My new paper, “*P* Values on Trial: Selective Reporting of (Best Practice Guides Against) Selective Reporting” is out in *Harvard Data Science Review (HDSR). HDSR *describes itself as a A Microscopic, Telescopic, and Kaleidoscopic View of Data Science. The editor-in-chief is Xiao-li Meng, a statistician at Harvard. He writes a short blurb on each article in his opening editorial of the issue. Continue reading

# significance tests

## My paper, “P values on Trial” is out in Harvard Data Science Review

## Posts of Christmas Past (1): 13 howlers of significance tests (and how to avoid them)

I’m reblogging a post from Christmas past–exactly 7 years ago. Guess what I gave as the number 1 (of 13) ~~howler~~ well-worn criticism of statistical significance tests, haunting us back in 2012–all of which are put to rest in Mayo and Spanos 2011? Yes, it’s the frightening allegation that statistical significance tests forbid using any background knowledge! The researcher is imagined to start with a “blank slate” in each inquiry (no memories of fallacies past), and then unthinkingly apply a purely formal, automatic, accept-reject machine. What’s newly frightening (in 2019) is the credulity with which this apparition is now being met (by some). I make some new remarks below the post from Christmas past: Continue reading

## TragiComedy hour: P-values vs posterior probabilities vs diagnostic error rates

The consequences of recent criticisms of statistical tests have breathed brand new life into some very old howlers, many of which have been discussed on this blog. What is not funny, though, is how standard notions such as frequentist error probabilities are being redefined in the process, and how we now have arguments built on equivocations. In fact, there are official guidebooks for the statistically perplexed giving inconsistent definitions to the same term (See for just 1 of many examples this post). How much more perplexed will that leave us! Since it’s near the 5-year anniversary of this blog, let’s listen in to a new comedy hour mixing one from **3 years ago **with some add-ons*.

*D id you hear the one about the frequentist significance tester when he was shown the nonfrequentist nature of p-values?*

Critic:I just simulated a long series of tests on a pool of null hypotheses, and I found that among tests with p-values of .05, at least 22%—and typically over 50%—of the null hypotheses are true!

Frequentist Significance Tester: Scratches head: But rejecting the null with a p-value of .05 ensures erroneous rejection no more than 5% of the time!

Raucous laughter ensues!

(Hah, hah… “So funny, I forgot to laugh! Or, I’m crying and laughing at the same time!) Continue reading

## Return to the Comedy Hour: P-values vs posterior probabilities (1)

Some recent criticisms of statistical tests of significance have breathed brand new life into some very old howlers, many of which have been discussed on this blog. One variant that returns to the scene every decade I think (for 50+ years?), takes a “disagreement on numbers” to show a problem with significance tests even from a “frequentist” perspective. Since it’s Saturday night, let’s listen in to one of the comedy hours from **3 years ago **(0) (new notes in red):

*D id you hear the one about the frequentist significance tester when he was shown the nonfrequentist nature of p-values?*

JB[Jim Berger]:I just simulated a long series of tests on a pool of null hypotheses, and I found that among tests with p-values of .05, at least 22%—and typically over 50%—of the null hypotheses are true!(1)

Frequentist Significance Tester: Scratches head: But rejecting the null with a p-value of .05 ensures erroneous rejection no more than 5% of the time!

Raucous laughter ensues!

(Hah, hah,…. I feel I’m back in high school: “So funny, I forgot to laugh!)

The frequentist tester should retort:

But you assumed 50% of the null hypotheses are true, and computed P(HFrequentist Significance Tester:_{0}|x) (imagining P(H_{0})= .5)—and then assumed my p-value should agree with the number you get, if it is not to be misleading!

