Difference between revisions of "Sandbox"

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==Making a table==
 
 
 
 
 
 
 
  
  
The following Forsooth is from the June 2009 RSS News.
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==Forsooth==
  
<center>http://www.dartmouth.edu/~chance/forwiki/poll.gif</center>
+
==Quotations==
 +
“We know that people tend to overestimate the frequency of well-publicized, spectacular
 +
events compared with more commonplace ones; this is a well-understood phenomenon in
 +
the literature of risk assessment and leads to the truism that when statistics plays folklore,
 +
folklore always wins in a rout.”
 +
<div align=right>-- Donald Kennedy (former president of Stanford University), ''Academic Duty'', Harvard University Press, 1997, p.17</div>
  
Infuse and Kuklo II
+
----
  
[http://plus.maths.org/issue9/features/benford/ This web site provides a wonderful pun] regarding Benford’s Law, “Looking out for number one.”  The authors write:
+
"Using scientific language and measurement doesn’t prevent a researcher from conducting flawed experiments and drawing wrong conclusions — especially when they confirm preconceptions."
“Go and look up some numbers. A whole variety of naturally-occurring numbers will do. Try the lengths of some of the world's rivers, or the cost of gas bills in Moldova; try the population sizes in Peruvian provinces, or even the figures in Bill Clinton's tax return. Then, when you have a sample of numbers, look at their first digits (ignoring any leading zeroes). Count how many numbers begin with 1, how many begin with 2, how many begin with 3, and so on - what do you find?
 
You might expect that there would be roughly the same number of numbers beginning with each different digit: that the proportion of numbers beginning with any given digit would be roughly 1/9. However, in very many cases, you'd be wrong!”
 
  
Instead, we get
+
<div align=right>-- Blaise Agüera y Arcas, Margaret Mitchell and Alexander Todoorov, quoted in: The racist history behind facial recognition, ''New York Times'', 10 July 2019</div>
  
<center>http://www.dartmouth.edu/~chance/forwiki/LeedingDidgit.gif</center>
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==In progress==
<center> Figure 1: The proportional frequency of each leading digit predicted by Benford's Law.</center>
+
[https://www.nytimes.com/2018/11/07/magazine/placebo-effect-medicine.html What if the Placebo Effect Isn’t a Trick?]<br>
 +
by Gary Greenberg, ''New York Times Magazine'', 7 November 2018
  
Should somebody try “to falsify, say, their tax return then invariably they will have to invent some data. When trying to do this, the tendency is for people to use too many numbers starting with digits in the mid range, 5,6,7 and not enough numbers starting with 1. This violation of Benford's Law sets the alarm bells ringing.”
+
[https://www.nytimes.com/2019/07/17/opinion/pretrial-ai.html The Problems With Risk Assessment Tools]<br>
 +
by Chelsea Barabas, Karthik Dinakar and Colin Doyle, ''New York Times'', 17 July 2019
  
It is a pity that unlike for accounting data, there is no forensic counterpart to Benford’s Law for determining when a journal article is entirely fraudulent.  As stated in [http://chance.dartmouth.edu/chancewiki/index.php/Chance_News_48#Infuse_and_Kuklo Infuse and Kuklo] you won’t be able to read [on the JBJS website] the fraudulent article, “Recombinant human morphogenetic protein-2 for type grade III open segmental tibial fractures from combat injuries in Iraq” by Timothy Kuklo, et al, which appeared in the JBJS in August, 2008 because it has been retracted.  However, [http://graphics8.nytimes.com/packages/pdf/business/20090513kuklo-journal-article.pdf it is available here.]  The immediate impression is that as far as statistics is concerned, it looks like any other article in the health field.
+
==Hurricane Maria deaths==
 +
Laura Kapitula sent the following to the Isolated Statisticians e-mail list:
  
The important statistics appear in Tables 1 and III
+
:[Why counting casualties after a hurricane is so hard]<br>
 
