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Weak Statistical Standards Implicated In Scientific Irreproducibility
ananyo writes "The plague of non-reproducibility in science may be mostly due to scientists' use of weak statistical tests, as shown by an innovative method developed by statistician Valen Johnson, at Texas A&M University. Johnson found that a P value of 0.05 or less — commonly considered evidence in support of a hypothesis in many fields including social science — still meant that as many as 17–25% of such findings are probably false (PDF). He advocates for scientists to use more stringent P values of 0.005 or less to support their findings, and thinks that the use of the 0.05 standard might account for most of the problem of non-reproducibility in science — even more than other issues, such as biases and scientific misconduct."
This would have the same problems, maybe even worse. The problem with statistics is usually that the model is wrong, and Bayesian stats offers two chances to fuck that up: in the prior, and in the generative model (=likelihood). Bayesian statistics still requires models (yes, you can do non-parametric Bayes, but you can do non-parametric frequentist stats also).
Contrary to the hype and buzzwords, Bayesian statistics is not some magical solution. It is incredibly useful when done right, of course.
The problem with frequentist statistics as used in the article is that its "recipe" character often results in people using statistics that do not understand its limitations (a good example is assuming a normal distribution when there is none). The bayesian approach does not suffer from this problem, also because it forces you to think a little bit more about the problem you are trying to solve compared to the frequentist approach. But that's also the problem with the cited article. Just remaining in the framework and going towards more discriminating thresholds is not really a solution of the problem that people do not understand their data analysis (a p-value based on the wrong distribution remains meaningless, even if you change your threshold...). Because it is more logical in its setup, the danger of making such mistakes is smaller in bayesian statistics. The telescoper over at http://telescoper.wordpress.com/2013/11/12/the-curse-of-p-values/ has a good discussion of these issues.
Personally, I've considered results with p values between 0.01 and 0.05 as merely 'suggestive': "It may be worth looking into this more closely to find out if this effect is real." Between 0.01 and 0.001 I'd take the result as tentatively true - I'll accept it until someone refutes it.
If you take p=0.04 as demonstrating a result is true, you're being foolish and statistically naive. However, unless you're a compulsive citation follower (which I'm not) you are somewhat at the mercy of other authors. If Alice says "In Bob (1998) it was shown that ..." I'll tend to accept it without realizing that Bob (1998) was a p=0.04 result.
Obligatory XKCD
Quattuor res in hoc mundo sanctae sunt: libri, liberi, libertas et liberalitas.
Yes, I agree. If a p-value of 0.05 actually "means" 0.20 when evaluated, then any sane frequentist will tell you that things are fucked, since the limiting probability does not match the nominal probability (this is the definition of frequentism).
The power of Bayesian stats is largely in being able to easily represent hierarchical models, which are very powerful for modeling dependence in the data through latent variables. But it's not the Bayesianism per se that fixes things, it's the breadth of models it allows. A mediocre modeler using Bayesian statistics will still create mediocre models, and if they use a bad prior, then things will be worse than they would be for a frequentist.
Consider that if Bayesian statisticians are doing a better job than frequentists at the moment, it may be because Bayesian stats hasn't yet been drilled into the minds of the mediocre, as frequentist stats has been for decades. People doing Bayesian stats tend to be better modelers to begin with.
Okay, here's the real problem with scientific studies.
All science is data compression, and all studies are are intended to compress data so that we can make future predictions. If you want to predict the trajectory of a cannonball, you don't need an almanac cross referencing cannonball weights, powder loads, and cannon angles - you can calculate the arc to any desired accuracy with a set of equations that fit on half a page. The half-page compresses the record of all prior experience with cannonball arcs, and allows us to predict future arcs.
Soft science studies typically make a set of observations which relate two measurable aspects. When plotted, the data points suggest a line or curve, and we accept the linear-regression (line or polynomial) as the best approximation for the data. The theory being that the underlying mechanism is the regression, and unrelated noise in the environment or measurement system causes random deviations of observation.
This is the wrong method. Regression is based on minimizing squared error, which was chosen by Laplace for no other reason that it is easy to calculate. There's lots of "rationalization" explanations of why it works and why it's "just the best possible thing to do", but there's no fundamental logic that can be used to deduce least squares from from fundamental assumptions.
Least squares introduces several problems:
1) Outliers will skew the values, and there is no computable way to detect or deal with outliers (source).
2) There is no computable way to determine whether the data represent a line or a curve - it's done by "eye" and justified with statistical tests.
3) The resultant function frequently looks "off" to the human eye, humans can frequently draw better matching curves; meaning: curves which better predict future data points.
4) There is no way to measure the predictive value of the results. Linear regression will always return the best line to fit the data, even when the data is random.
The right way is to show how much the observation data is compressed. If the regression function plus data (represented as offsets from the function) take fewer bits than the data alone, then you can say that the conclusions are valid. Further, you can tell how relevant the conclusions are, and rank and sort different conclusions (linear, curved) by their compression factor and choose the best one.
Scientific studies should have a threshold of "compresses data by N bits", rather than "1-in-20 of all studies are due to random chance".