Yet, our significance tester is not heard from as they move on to the next joke…. Continue reading

## WHIPPING BOYS AND WITCH HUNTERS (ii)

At least as apt today as 3 years ago…* HAPPY HALLOWEEN!* Memory Lane with new comments in

**blue**.

In an earlier post I alleged that frequentist hypotheses tests often serve as whipping boys, by which I meant “scapegoats”, for the well-known misuses, abuses, and flagrant misinterpretations of tests (both simple Fisherian significance tests and Neyman-Pearson tests, although in different ways)—as well as for what really boils down to a field’s weaknesses in modeling, theorizing, experimentation, and data collection. Checking the history of this term however, there is a certain disanalogy with at least the original meaning of a “whipping boy,” namely, an innocent boy who was punished when a medieval prince misbehaved and was in need of discipline. It was thought that seeing an innocent companion, often a friend, beaten for his own transgressions would supply an effective way to ensure the prince would not repeat the same mistake. But significance tests floggings, rather than a tool for a humbled self-improvement and commitment to avoiding flagrant rule violations, has tended instead to yield declarations that it is the rules that are invalid! The violators are excused as not being able to help it! The situation is more akin to that of witch hunting that in some places became an occupation in its own right.

Now some early literature, e.g., Morrison and Henkel’s *Significance Test Controversy* (1962), performed an important service over fifty years ago. They alerted social scientists to the fallacies of significance tests: misidentifying a statistically significant difference with one of substantive importance, interpreting insignificant results as evidence for the null hypothesis—especially problematic with insensitive tests, and the like. Chastising social scientists for applying significance tests in slavish and unthinking ways, contributors call attention to a cluster of pitfalls and fallacies of testing. Continue reading

## Statistical “reforms” without philosophy are blind (v update)

Is it possible, today, to have a fair-minded engagement with debates over statistical foundations? I’m not sure, but I know it is becoming of pressing importance to try. Increasingly, people are getting serious about methodological reforms—some are quite welcome, others are quite radical. Too rarely do the reformers bring out the philosophical presuppositions of the criticisms and proposed improvements. Today’s (radical?) reform movements are typically launched from criticisms of statistical significance tests and P-values, so I focus on them. Regular readers know how often the P-value (that most unpopular girl in the class) has made her appearance on this blog. Here, I tried to quickly jot down some queries. (Look for later installments and links.) *What are some key questions we need to ask to tell what’s true about today’s criticisms of P-values? *

*I. To get at philosophical underpinnings, the single most import question is this:*

**(1) Do the debaters distinguish different views of the nature of statistical inference and the roles of probability in learning from data? ** Continue reading

## “Probabilism as an Obstacle to Statistical Fraud-Busting”

“Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?” was my presentation at the 2014 Boston Colloquium for the Philosophy of Science):**“Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge.” **

** **As often happens, I never put these slides into a stand alone paper. But I have incorporated them into my book (in progress*), “How to Tell What’s True About Statistical Inference”. Background and slides were posted last year.

Slides (draft from Feb 21, 2014)

Download the 54th Annual Program

Cosponsored by the Department of Mathematics & Statistics at Boston University.

10 a.m. – 5:30 p.m.

Photonics Center, 9th Floor Colloquium Room (Rm 906)

8 St. Mary’s Street

## Who ya gonna call for statistical Fraudbusting? R.A. Fisher, P-values, and error statistics (again)

*If there’s somethin’ strange in your neighborhood. Who ya gonna call?(Fisherian Fraudbusters!)**

*[adapted from R. Parker’s “Ghostbusters”]

When you need to warrant serious accusations of bad statistics, if not fraud, where do scientists turn? Answer: To the frequentist error statistical reasoning and to p-value scrutiny, first articulated by R.A. Fisher[i].The latest accusations of big time fraud in social psychology concern the case of Jens Förster. As Richard Gill notes:

## Fallacies of statistics & statistics journalism, and how to avoid them: Summary & Slides Day #8 (Phil 6334)

We spent the first half of Thursday’s seminar discussing the Fisher, Neyman, and E. Pearson “triad”[i]. So, since it’s Saturday night, join me in rereading for the nth time these three *very short* articles. The key issues were: error of the second kind, behavioristic vs evidential interpretations, and Fisher’s mysterious fiducial intervals. Although we often hear exaggerated accounts of the differences in the Fisherian vs Neyman-Pearson (NP) methodology, in fact, N-P were simply providing Fisher’s tests with a logical ground (even though other foundations for tests are still possible), and Fisher welcomed this gladly. Notably, with the single null hypothesis, N-P showed that it was possible to have tests where the probability of rejecting the null when true exceeded the probability of rejecting it when false. Hacking called such tests “worse than useless”, and N-P develop a theory of testing that avoids such problems. Statistical journalists who report on the alleged “inconsistent hybrid” (a term popularized by Gigerenzer) should recognize the extent to which the apparent disagreements on method reflect professional squabbling between Fisher and Neyman after 1935 [A recent example is a Nature article by R. Nuzzo in ii below]. The two types of tests are best seen as asking different questions in different contexts. They both follow error-statistical reasoning. Continue reading