+
:by Jo Craven McGinty, Wall Street Journal, 7 September 2018
<center>http://www.dartmouth.edu/~chance/forwiki/TableoneKuklo.jpg </center>
 
<center>http://www.dartmouth.edu/~chance/forwiki/TablethreeKuklo.jpg </center>
 
  
 +
The article is subtitled: Indirect deaths—such as those caused by gaps in medication—can occur months after a storm, complicating tallies
 
   
 
   
Note that there is no claim that everyone in Group 2 (the group using Infuse) did well or that everyone in Group 1 fared poorly. Further, as in legitimate studies, there are patients who were not included because of an additional problem (head injury) or were lost to follow up. The data is there for reviewers and others to do the calculations which in this paper are the difference in proportions, a standard statistical technique.  Small but not immodest p-values indicate that statistical significance is obtained; detailed discussion about the fractures indicates that practical significance is also realized.  The bibliography has 39 entries, only one of which has Kuklo as the author; the same entry includes one of the ghost co-authors in the retracted paper.  Nothing statistically or otherwise suspicious whatsoever.
+
Laura noted that  
 +
:[https://www.washingtonpost.com/news/fact-checker/wp/2018/06/02/did-4645-people-die-in-hurricane-maria-nope/?utm_term=.0a5e6e48bf11 Did 4,645 people die in Hurricane Maria? Nope.]<br>
 +
:by Glenn Kessler, ''Washington Post'', 1 June 2018
  
Freudian psychology is currently out of favor but Freud's notion of a [http://www.thetruthseeker.co.uk/article.asp?ID=1602 death wish] still seems plausibleHow else to explain the pushing of the envelope past falsification of data, denial of connection to the manufacturers of Infuse, and forging of not one, not two but four ghost authors?  The aptly titled 1995 book by Feinberg and Tarrant, ''Why Smart People Do Dumb Things,'' attributes such behavior to what they deem “the four pillars of stupidity”: hubris, arrogance, narcissism and unconscious need to fail.  The first three are overwhelmingly obvious, but the last named cause sounds deeply Freudian.
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The source of the 4645 figure is a [https://www.nejm.org/doi/full/10.1056/NEJMsa1803972 NEJM article].  Point estimate, the 95% confidence interval ran from 793 to 8498.
  
[http://www.nytimes.com/2009/06/06/business/06surgeon.html A New York Times update] appears on June 5, 2009 and shows how Kuklo forged the signatures; “He used a distinctively different handwriting style for each of them, a form he submitted to the British journal shows.”
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President Trump has asserted that the actual number is
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[https://twitter.com/realDonaldTrump/status/1040217897703026689 6 to 18].
 +
The ''Post'' article notes that Puerto Rican official had asked researchers at George Washington University to do an estimate of the death toll.  That work is not complete.
 +
[https://prstudy.publichealth.gwu.edu/ George Washington University study]
  
http://www.dartmouth.edu/~chance/forwiki/Kuklosignatures.jpg <br>
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:[https://fivethirtyeight.com/features/we-still-dont-know-how-many-people-died-because-of-katrina/?ex_cid=538twitter We sttill don’t know how many people died because of Katrina]<br>
 +
:by Carl Bialik, FiveThirtyEight, 26 August 2015
  
Dr. Timothy R. Kuklo and copies of the signatures of other Army doctors on his study that authorities say he forged.
+
----
 +
[https://www.nytimes.com/2018/09/11/climate/hurricane-evacuation-path-forecasts.html These 3 Hurricane Misconceptions Can Be Dangerous. Scientists Want to Clear Them Up.]<br>
 +
[https://journals.ametsoc.org/doi/abs/10.1175/BAMS-88-5-651 Misinterpretations of the “Cone of Uncertainty” in Florida during the 2004 Hurricane Season]<br>
 +
[https://www.nhc.noaa.gov/aboutcone.shtml Definition of the NHC Track Forecast Cone]
 +
----
 +
[https://www.popsci.com/moderate-drinking-benefits-risks Remember when a glass of wine a day was good for you? Here's why that changed.]
 +
''Popular Science'', 10 September 2018
 +
----
 +
[https://www.economist.com/united-states/2018/08/30/googling-the-news Googling the news]<br>
 +
''Economist'', 1 September 2018
  
