## Archive for The American Statistician

## abandoned, one year ago…

Posted in Books, Statistics, University life with tags birthday, p-values, statistical significance, Taylor & Francis, The American Statistician on March 17, 2020 by xi'an## retire statistical significance [follow-up]

Posted in Statistics with tags American Statistical Association, Brain and Neuroscience Advances, Demographic Research, European Journal of Clinical Investigation, Gynecologic & Neonatal Nursing, Journal of Bone and Mineral Research, Journal of Obstetric, Journal of Wildlife Management, National Institute of Statistical Sciences, Nature, Pediatric Anesthesia, Significance, statistical significance, The American Statistician, The New England Journal of Medicine on December 9, 2019 by xi'an*[Here is a brief update sent by my coauthors Valentin, Sander, and Blake on events following the Nature comment “Retire Statistical Significance“.]*

In the eight months since publication of the comment and of the special issue of *The American Statistician*, we are glad to see a rich discussion on internet blogs and in scholarly publications and popular media.Nature

One important indication of change is that since March numerous scientific journals have published editorials or revised their author guidelines. We have selected eight editorials that not only discuss statistics reform but give concrete new guidelines to authors. As you will see, the journals differ in how far they want to go with the reform (all but one of the following links are open access).

1) *The New England Journal of Medicine*, “New Guidelines for Statistical Reporting in the Journal”

2) *Pediatric Anesthesia*, “Embracing uncertainty: The days of statistical significance are numbered”

3) *Journal of Obstetric, Gynecologic & Neonatal Nursing*, “The Push to Move Health Care Science Beyond p < .05“

4) *Brain and Neuroscience Advances*, “Promoting and supporting credibility in neuroscience”

5) *Journal of Wildlife Management*, “Vexing Vocabulary in Submissions to the Journal of Wildlife Management”

6) *Demographic Research*, “P-values, theory, replicability, and rigour”

7) *Journal of Bone and Mineral Research*, “New Guidelines for Data Reporting and Statistical Analysis: Helping Authors With Transparency and Rigor in Research“

8) *Significance*, “The S word … and what to do about it”

Further, some of you took part in a survey by Tom Hardwicke and John Ioannidis that was published in the *European Journal of Clinical Investigation* along with editorials by Andrew Gelman and Deborah Mayo.

We replied with a short commentary in that journal, “Statistical Significance Gives Bias a Free Pass“

And finally, joining with the American Statistical Association (ASA), the National Institute of Statistical Sciences (NISS) in the United States has also taken up the reform issue.

## Galton’s board all askew

Posted in Books, Kids, R with tags Francis Galton, Pascal triangle, Quanta Magazine, quincunx, R, simulated annealing, The American Statistician, uncunx on November 19, 2019 by xi'an**S**ince Galton’s quincunx has fascinated me since the (early) days when I saw a model of it as a teenager in an industry museum near Birmingham, I jumped on the challenge to build an uneven nail version where the probabilities to end up in one of the boxes were not the Binomial ones. For instance, producing a uniform distribution with the maximum number of nails with probability ½ to turn right. And I obviously chose to try simulated annealing to figure out the probabilities, facing as usual the unpleasant task of setting the objective function, calibrating the moves and the temperature schedule. Plus, less usually, a choice of the space where the optimisation takes place, i.e., deciding on a common denominator for the (rational) probabilities. Should it be 2⁸?! Or more (since the solution with two levels also involves 1/3)? Using the functions

evol<-function(P){ Q=matrix(0,7,8) Q[1,1]=P[1,1];Q[1,2]=1-P[1,1] for (i in 2:7){ Q[i,1]=Q[i-1,1]*P[i,1] for (j in 2:i) Q[i,j]=Q[i-1,j-1]*(1-P[i,j-1])+Q[i-1,j]*P[i,j] Q[i,i+1]=Q[i-1,i]*(1-P[i,i]) Q[i,]=Q[i,]/sum(Q[i,])} return(Q)}

and

temper<-function(T=1e3){ bestar=tarP=targ(P<-matrix(1/2,7,7)) temp=.01 while (sum(abs(8*evol(R.01){ for (i in 2:7) R[i,sample(rep(1:i,2),1)]=sample(0:deno,1)/deno if (log(runif(1))/temp<tarP-(tarR<-targ(R))){P=R;tarP=tarR} for (i in 2:7) R[i,1:i]=(P[i,1:i]+P[i,i:1])/2 if (log(runif(1))/temp<tarP-(tarR<-targ(R))){P=R;tarP=tarR} if (runif(1)<1e-4) temp=temp+log(T)/T} return(P)}

I first tried running my simulated annealing code with a target function like

targ<-function(P)(1+.1*sum(!(2*P==1)))*sum(abs(8*evol(P)[7,]-1))

where P is the 7×7 lower triangular matrix of nail probabilities, all with a 2⁸ denominator, reaching

**60**

126 35

107 81 20

104 71 22 0

126 44 26 **69** 14

**61** 123 113 92 91 38

109 **60** 7 19 44 74 50

for 128P. With four entries close to 64, i.e. ½’s. Reducing the denominator to 16 produced once

