Author Archives: Mayo

Cox’s (1958) Chestnut: You should not get credit (or blame) for something you didn’t do

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Just as you keep up your physical exercise during the pandemic (sure), you want to keep up with mental gymnastics too. With that goal in mind, and given we’re just a few days from the New Year (and given especially my promised presentation for January 7), here’s one of the two simple examples that will limber you up for the puzzle to ensue. It’s the famous weighing machine example from Sir David Cox (1958)[1]. It is one of the “chestnuts” in the museum exhibits of “chestnuts and howlers” in Excursion 3 (Tour II) of my book Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (SIST, 2018). So block everything else out for a few minutes and consider 3 pages from SIST …  Continue reading

Categories: Birnbaum, Statistical Inference as Severe Testing, strong likelihood principle | 4 Comments

Next Phil Stat Forum: January 7: D. Mayo: Putting the Brakes on the Breakthrough (or “How I used simple logic to uncover a flaw in …..statistical foundations”)

The fourth meeting of our New Phil Stat Forum*:

The Statistics Wars
and Their Casualties

January 7, 16:00 – 17:30  (London time)
11 am-12:30 pm (New York, ET)**
**note time modification and date change

Putting the Brakes on the Breakthrough,

or “How I used simple logic to uncover a flaw in a controversial 60-year old ‘theorem’ in statistical foundations” 

Deborah G. Mayo

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HOW TO JOIN US: SEE THIS LINK

ABSTRACT: An essential component of inference based on familiar frequentist (error statistical) notions p-values, statistical significance and confidence levels, is the relevant sampling distribution (hence the term sampling theory). This results in violations of a principle known as the strong likelihood principle (SLP), or just the likelihood principle (LP), which says, in effect, that outcomes other than those observed are irrelevant for inferences within a statistical model. Now Allan Birnbaum was a frequentist (error statistician), but he found himself in a predicament: He seemed to have shown that the LP follows from uncontroversial frequentist principles! Bayesians, such as Savage, heralded his result as a “breakthrough in statistics”! But there’s a flaw in the “proof”, and that’s what I aim to show in my presentation by means of 3 simple examples:

  • Example 1: Trying and Trying Again
  • Example 2: Two instruments with different precisions
    (you shouldn’t get credit/blame for something you didn’t do)
  • The Breakthrough: Don’t Birnbaumize that data my friend

As in the last 9 years, I will post an imaginary dialogue with Allan Birnbaum at the stroke of midnight, New Year’s Eve, and this will be relevant for the talk.

The Phil Stat Forum schedule is at the Phil-Stat-Wars.com blog 

 
 
 
Categories: Birnbaum, Birnbaum Brakes, Likelihood Principle | 1 Comment

The Statistics Debate (NISS) in Transcript Form

I constructed, together with Jean Miller, a transcript from the October 15 Statistics Debate (with me, J. Berger and D. Trafimow and moderator D. Jeske), sponsored by NISS. It’s so much easier to access the material this way rather than listening to it on the video. Using this link, you can see the words and hear the video at the same time, as well as pause and jump around. Below, I’ve pasted our responses to Question #1. Have fun and please share your comments.

Dan Jeske: [QUESTION 1] Given the issues surrounding the misuses and abuse of p values, do you think they should continue to be used or not? Why or why not?

Deborah Mayo  03:46

Thank you so much. And thank you for inviting me, I’m very pleased to be here. Yes, I say we should continue to use p values and statistical significance tests. Uses of p values are really just a piece in a rich set of tools intended to assess and control the probabilities of misleading interpretations of data, i.e., error probabilities. They’re the first line of defense against being fooled by randomness as Yoav Benjamini puts it. If even larger, or more extreme effects than you observed are frequently brought about by chance variability alone, i.e., p value not small, clearly you don’t have evidence of incompatibility with the mere chance hypothesis. It’s very straightforward reasoning. Even those who criticize p values you’ll notice will employ them, at least if they care to check their assumptions of their models. And this includes well known Bayesian such as George Box, Andrew Gelman, and Jim Berger. Critics of p values often allege it’s too easy to obtain small p values. But notice the whole replication crisis is about how difficult it is to get small p values with preregistered hypotheses. This shows the problem isn’t p values, but those selection effects and data dredging. However, the same data drenched hypothesis can occur in other methods, likelihood ratios, Bayes factors, Bayesian updating, except that now we lose the direct grounds to criticize inferences for flouting error statistical control. The introduction of prior probabilities, which may also be data dependent, offers further researcher flexibility. Those who reject p values are saying we should reject the method because it can be used badly. And that’s a bad argument. We should reject misuses of p values. But there’s a danger of blindly substituting alternative tools that throw out the error control baby with the bad statistics bathwater.

