Beyond the Statistics

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Statistical Inference as Severe Testing:. The problem is that high powered methods can make it easy to uncover impressive-looking findings even if they are false: spurious correlations and other errors have not been severely probed. We set sail with a simple tool: If little or nothing has been done to rule out flaws in inferring a claim, then it has not passed a severe test. In the severe testing view, probability arises in scientific contexts to assess and control how capable methods are at uncovering and avoiding erroneous interpretations of data.

A claim is severely tested to the extent it has been subjected to and passes a test that probably would have found flaws, were they present. You may be surprised to learn that many methods advocated by experts do not stand up to severe scrutiny, are even in tension with successful strategies for blocking or accounting for cherry-picking and selective reporting!

Visions of possibility

The severe testing perspective substantiates, using modern statistics, the idea Karl Popper promoted, but never cashed out. The goal of highly well tested claims differs sufficiently from highly probable ones that you can have your cake and eat it too: retaining both for different contexts. The testing metaphor grows out of the idea that before we have evidence for a claim, it must have passed an analysis that could have found it flawed.

The probability that a method commits an erroneous interpretation of data is an error probability. Statistical methods based on error probabilities I call error statistics. The value of error probabilities, I argue, is not merely to control error in the long-run, but because of what they teach us about the source of the data in front of us.

The concept of severe testing is sufficiently general to apply to any of the methods now in use, whether for exploration, estimation, or prediction. Getting Beyond the Statistics Wars:. Philosophy of science can also alleviate such conceptual discomforts. Nevertheless, important consequences will follow once this tool is used.

Critical Statistics

First there will be a reformulation of existing tools tests, confidence intervals and others so as to avoid misinterpretations and abuses. The debates on statistical inference generally concern inference after a statistical model and data statements are in place, when in fact the most interesting work involves the local inferences needed to get to that point.

A primary asset of error statistical methods is their contributions to designing, collecting, modeling, and learning from data. Second, instead of rehearsing the same criticisms over and over again, challengers on all sides should now begin by grappling with the arguments we trace within. Kneejerk assumptions about the superiority of one or another method will not do. Join me, then on a series of 6 excursions and 16 tours, during which we will visit 3 leading museums of statistical science and philosophy of science, and engage with a host of tribes marked by family quarrels, peace treaties, and shifting alliances.

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Some work of this kind has been done or is currently done; results are not always positive an early example is Easterling and Anderson The issues listed in Section 3 are in my view important and worthy of investigation. Such investigation has already been done to some extent, but there are many open problems.

I believe that some of these can be solved, some are very hard, and some are impossible to solve or may lead to negative results particularly connected to lack of identifiability. References: Chang, H.

Evidence, Realism and Pluralism. Dordrecht: Springer. Donoho, D. Annals of Statistics 16, Easterling, R. Journal of Statistical Computation and Simulation 8, Gelman, A.

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Hampel, F. New York: Wiley. Hennig, C. Foundations of Science 15, 29— Philosophia Mathematica 15, Struggling is a good thing here, I think! In statistics—maybe in science more generally—philosophical paradoxes are sometimes resolved by technological advances. Problem solved. Rapid technological progress resolves many problems in ways that were never anticipated. This is all to say that any philosophical perspective is time-bound.

In a class for first-year statistics Ph. Experimental design? This is the principle of the great Raymond Smullyan: To understand the past, we must first know the future. So is data analysis the most fundamental thing? Maybe so, but what method of data analysis? Last I heard, there are many schools. Bayesian data analysis, perhaps? We can back into a more fundamental, or statistical, justification of Bayesian inference and hierarchical modeling by first considering the principle of external validation of predictions, then showing both empirically and theoretically that a hierarchical Bayesian approach performs well based on this criterion—and then following up with the Jaynesian point that, when Bayesian inference fails to perform well, this recognition represents additional information that can and should be added to the model.