**8**

12 1

13 11 3

16 7 6 2

14 13 16 15 0

15 15 2 7 7 4

** 8 ** 0 **8** 9 **8** 16 **8
**

as 16P, with five ½’s (8). But none of the solutions had exactly a uniform probability of 1/8 to reach all endpoints. Success (with exact 1/8’s and a denominator of 4) was met with the new target

(1+,1*sum(!(2*P==1)))*(.01+sum(!(8*evol(P)[7,]==1)))

imposing precisely 1/8 on the final line. With a solution with 11 ½’s

**0.5**

1.0 0.0

1.0 0.0 0.0

1.0 **0.5** 1.0 **0.5**

**0.5** **0.5** 1.0 0.0 0.0

1.0 0.0 **0.5** 0.0 **0.5** 0.0

**0.5 0.5 0.5** 1.0 1.0 1.0 **0.5**

and another one with 12 ½’s:

**0.5**

1.0 0.0

1.0 .375 0.0

1.0 1.0 .625 **0.5**

**0.5** **0.5 0.5 0.5** 0.0

1.0 0.0 **0.5 0.5** 0.0 **0.5**

**0.5 ** 1.0 **0.5** 0.0 1.0 **0.5** 0.0

Incidentally, Michael Proschan and my good friend Jeff Rosenthal have an 2009 American Statistician paper on another modification of the quincunx they call the uncunx! Playing a wee bit further with the annealing, and using a denominator of 840 let to a 60P with 13 ½’s out of 28

**30**

60 0

60 1 0

**30 30 30** 0

**30 30 30 30 30**

60 60 60 0 60 0

60 **30** 0 **30 ** **30** 60 **30**

## abandon ship [value]!!!

Posted in Books, Statistics, University life with tags Andrew Gelman, hypothesis testing, Nature, p-values, special issue, Statistical decision theory, statistical significance, The American Statistician, threshold, uncertainty quantification on March 22, 2019 by xi'an**T**he Abandon Statistical Significance paper we wrote with “. A 400 page special issue with 43 papers available on-line and open-source! Food for thought likely to be discussed further here (and elsewhere). The paper and the ideas within have been discussed quite a lot on Andrew’s blog and I will not repeat them here, simply quoting from the conclusion of the paper

In this article, we have proposed to abandon statistical significance and offered recommendations for how this can be implemented in the scientific publication process as well as in statistical decision making more broadly. We reiterate that we have no desire to “ban” p-values or other purely statistical measures. Rather, we believe that such measures should not be thresholded and that, thresholded or not, they should not take priority over the currently subordinate factors.

Which also introduced in a comment by Valentin Amrhein, Sander Greenland, and Blake McShane published in Nature today (and supported by 800+ signatures). Again discussed on Andrew’s blog.

## absurdly unbiased estimators

Posted in Books, Kids, Statistics with tags best unbiased estimator, completeness, conditioning, Erich Lehmann, sufficiency, The American Statistician, UMVUE, unbiased estimation on November 8, 2018 by xi'an

“…there are important classes of problems for which the mathematics forces the existence of such estimators.”

**R**ecently I came through a short paper written by Erich Lehmann for The American Statistician, Estimation with Inadequate Information. He analyses the apparent absurdity of using unbiased estimators or even best unbiased estimators in settings like the Poisson P(λ) observation X producing the (unique) unbiased estimator of exp(-bλ) equal to

which is indeed absurd when b>1. My first reaction to this example is that the question of what is “best” for a single observation is not very meaningful and that adding n independent Poisson observations replaces b with b/n, which gets eventually less than one. But Lehmann argues that the paradox stems from a case of missing information, as for instance in the Poisson example where the above quantity is the probability **P**(T=0) that T=0, when T=X+Y, Y being another unobserved Poisson with parameter (b-1)λ. In a lot of such cases, there is no unbiased estimator at all. When there is any, it must take values outside the (0,1) range, thanks to a lemma shown by Lehmann that the conditional expectation of this estimator given T is either zero or one.

I find the short paper quite interesting in exposing some reasons why the estimators cannot find enough information within the data (often a single point) to achieve an efficient estimation of the targeted function of the parameter, even though the setting may appear rather artificial.

## almost uniform but far from straightforward

Posted in Books, Kids, Statistics with tags counterexample, cross validated, maximum likelihood estimation, order statistics, statistics exam, teaching, The American Statistician, triangular distribution on October 24, 2018 by xi'an**A** question on X validated about a [not exactly trivial] maximum likelihood for a triangular function led me to a fascinating case, as exposed by Olver in 1972 in The American Statistician. When considering an asymmetric triangle distribution on (0,þ), þ being fixed, the MLE for the location of the tip of the triangle is necessarily one of the observations [which was not the case in the original question on X validated ]. And not in an order statistic of rank j that does not stand in the j-th uniform partition of (0,þ). Furthermore there are opportunities for observing several global modes… In the X validated case of the symmetric triangular distribution over (0,θ), with ½θ as tip of the triangle, I could not figure an alternative to the pedestrian solution of looking separately at each of the (n+1) intervals where θ can stand and returning the associated maximum on that interval. Definitely a good (counter-)example about (in)sufficiency for class or exam!