Dan Jeske  05:58

Thank you, Deborah, Jim, would you like to comment on Deborah’s remarks and offer your own?

Jim Berger  06:06

Okay, yes. Well, I certainly agree with much of what Deborah said, after all, a p value is simply a statistic. And it’s an interesting statistic that does have many legitimate uses, when properly calibrated. And Deborah mentioned one such case is model checking where Bayesians freely use some version of p values for model checking. You know, on the other hand, that one interprets this question, should they continue to be used in the same way that they’re used today? Then my, my answer would be somewhat different. I think p values are commonly misinterpreted today, especially when when they’re used to test a sharp null hypothesis. For instance, of a p value of .05, is commonly interpreted as by many is indicating the evidence is 20 to one in favor of the alternative hypothesis. And that just that just isn’t true. You can show for instance, that if I’m testing with a normal mean of zero versus nonzero, the odds of the alternative hypothesis to the null hypothesis can at most be seven to one. And that’s just a probabilistic fact, doesn’t involve priors or anything. It just is, is a is an answer covering all probability. And so that 20 to one cannot be if it’s, if it’s, if a p value of .05 is interpreted as 20 to one, it’s just, it’s just being interpreted wrongly, and the wrong conclusions are being reached. I’m reminded of an interesting paper that was published some time ago now, which was reporting on a survey that was designed to determine whether clinical practitioners understood what a p value was. The results of the survey were published and were not surprising. Most clinical practitioners interpreted the p value as something like a p value of .05 as something like 20 to one odds against the null hypothesis, which again, is incorrect. The fascinating aspect of the paper is that the authors also got it wrong. Deborah pointed out that the p value is the probability under the null hypothesis of the data or something more extreme. The author’s stated that the correct answer was the p value is the probability of the data under the null hypothesis, they forgot the more extreme. So, I love this article, because the scientists who set out to show that their colleagues did not understand the meaning of p values themselves did not understand the meaning of p values. 

Dan Jeske  08:42

David?

David Trafimow  08:44

Okay. Yeah, Um, like Deborah and Jim, I’m delighted to be here. Thanks for the invitation. Um and I partly agree with what both Deborah and Jim said, um, it’s certainly true that people misuse p values. So, I agree with that. However, I think p values are more problematic than the other speakers have mentioned. And here’s here’s the problem for me. We keep talking about p values relative to hypotheses, but that’s not really true. P values are relative to hypotheses plus additional assumptions. So, if we call, if we use the term model to describe the null hypothesis, plus additional assumptions, then p values are based on models, not on hypotheses, or only partly on hypotheses. Now, here’s the thing. What are these other assumptions? An example would be random selection from the population, an assumption that is not true in any one of the thousands of papers I’ve read in psychology. And there are other assumptions, a lack of systematic error, linearity, and then we can go on and on, people have even published taxonomies of the assumptions because there are so many of them. See, it’s tantamount to impossible that the model is correct, which means that the model is wrong. And so, what you’re in essence doing then, is you’re using the p value to index evidence against a model that is already known to be wrong. And even the part about indexing evidence is questionable, but I’ll go with it for the moment. But the point is the model was wrong. And so, there’s no point in indexing evidence against it. So given that, I don’t really see that there’s any use for them. There’s, p values don’t tell you how close the model is to being right. P values don’t tell you how valuable the model is. P values pretty much don’t tell you anything that researchers might want to know, unless you misuse them. Anytime you draw a conclusion from a p value, you are guilty of misuse. So, I think the misuse problem is much more subtle than is perhaps obvious at firsthand. So, that’s really all I have to say at the moment.

Dan Jeske  11:28

Thank you. Jim, would you like to follow up?

Jim Berger  11:32

Yes,  so, so,  I certainly agree that that assumptions are often made that are wrong. I won’t say that that’s always the case. I mean, I know many scientific disciplines where I think they do a pretty good job, and work with high energy physicists, and they do a pretty good job of checking their assumptions. Excellent job. And they use p values. It’s something to watch out for. But any statistical analysis, you know, can can run into this problem. If the assumptions are wrong, it’s, it’s going to be wrong.