## “Probabilism as an Obstacle to Statistical Fraud-Busting” (draft iii)

Update: Feb. 21, 2014 (slides at end): Ever find when you begin to “type” a paper to which you gave an off-the-cuff title months and months ago that you scarcely know just what you meant or feel up to writing a paper with that (provocative) title? But then, pecking away at the outline of a possible paper crafted to fit the title, you discover it’s just the paper you’re *up to* writing right now? That’s how I feel about “Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?” (the impromptu title I gave for my paper for the Boston Colloquium for the Philosophy of Science):

**The conference is called: “Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge.” **

** **Here are some initial chicken-scratchings (draft (i)). Share comments, queries. (I still have 2 weeks to come up with something*.) Continue reading

## A. Spanos lecture on “Frequentist Hypothesis Testing”

I attended a lecture by Aris Spanos to his graduate econometrics class here at Va Tech last week[i]. This course, which Spanos teaches every fall, gives a superb illumination of the disparate pieces involved in statistical inference and modeling, and affords clear foundations for how they are linked together. His slides follow the intro section. Some examples with severity assessments are also included.

**Frequentist Hypothesis Testing: A Coherent Approach**

Aris Spanos

1 Inherent difficulties in learning statistical testing

Statistical testing is arguably the most important, but also the most difficult and confusing chapter of statistical inference for several reasons, including the following.

(i) The need to introduce numerous new notions, concepts and procedures before one can paint — even in broad brushes — a coherent picture of hypothesis testing.

(ii) The current textbook discussion of statistical testing is both highly confusing and confused. There are several sources of confusion.

- (a) Testing is conceptually one of the most sophisticated sub-fields of any scientific discipline.
- (b) Inadequate knowledge by textbook writers who often do not have the technical skills to read and understand the original sources, and have to rely on second hand accounts of previous textbook writers that are often misleading or just outright erroneous. In most of these textbooks hypothesis testing is poorly explained as an idiot’s guide to combining off-the-shelf formulae with statistical tables like the Normal, the Student’s t, the chi-square, etc., where the underlying statistical model that gives rise to the testing procedure is hidden in the background.
- (c) The misleading portrayal of Neyman-Pearson testing as essentially decision-theoretic in nature, when in fact the latter has much greater affinity with the Bayesian rather than the frequentist inference.
- (d) A deliberate attempt to distort and cannibalize frequentist testing by certain Bayesian drumbeaters who revel in (unfairly) maligning frequentist inference in their attempts to motivate their preferred view on statistical inference.

(iii) The discussion of frequentist testing is rather incomplete in so far as it has been beleaguered by serious foundational problems since the 1930s. As a result, different applied fields have generated their own secondary literatures attempting to address these problems, but often making things much worse! Indeed, in some fields like psychology it has reached the stage where one has to correct the ‘corrections’ of those chastising the initial correctors!

In an attempt to alleviate problem (i), the discussion that follows uses a sketchy historical development of frequentist testing. To ameliorate problem (ii), the discussion includes ‘red flag’ pointers (¥) designed to highlight important points that shed light on certain erroneous in- terpretations or misleading arguments. The discussion will pay special attention to (iii), addressing some of the key foundational problems.

[i] It is based on Ch. 14 of Spanos (1999) *Probability Theory and Statistical Inference. *Cambridge[ii].

[ii] You can win a free copy of this 700+ page text by creating a simple palindrome! https://errorstatistics.com/palindrome/march-contest/

## WHIPPING BOYS AND WITCH HUNTERS

This, from 2 years ago, “fits” at least as well today…HAPPY HALLOWEEN! Memory Lane

In an earlier post I alleged that frequentist hypotheses tests often serve as whipping boys, by which I meant “scapegoats”, for the well-known misuses, abuses, and flagrant misinterpretations of tests (both simple Fisherian significance tests and Neyman-Pearson tests, although in different ways). Checking the history of this term however, there is a certain disanalogy with at least the original meaning of a of “whipping boy,” namely, an innocent boy who was punished when a medieval prince misbehaved and was in need of discipline. It was thought that seeing an innocent companion, often a friend, beaten for his own transgressions would supply an effective way to ensure the prince would not repeat the same mistake. But significance tests floggings, rather than a tool for a humbled self-improvement and commitment to avoiding flagrant rule violations, has tended instead to yield declarations that it is the rules that are invalid! The violators are excused as not being able to help it! The situation is more akin to that of witch hunting, that in some places became an occupation in its own right.