A putative co-author “suspected that Dr. Kuklo had fabricated the comparison groups, because many soldiers had received both Infuse and a bone graft not one or the other.”  This person said, “It was like he was comparing apples and oranges.  But there weren’t any apples or oranges to compare.”
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[https://www.cnbc.com/2018/09/17/google-tests-changes-to-its-search-algorithm-how-search-works.html We sat in on an internal Google meeting where they talked about changing the search algorithm here's what we learned]
 +
----
 +
[http://www.wyso.org/post/stats-stories-reading-writing-and-risk-literacy Reading , Writing and Risk Literacy]
  
Returning to the statistical aspect of the paper, Table III says 19 of 67 (28%) in Group 1 were patients who had further surgery while 5 of 62 (8%) in Group 2 (Infuse group) had further surgery.  Presumably, via a chi-square test, the p-value is listed as .003. Minitab produces the same numerical result of .003 via the Fisher exact test:
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[http://www.riskliteracy.org/]
 +
-----
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[https://twitter.com/i/moments/1025000711539572737?cn=ZmxleGlibGVfcmVjc18y&refsrc=email Today is the deadliest day of the year for car wrecks in the U.S.]
  
 +
==Some math doodles==
 +
<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>
  
Sample   X    N    Sample p<br>
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<math>P(E)   = {n \choose k} p^k (1-p)^{ n-k}</math>
1       5    62    0.080645<br>
 
2      19    67    0.283582<br>
 
  
 +
<math>\hat{p}(H|H)</math>
  
Difference = p (1) - p (2)<br>
+
<math>\hat{p}(H|HH)</math>
Estimate for difference:  -0.202937<br>
 
95% CI for difference:  (-0.330382, -0.0754923)<br>
 
Test for difference = 0 (vs not = 0):  Z = -3.12  P-Value = 0.002<br>
 
  
Fisher's exact test: P-Value = 0.003
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==Accidental insights==
  
Some numerical discrepancies arise, however, for Table ITable I says 51 of 67 (76%) in Group 1 had a successful “union” while 57 of 62 (92%) in Group 2 (Infuse group) had a successful unionPresumably, via a chi-square test, the p-value is listed as .015.  Minitab produces the following indicating that because of the small sample sizes, the Fisher exact test yields .017 instead:
+
My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end.  I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamicsBut, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.
  
Sample  X        N    Sample p<br>
+
While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash.
1      57      62    0.919355<br>
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<center>[[File:BrokenTile.jpg | 400px]]</center>
2      51      67    0.761194<br>
+
As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.”  Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.
  
 +
<center>
 +
{| class="wikitable"
 +
|-
 +
! Piece !! Sq. Inches !! % of Total
 +
|-
 +
| 1 || 43.25 || 31.9%
 +
|-
 +
| 2 || 35.25 ||26.0%
 +
|-
 +
|  3 || 23.25 || 17.2%
 +
|-
 +
| 4 || 14.10 || 10.4%
 +
|-
 +
| 5 || 7.10 || 5.2%
 +
|-
 +
| 6 || 4.70 || 3.5%
 +
|-
 +
| 7 || 3.60 || 2.7%
 +
|-
 +
| 8 || 3.03 || 2.2%
 +
|-
 +
| 9 || 0.66 || 0.5%
 +
|-
 +
| 10 || 0.61 || 0.5%
 +
|}
 +
</center>
 +
<center>[[File:Montante_plot1.png | 500px]]</center>
 +
The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line.  I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect?  What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head:
 +
“On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use” and “Chance favors only the prepared mind.”
  