Dan Jeske  12:09

Deborah…

Deborah Mayo  12:11

Okay. Well, Jim thinks that we should evaluate the p value by looking at the Bayes factor when he does, and he finds that they’re exaggerating, but we really shouldn’t expect agreement on numbers from methods that are evaluating different things. This is like supposing that if we switch from a height to a weight standard, that if we use six feet with the height, we should now require six stone, to use an example from Stephen Senn. On David, I think he’s wrong about the worrying assumptions with using the p value since they have the least assumptions of any other method, which is why people and why even Bayesians will say we need to apply them when we need to test our assumptions. And it’s something that we can do, especially with randomized controlled trials, to get the assumptions to work. The idea that we have to misinterpret p values to have them be relevant, only rests on supposing that we need something other than what the p value provides.

Dan Jeske  13:19

David, would you like to give some final thoughts on this question?

David Trafimow  13:23

Sure. As it is, as far as Jim’s point, and Deborah’s point that we can do things to make the assumptions less wrong. The problem is the model is wrong or it isn’t wrong. Now if the model is close, that doesn’t justify the p value because the p value doesn’t give the closeness of the model. And that’s the, that’s the problem. We’re not we’re not using, for example, a sample mean, to estimate a population mean, in which case, yeah, you wouldn’t expect the sample mean to be exactly right. If it’s close, it’s still useful. The problem is that p values don’t tell you p values aren’t being used to estimate anything. So, if you’re not estimating anything, then you’re stuck with either correct or incorrect, and the answer is always incorrect that, you know, this is especially true in psychology, but I suspect it might even be true in physics. I’m not the physicist that Jim is. So, I can’t say that for sure.

Dan Jeske  14:35

Jim, would you like to offer Final Thoughts?

Jim Berger  14:37

Let me comment on Deborah’s comment about Bayes factors are just a different scale of measurement. My my point was that it seems like people invariably think of p values as something like odds or probability of the null hypothesis, if that’s the way they’re thinking, because that’s the way their minds reason. I believe we should provide them with odds. And so, I try to convert p values into odds or Bayes factors, because I think that’s much more readily understandable by people.

Dan Jeske  15:11

Deborah, you have the final word on this question.

Deborah Mayo  15:13

I do think that we need a proper philosophy of statistics to interpret p values. But I think also that what’s missing in the reject p values movement is a major reason for calling in statistics in science is to give us tools to inquire whether an observed phenomena can be a real effect, or just noise in the data and the P values have intrinsic properties for this task, if used properly, other methods don’t, and to reject them is to jeopardize this important role. As Fisher emphasizes, we need randomized control trials precisely to ensure the validity of statistical significance tests, to reject them because they don’t give us posterior probabilities is illicit. In fact, I think that those claims that we want such posteriors need to show for any way we can actually get them, why. 

You can watch the debate at the NISS website or in this blog post.

You can find the complete audio transcript at this LINK: https://otter.ai/u/hFILxCOjz4QnaGLdzYFdIGxzdsg
[There is a play button at the bottom of the page that allows you to start and stop the recording. You can move about in the transcript/recording by using the pause button and moving the cursor to another place in the dialog and then clicking the play button to hear the recording from that point. (The recording is synced to the cursor.)]

Categories: D. Jeske, D. Trafimow, J. Berger, NISS, statistics debate | 1 Comment

Is it impossible to commit Type I errors in statistical significance tests? (i)

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While immersed in our fast-paced, remote, NISS debate (October 15) with J. Berger and D. Trafimow, I didn’t immediately catch all that was said by my co-debaters (I will shortly post a transcript). We had all opted for no practice. But  looking over the transcript, I was surprised that David Trafimow was indeed saying the answer to the question in my title is yes. Here are some excerpts from his remarks: Continue reading

Categories: D. Trafimow, J. Berger, National Institute of Statistical Sciences (NISS), Testing Assumptions | 29 Comments

S. Senn: “A Vaccine Trial from A to Z” with a Postscript (guest post)

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Stephen Senn
Consultant Statistician
Edinburgh, Scotland

Alpha and Omega (or maybe just Beta)

Well actually, not from A to Z but from AZ. That is to say, the trial I shall consider is the placebo- controlled trial of the Oxford University vaccine for COVID-19 currently being run by AstraZeneca (AZ) under protocol AZD1222 – D8110C00001 and which I considered in a previous blog, Heard Immunity. A summary of the design  features is given in Table 1. The purpose of this blog is to look a little deeper at features of the trial and the way I am going to do so is with the help of geometric representations of the sample space, that is to say the possible results the trial could produce. However, the reader is warned that I am only an amateur in all this. The true professionals are the statisticians at AZ who, together with their life science colleagues in AZ and Oxford, designed the trial. Continue reading

Categories: covid-19, RCTs, Stephen Senn | 14 Comments

Phil Stat Forum: November 19: Stephen Senn, “Randomisation and Control in the Age of Coronavirus?”