Now some early literature, e.g., Morrison and Henkel’s *Significance Test Controversy* (1962), performed an important service over fifty years ago. They alerted social scientists to the fallacies of significance tests: misidentifying a statistically significant difference with one of substantive importance, interpreting insignificant results as evidence for the null hypothesis–especially problematic with insensitive tests, and the like. Chastising social scientists for applying significance tests in slavish and unthinking ways, contributors call attention to a cluster of pitfalls and fallacies of testing.

The volume describes research studies conducted for the sole purpose of revealing these flaws. Rosenthal and Gaito (1963) document how it is not rare for scientists to mistakenly regard a statistically significant difference, say at level .05, as indicating a greater discrepancy from the null when arising from a large sample size rather than a smaller sample size—even though a correct interpretation of tests indicates the reverse. By and large, these critics are not espousing a Bayesian line but rather see themselves as offering “reforms” e.g., supplementing simple significance tests with power (e.g., Jacob Cohen’s “power analytic movement), and most especially, replacing tests with confidence interval estimates of the size of discrepancy (from the null) indicated by the data. Of course, the use of power is central for (frequentist) Neyman-Pearson tests, and (frequentist) confidence interval estimation even has a duality with hypothesis tests!)

But rather than take a temporary job of pointing up some understandable fallacies in the use of newly adopted statistical tools by social scientific practitioners, or lead by example of right-headed statistical analyses, the New Reformers have seemed to settle into a permanent career of showing the same fallacies. Yes, they advocate “alternative” methods, e.g., “effect size” analysis, power analysis, confidence intervals, meta-analysis. But never having adequately unearthed the essential reasoning and rationale of significance tests—admittedly something that goes beyond many typical expositions—their supplements and reforms often betray the same confusions and pitfalls that underlie the methods they seek to supplement or replace! (I will give readers a chance to demonstrate this in later posts.)

We all reject the highly lampooned, recipe-like uses of significance tests; I and others insist on interpreting tests to reflect the extent of discrepancy indicated or not (back when I was writing my doctoral dissertation and EGEK 1996). I never imagined that hypotheses tests (of all stripes) would continue to be flogged again and again, in the same ways!

Frustrated with the limited progress in psychology, apparently inconsistent results, and lack of replication, an imagined malign conspiracy of significance tests is blamed: traditional reliance on statistical significance testing, we hear,

“has a debilitating effect on the general research effort to develop cumulative theoretical knowledge and understanding. However, it is also important to note that it destroys the usefulness of psychological research as a means for solving practical problems in society” (Schmidt 1996, 122)[i].

Meta-analysis was to be the cure that would provide cumulative knowledge to psychology: Lest enthusiasm for revisiting the same cluster of elementary fallacies of tests begin to lose steam, the threats of dangers posed become ever shriller: just as the witch is responsible for whatever ails a community, the significance tester is portrayed as so powerful as to be responsible for blocking scientific progress. In order to keep the gig alive, a certain level of breathless hysteria is common: “statistical significance is hurting people, indeed killing them” (Ziliak and McCloskey 2008, 186)[ii]; significance testers are members of a “cult” led by R.A. Fisher” whom they call “The Wasp”. To the question, “What if there were no Significance Tests,” as the title of one book inquires[iii], surely the implication is that once tests are extirpated, their research projects would bloom and thrive; so let us have Task Forces[iv] to keep reformers busy at journalistic reforms to banish the test once and for all!

Harlow, L., Mulaik, S., Steiger, J. (Eds.) *What if there were no significance tests?* (pp. 37-64). Mahwah, NJ: Lawrence Erlbaum Associates.

Hunter, J.E. (1997), “Needed: A Ban on the Significance Test,”, American Psychological Society 8:3-7.