Anyway, to continue. Not unbiasedness, not p-values, and not type 1 or type 2 errors, but frequency properties nevertheless. So, I want to separate the principle of frequency evaluation—the idea that frequency evaluation and criticism represents one of the three foundational principles of statistics with the other two being mathematical modeling and the understanding of variation —from specific statistical methods, whether they be methods that I like Bayesian inference, estimates and standard errors, Fourier analysis, lasso, deep learning, etc.

We can be frequentists, use mathematical models to solve problems in statistical design and data analysis, and engage in model criticism, without making decisions based on type 1 error probabilities etc. To say it another way, bringing in the title of the book under discussion: I would not quite say that statistical inference is severe testing, but I do think that severe testing is a crucial part of statistics.

Severe testing is fundamental, in that prospect of revolution is a key contributor to the success of normal science.

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We lean on our models in large part because they have been, and will continue to be, put to the test. And we choose our statistical methods in large part because, under certain assumptions, they have good frequency properties. Phony Bayesmania has bitten the dust. I expect that Mayo will respond to these, and also to any comments that follow in this thread, once she has time to digest it all. As I might be the first commenting, I would like to thank you for organizing a reasonable number of thoughtful people to comment first and only then share.

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Thanks for being so clear about that and clarifying general notions of frequency evaluation. I believe Deborah and Chang would confirm the major source of their views on this are from CS Peirce. Sorry could not help myself and I do believe the sources of ideas are important to be aware of. Chang may have learned something about these themes from me he wrote a wonderful review of EGEK 20 years ago. Note, however, that the specific value of the angle is not a prediction of the standard model: it is an open, unfixed parameter.

However, it is constrained and predicted through other measurements of standard model quantities. At this time, there is no generally accepted theory that explains why the measured value is what it is. Certain classes of gauge theory models predict no observable parity violations in experiments such as ours. Among these are those left — right symmetric models in which the difference between neutral current neutrino and anti-neutrino scattering cross sections is explained as a consequence of the handedness o f the neutrino and anti-neutrino, while the underlying dynamics are parity conserving.

Such models are incompatible with the results presented here. Within this framework the original Weinberg-Salam W — S model makes specific weak isospin assignments: the left-handed electron and quarks are in doublets, the right-handed electron and quarks are singlets [19]. Other assignments are possible, however. To make specific predictions for parity violation in inelastic electron scattering, it is necessary to have a model for the nucleon, and the customary one is the simple quark-parton model.

The predicted asymmetries depend on the kinematic variable y as well as on the weak isospin assignments and on sin20w, where 0 w is the Weinberg angle. Prescott, C. Parity non-conservation in inelastic electron scattering. Physics Letters B, 77 3 , — Due to the free parameter, predictions of these models are more vague than a point prediction. The errors are combined from statistical and systematic contributions; the inner error bar on each point shows the statistical error alone.

These two models differ in the assumed assignment of the right-handed electron. The original Weinberg -Salam model W-S [15], extended to include quarks[16], assumes that left-handed leptons and quarks are placed in weak isospin doublets and the right-handed leptons and quarks are in singlets. To describe inelastic scattering from the nucleon, we use the simple quark — parton model [5]. The predicted asymmetry at each y-value depends on the mixing parameter sin20w. The error given on sin20w comes from a fit error of 0.

The hybrid model assumes the same isospin assignment for the quarks, but places the right-handed electron in a doublet with a hypothesized heavy neutral lepton [5]. Further measurements of parity non-conservation in inelastic electron scattering. Physics Letters B, 84 4 , — They do not consider one model in isolation, rather they compare the relative fit of a variety of possible explanations and choose the best.

Reports & Data

You can just compare the likelihoods using the single best-fit parameter for each. However, I wonder if those models that predicted a value of exactly zero got dismissed too easily. Not sure if this matters. The tails will be included for all terms so will somewhat cancel out…. From this case, I would guess use of a p-value to approximate the likelihood will tend to exaggerate the support for models that are relatively accurate.

The integration of several perspectives on the book of Mayo is really nice — thank you for this initiative. Let me share my perspective: Statistics is about information quality. If you deal with lab data, clinical trials, industrial problems or marketing data, it is always about the generation of information, and statistics should enable information quality.