For information about the Phil Stat Wars forum and how to join, see this post and this pdf. 


Continue reading

Categories: Error Statistics, randomization | Leave a comment

S. Senn: Testing Times (Guest post)

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Stephen Senn
Consultant Statistician
Edinburgh, Scotland

Testing Times

Screening for attention

There has been much comment on Twitter and other social media about testing for coronavirus and the relationship between a test being positive and the person tested having been infected. Some primitive form of Bayesian reasoning is often used  to justify concern that an apparent positive may actually be falsely so, with specificity and sensitivity taking the roles of likelihoods and prevalence that of a prior distribution. This way of looking at testing dates back at least to a paper of 1959 by Ledley and Lusted[1]. However, as others[2, 3] have pointed out, there is a trap for the unwary in this, in that it is implicitly assumed that specificity and sensitivity are constant values unaffected by prevalence and it is far from obvious that this should be the case. Continue reading

Categories: S. Senn, significance tests, Testing Assumptions | 14 Comments

Souvenir From the NISS Stat Debate for Users of Bayes Factors (& P-Values)

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What would I say is the most important takeaway from last week’s NISS “statistics debate” if you’re using (or contemplating using) Bayes factors (BFs)–of the sort Jim Berger recommends–as replacements for P-values? It is that J. Berger only regards the BFs as appropriate when there’s grounds for a high concentration (or spike) of probability on a sharp null hypothesis,            e.g.,H0: θ = θ0.

Thus, it is crucial to distinguish between precise hypotheses that are just stated for convenience and have no special prior believability, and precise hypotheses which do correspond to a concentration of prior belief. (J. Berger and Delampady 1987, p. 330).

Continue reading

Categories: bayes factors, Berger, P-values, S. Senn | 4 Comments

My Responses (at the P-value debate)

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How did I respond to those 7 burning questions at last week’s (“P-Value”) Statistics Debate? Here’s a fairly close transcript of my (a) general answer, and (b) final remark, for each question–without the in-between responses to Jim and David. The exception is question 5 on Bayes factors, which naturally included Jim in my general answer. 

The questions with the most important consequences, I think, are questions 3 and 5. I’ll explain why I say this in the comments. Please share your thoughts. Continue reading

Categories: bayes factors, P-values, Statistics, statistics debate NISS | 1 Comment

The P-Values Debate

 

 

National Institute of Statistical Sciences (NISS): The Statistics Debate (Video)

Categories: J. Berger, P-values, statistics debate | 14 Comments

The Statistics Debate! (NISS DEBATE, October 15, Noon – 2 pm ET)

October 15, Noon – 2 pm ET (Website)

Where do YOU stand?

Given the issues surrounding the misuses and abuse of p-values, do you think p-values should be used? Continue reading

Categories: Announcement, J. Berger, P-values, Philosophy of Statistics, reproducibility, statistical significance tests, Statistics | Tags: | 9 Comments

CALL FOR PAPERS (Synthese) Recent Issues in Philosophy of Statistics: Evidence, Testing, and Applications

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Call for Papers: Topical Collection in Synthese

Title: Recent Issues in Philosophy of Statistics: Evidence, Testing, and Applications

The deadline for submissions is 1 November, 2020 1 December 2020

Description: Continue reading

Categories: Announcement, CFP, Synthese | Leave a comment

G.A. Barnard’s 105th Birthday: The Bayesian “catch-all” factor: probability vs likelihood

barnard-1979-picture

G. A. Barnard: 23 Sept 1915-30 July, 2002

Yesterday was statistician George Barnard’s 105th birthday. To acknowledge it, I reblog an exchange between Barnard, Savage (and others) on likelihood vs probability. The exchange is from pp 79-84 (of what I call) “The Savage Forum” (Savage, 1962).[i] A portion appears on p. 420 of my Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (2018, CUP). Six other posts on Barnard are linked below, including 2 guest posts, (Senn, Spanos); a play (pertaining to our first meeting), and a letter Barnard wrote to me in 1999.  Continue reading

Categories: Barnard, phil/history of stat, Statistics | 10 Comments

Live Exhibit: Bayes Factors & Those 6 ASA P-value Principles

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Live Exhibit: So what happens if you replace “p-values” with “Bayes Factors” in the 6 principles from the 2016 American Statistical Association (ASA) Statement on P-values? (Remove “or statistical significance” in question 5.)