Morrison, D. and Henkel, R. (eds.) (1970), *The Significance Test Controversy*, Aldine, Chicago.

MSERA (1998), *Research in the Schools*, 5(2) “Special Issue: Statistical Significance Testing,” Birmingham, Alabama.

Rosenthal, R. and Gaito, J. (1963), “The Interpretation of Levels of Significance by Psychologicl Researchers,” *Journal of Psychology* 55:33-38.

Ziliak, T. and McCloskey, D. (2008), The Cult of Statistical Significance, University of Michigan Press.

[i]Schmidt was the one Erich Lehmann wrote to me about, expressing great concern.

[ii] While setting themselves up as High Priest and Priestess of “reformers” their own nostroms reveal they fall into the same fallacy pointed up by Rosenthal and Gaito (among many others) nearly a half a century ago. That’s what should scare us!

[iii] In Lisa A. Harlow, Stanley A. Mulaik, and James H. Steiger (Eds.) *What if there were no significance tests?* (pp. 37-64). Mahwah, NJ: Lawrence Erlbaum Associates.

[iv] MSERA (1998): ‘Special Issue: Statistical Significance Testing,’ *Research in the Schools*, 5. See also Hunter (1997). The last I heard, they have not succeeded in their attempt at an all-out “test ban”. Interested readers might check the status of the effort, and report back.

Related posts:

“Saturday night brainstorming and taskforces”

“What do these share in common: MMs, limbo stick, ovulation, Dale Carnegie?: Sat. night potpourri”

## Gelman’s response to my comment on Jaynes

Gelman responds to the comment[i] I made on my 8/31/13 post:

*Popper and Jaynes*

Posted by Andrew on 3 September 2013

Deborah Mayo quotes me as saying, “Popper has argued (convincingly, in my opinion) that scientific inference is not inductive but deductive.” She then follows up with:

Gelman employs significance test-type reasoning to reject a model when the data sufficiently disagree.

Now, strictly speaking, a model falsification, even to inferring something as weak as “the model breaks down,” is not purely deductive, but Gelman is right to see it as about as close as one can get, in statistics, to a deductive falsification of a model. But where does that leave him as a Jaynesian?

My reply:

I was influenced by reading a toy example from Jaynes’s book where he sets up a model (for the probability of a die landing on each of its six sides) based on first principles, then presents some data that contradict the model, then expands the model.

I’d seen very little of this sort of this reasoning before in statistics! In physics it’s the standard way to go: you set up a model based on physical principles and some simplifications (for example, in a finite-element model you assume the various coefficients aren’t changing over time, and you assume stability within each element), then if the model doesn’t quite work, you figure out what went wrong and you make it more realistic.

But in statistics we weren’t usually seeing this. Instead, model checking typically was placed in the category of “hypothesis testing,” where the rejection was the goal. Models to be tested were straw man, build up only to be rejected. You can see this, for example, in social science papers that list research hypotheses that are

notthe same as the statistical “hypotheses” being tested. A typical research hypothesis is “Y causes Z,” with the corresponding statistical hypothesis being “Y has no association with Z after controlling for X.” Jaynes’s approach—or, at least, what I took away from Jaynes’s presentation—was more simpatico to my way of doing science. And I put a lot of effort into formalizing this idea, so that the kind of modeling I talk and write about can be the kind of modeling I actually do.I don’t want to overstate this—as I wrote earlier, Jaynes is no guru—but I do think this combination of model building and checking is important. Indeed, just as a chicken is said to be an egg’s way of making another egg, we can view inference as a way of sharpening the implications of an assumed model so that it can better be checked.

P.S. In response to Larry’s post here, let me give a quick +1 to this comment and also refer to this post, which remains relevant 3 years later.

I still don’t see how one learns about falsification from Jaynes when he alleges that the entailment of * x* from

*H*disappears once

*H*is rejected. But put that aside. In my quote from Gelman 2011, he was alluding to simple significance tests–without an alternative–for checking consistency of a model; whereas, he’s now saying what he wants is to infer an alternative model, and furthermore suggests one doesn’t see this in statistical hypotheses tests. But of course Neyman-Pearson testing always has an alternative, and even Fisherian simple significance tests generally indicate a direction of departure. However, neither type of statistical test method would automatically license going directly from a rejection of one statistical hypotheses to inferring an alternative model that was constructed to account for the misfit. A parametric discrepancy,δ, from a null may be indicated if the test very probably would not have resulted in so large an observed difference, were such a discrepancy absent (i.e., when the inferred alternative passes severely). But I’m not sure Gelman is limiting himself to such alternatives.

