and p-values, "....The ASA statement is intended to steer research into a ‘post p<0.05 era.’"
This statement contains 6 principles that address the misuse of the p-value:
- P-values can indicate how incompatible the data are with a specified statistical model.
- P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.
- Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.
- Proper inference requires full reporting and transparency.
- A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.
- By itself, a p-value does not provide a good measure of evidence regarding a model or hypothesis.