Does the one positive assertion hold? Are the 5 “don’ts” true? Continue reading

Categories: ASA Guide to P-values, bayes factors | 2 Comments

September 24: Bayes factors from all sides: who’s worried, who’s not, and why (R. Morey)

Information and directions for joining our forum are here.

Continue reading

Categories: Announcement, bayes factors, Error Statistics, Phil Stat Forum, Richard Morey | 1 Comment

All She Wrote (so far): Error Statistics Philosophy: 9 years on

Dear Reader: I began this blog 9 years ago (Sept. 3, 2011)! A double celebration is taking place at the Elbar Room tonight (a smaller one was held earlier in the week), both for the blog and the 2 year anniversary of the physical appearance of my book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars [SIST] (CUP, 2018). A special rush edition made an appearance on Sept 3, 2018 in time for the RSS meeting in Cardiff. If you’re in the neighborhood, stop by for some Elba Grease.

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Many of the discussions in the book were importantly influenced (corrected and improved) by reader’s comments on the blog over the years. I posted several excerpts and mementos from SIST here. I thank readers for their input. Readers should look up the topics in SIST on this blog to check out the comments, and see how ideas were developed, corrected and turned into “excursions” in SIST. Continue reading

Categories: blog contents, Metablog | Leave a comment

5 September, 2018 (w/updates) RSS 2018 – Significance Tests: Rethinking the Controversy

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Day 2, Wed 5th September, 2018:

The 2018 Meeting of the Royal Statistical Society (Cardiff)

11:20 – 13:20

Keynote 4 – Significance Tests: Rethinking the Controversy Assembly Room

Speakers:
Sir David Cox, Nuffield College, Oxford
Deborah Mayo, Virginia Tech
Richard Morey, Cardiff University
Aris Spanos, Virginia Tech

Intermingled in today’s statistical controversies are some long-standing, but unresolved, disagreements on the nature and principles of statistical methods and the roles for probability in statistical inference and modelling. In reaction to the so-called “replication crisis” in the sciences, some reformers suggest significance tests as a major culprit. To understand the ramifications of the proposed reforms, there is a pressing need for a deeper understanding of the source of the problems in the sciences and a balanced critique of the alternative methods being proposed to supplant significance tests. In this session speakers offer perspectives on significance tests from statistical science, econometrics, experimental psychology and philosophy of science. There will be also be panel discussion.

5 Sept. 2018 (taken by A.Spanos)

Continue reading

Categories: Error Statistics | Tags: | Leave a comment

The Physical Reality of My New Book! Here at the RSS Meeting (2 years ago)

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You can find several excerpts and mementos from the book, including whole “tours” (in proofs) updated June 2020 here.

Categories: SIST | Leave a comment

Statistical Crises and Their Casualties–what are they?

What do I mean by “The Statistics Wars and Their Casualties”? It is the title of the workshop I have been organizing with Roman Frigg at the London School of Economics (CPNSS) [1], which was to have happened in June. It is now the title of a forum I am zooming on Phil Stat that I hope you will want to follow. It’s time that I explain and explore some of the key facets I have in mind with this title. Continue reading

Categories: Error Statistics | 4 Comments

New Forum on The Statistics Wars & Their Casualties: August 20, Preregistration (D. Lakens)

I will now hold a monthly remote forum on Phil Stat: The Statistics Wars and Their Casualties–the title of the workshop I had scheduled to hold at the London School of Economics (Centre for Philosophy of Natural and Social Science: CPNSS) on 19-20 June 2020. (See the announcement at the bottom of this blog). I held the graduate seminar in Philosophy (PH500) that was to precede the workshop remotely (from May 21-June 25), and this new forum will be both an extension of that and a linkage to the planned workshop. The issues are too pressing to put off for a future in-person workshop, which I still hope to hold. It will begin with presentations by workshop participants, with lots of discussion. If you want to be part of this monthly forum and engage with us, please go to the information and directions page. The links are now fixed, sorry. (It also includes readings for Aug 20.)  If you are already on our list, you’ll automatically be notified of new meetings. (If you have questions, email me.) Continue reading

Categories: Announcement | Leave a comment

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