As I wrote in a follow-up comment: “*there’s no warrant to infer a particular model that happens to do a better job fitting the data x–at least on x alone. Insofar as there are many alternatives that could patch things up, an inference to one particular alternative fails to pass with severity. I don’t understand how it can be that some of the critics of the (bad) habit of some significance testers to move from rejecting the null to a particular alternative, nevertheless seem prepared to allow this in Bayesian model testing. But maybe they carry out further checks down the road; I don’t claim to really get the methods of correcting Bayesian priors (as part of a model)”*

A published discussion of Gelman and Shalizi on this matter is here.

[i] My comment was:

” If followers of Jaynes agree with [one of the commentators] (and Jaynes, apparently) that as soon asHis falsified, the grounds on which the test was based disappear!—a position that is based on a fallacy– then I’m confused as to how Andrew Gelman can claim to follow Jaynes at all. “Popper has argued (convincingly, in my opinion) that scientific inference is not inductive but deductive…” (Gelman, 2011, bottom p. 71).Gelman employs significance test-type reasoning to reject a model when the data sufficiently disagree. Now, strictly speaking, a model falsification, even to inferring something as weak as “the model breaks down,” is not purely deductive, but Gelman is right to see it as about as close as one can get, in statistics, to a deductive falsification of a model. But where does that leave him as a Jaynesian? Perhaps he’s not one of the ones in Paul’s Jaynes/Bayesian audience who is laughing, but is rather shaking his head?”

## PhilStatLaw: Reference Manual on Scientific Evidence (3d ed) on Statistical Significance (Schachtman)

**Memory Lane: One Year Ago on ****error statistics.com**

**A quick perusal of the “Manual” on Nathan Schachtman’s legal blog shows it to be chock full of revealing points of contemporary legal statistical philosophy. The following are some excerpts, read the full blog here. I make two comments at the end.**

July 8th, 2012

Nathan Schachtman

How does the new Reference Manual on Scientific Evidence (RMSE3d 2011) treat statistical significance? Inconsistently and at times incoherently.

Professor Berger’s IntroductionIn her introductory chapter, the late Professor Margaret A. Berger raises the question of the role statistical significance should play in evaluating a study’s support for causal conclusions:

“What role should statistical significance play in assessing the value of a study? Epidemiological studies that are not conclusive but show some increased risk do not prove a lack of causation. Some courts find that they therefore have some probative value, 62 at least in proving general causation. 63”

Margaret A. Berger, “The Admissibility of Expert Testimony,” in RMSE3d 11, 24 (2011).

This seems rather backwards. Berger’s suggestion that inconclusive studies do not prove lack of causation seems nothing more than a tautology. And how can that tautology support the claim that inconclusive studies “therefore ” have some probative value? This is a fairly obvious logical invalid argument, or perhaps a passage badly in need of an editor.

…………

Chapter on StatisticsThe RMSE’s chapter on statistics is relatively free of value judgments about significance probability, and, therefore, a great improvement upon Berger’s introduction. The authors carefully describe significance probability and p-values, and explain:

“Small p-values argue against the null hypothesis. Statistical significance is determined by reference to the p-value; significance testing (also called hypothesis testing) is the technique for computing p-values and determining statistical significance.”

David H. Kaye and David A. Freedman, “Reference Guide on Statistics,” in RMSE3d 211, 241 (3ed 2011). Although the chapter confuses and conflates Fisher’s interpretation of p-values with Neyman’s conceptualization of hypothesis testing as a dichotomous decision procedure, this treatment is unfortunately fairly standard in introductory textbooks.

Kaye and Freedman, however, do offer some important qualifications to the untoward consequences of using significance testing as a dichotomous outcome:

“Artifacts from multiple testing are commonplace. Because research that fails to uncover significance often is not published, reviews of the literature may produce an unduly large number of studies finding statistical significance.111 Even a single researcher may examine so many different relationships that a few will achieve statistical significance by mere happenstance. Almost any large data set—even pages from a table of random digits—will contain some unusual pattern that can be uncovered by diligent search. Having detected the pattern, the analyst can perform a statistical test for it, blandly ignoring the search effort. Statistical significance is bound to follow.

There are statistical methods for dealing with multiple looks at the data, which permit the calculation of meaningful p-values in certain cases.112 However, no general solution is available, and the existing methods would be of little help in the typical case where analysts have tested and rejected a variety of models before arriving at the one considered the most satisfactory (see infra Section V on regression models). In these situations, courts should not be overly impressed with claims that estimates are significant. Instead, they should be asking how analysts developed their models.113 ”

Id. at 256 -57. This qualification is omitted from the overlapping discussion in the chapter on epidemiology, where it is very much needed. Continue reading

## Update on Higgs data analysis: statistical flukes (part 1)

I am always impressed at how researchers flout the popular philosophical conception of scientists as being happy as clams when their theories are ‘born out’ by data, while terribly dismayed to find any anomalies that might demand “revolutionary science” (as Kuhn famously called it). Scientists, says Kuhn, are really only trained to do “normal science”—science within a paradigm of hard core theories that are almost never, ever to be questioned.[i] It is rather the opposite, and the reports out last week updating the Higgs data analysis reflect this yen to uncover radical anomalies from which scientists can push the boundaries of knowledge. While it is welcome news that the new data do not invalidate the earlier inference of a Higgs-like particle, many scientists are somewhat dismayed to learn that it appears to be quite in keeping with the Standard Model. In a March 15 article in National Geographic News:

Although a full picture of the Higgs boson has yet to emerge, some physicists have expressed disappointment that the new particle is so far behaving exactly as theory predicts. Continue reading

## 13 well-worn criticisms of significance tests (and how to avoid them)

2013 is right around the corner, and here are 13 well-known criticisms of statistical significance tests, and how they are addressed within the error statistical philosophy, as discussed in Mayo, D. G. and Spanos, A. (2011) “Error Statistics“.

- (#1) error statistical tools forbid using any background knowledge.
- (#2) All statistically signiﬁcant results are treated the same.
- (#3) The p-value does not tell us how large a discrepancy is found.
- (#4) With large enough sample size even a trivially small discrepancy from the null can be detected.
- (#5) Whether there is a statistically signiﬁcant diﬀerence from the null depends on which is the null and which is the alternative.
- (#6) Statistically insigniﬁcant results are taken as evidence that the null hypothesis is true.
- (#7) Error probabilities are misinterpreted as posterior probabilities.
- (#8) Error statistical tests are justiﬁed only in cases where there is a very long (if not inﬁnite) series of repetitions of the same experiment.
- (#9) Specifying statistical tests is too arbitrary.
- (#10) We should be doing conﬁdence interval estimation rather than signiﬁcance tests.
- (#11) Error statistical methods take into account the intentions of the scientists analyzing the data.
- (#12) All models are false anyway.
- (#13) Testing assumptions involves illicit data-mining.

You can read how we avoid them in the full paper here.

*Mayo, D. G. and Spanos, A. (2011) “Error Statistics” in Philosophy of Statistics , Handbook of Philosophy of Science Volume 7 Philosophy of Statistics, (General editors: Dov M. Gabbay, Paul Thagard and John Woods; Volume eds. Prasanta S. Bandyopadhyay and Malcolm R. Forster.) Elsevier: 1-46.*

## “Bad statistics”: crime or free speech?

Hunting for “nominally” significant differences, trying different subgroups and multiple endpoints, can result in a much higher probability of erroneously inferring evidence of a risk or benefit than the nominal p-value, even in randomized controlled trials. This was an issue that arose in looking at RCTs in development economics (an area introduced to me by Nancy Cartwright), as at our symposium at the Philosophy of Science Association last month[i][ii]. Reporting the results of hunting and dredging in just the same way as if the relevant claims were predesignated can lead to misleading reports of actual significance levels.[iii]

Still, even if reporting spurious statistical results is considered “bad statistics,” is it criminal behavior? I noticed this issue in Nathan Schachtman’s blog over the past couple of days. The case concerns a biotech company, InterMune, and its previous CEO, Dr. Harkonen. Here’s an excerpt from Schachtman’s discussion (part 1). Continue reading

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