Difference = p (1) - p (2)<br>
+
<center>[[File:Montante_plot2.png | 500px]]</center>
Estimate for difference: 0.158161<br>
+
95% CI for difference:  (0.0356210, 0.280701)<br>
+
My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from ''Nature News'' on research by Hans Herrmann, et. al. [http://www.nature.com/news/2004/040227/full/news040223-11.html Shattered eggs reveal secrets of explosions]As described there, researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions.
Test for difference = 0 (vs not = 0): Z = 2.53  P-Value = 0.011<br>
+
Bill also provided a link to [http://cran.r-project.org/web/packages/poweRlaw/vignettes/poweRlaw.pdf a vignette from CRAN] describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.
 
 
Fisher's exact test: P-Value = 0.017
 
 
 
Table I also says 10 of 67 (14%) in Group 1 had post-operative infections while 2 of 62 (3.2%) in Group 2 (Infuse group) had post-operative infectionsPresumably, via a chi-square test, the p-value is listed as .001. Minitab produces the following quite different p-value of .032:
 
 
 
Sample  X      N    Sample p<br>
 
1      10      67    0.149254<br>
 
2        2      62    0.032258<br>
 
 
 
 
 
Difference = p (1) - p (2)<br>
 
Estimate for difference:  0.116996<br>
 
95% CI for difference:  (0.0210037, 0.212988)<br>
 
Test for difference = 0 (vs not = 0):  Z = 2.39  P-Value = 0.017<br>
 
  
Fisher's exact test: P-Value = 0.032
+
Submitted by William Montante
  
However, these discrepancies are hardly in the Benford class.  They may merely indicate what happens when a non-statistician medical doctor acts alone.
+
----

Latest revision as of 20:58, 17 July 2019


Forsooth

Quotations

“We know that people tend to overestimate the frequency of well-publicized, spectacular events compared with more commonplace ones; this is a well-understood phenomenon in the literature of risk assessment and leads to the truism that when statistics plays folklore, folklore always wins in a rout.”

-- Donald Kennedy (former president of Stanford University), Academic Duty, Harvard University Press, 1997, p.17

"Using scientific language and measurement doesn’t prevent a researcher from conducting flawed experiments and drawing wrong conclusions — especially when they confirm preconceptions."

-- Blaise Agüera y Arcas, Margaret Mitchell and Alexander Todoorov, quoted in: The racist history behind facial recognition, New York Times, 10 July 2019

In progress

What if the Placebo Effect Isn’t a Trick?
by Gary Greenberg, New York Times Magazine, 7 November 2018

The Problems With Risk Assessment Tools
by Chelsea Barabas, Karthik Dinakar and Colin Doyle, New York Times, 17 July 2019

Hurricane Maria deaths

Laura Kapitula sent the following to the Isolated Statisticians e-mail list:

[Why counting casualties after a hurricane is so hard]
by Jo Craven McGinty, Wall Street Journal, 7 September 2018

The article is subtitled: Indirect deaths—such as those caused by gaps in medication—can occur months after a storm, complicating tallies

Laura noted that

Did 4,645 people die in Hurricane Maria? Nope.
by Glenn Kessler, Washington Post, 1 June 2018

The source of the 4645 figure is a NEJM article. Point estimate, the 95% confidence interval ran from 793 to 8498.

President Trump has asserted that the actual number is 6 to 18. The Post article notes that Puerto Rican official had asked researchers at George Washington University to do an estimate of the death toll. That work is not complete. George Washington University study

We sttill don’t know how many people died because of Katrina
by Carl Bialik, FiveThirtyEight, 26 August 2015

These 3 Hurricane Misconceptions Can Be Dangerous. Scientists Want to Clear Them Up.
Misinterpretations of the “Cone of Uncertainty” in Florida during the 2004 Hurricane Season
Definition of the NHC Track Forecast Cone


Remember when a glass of wine a day was good for you? Here's why that changed. Popular Science, 10 September 2018


Googling the news
Economist, 1 September 2018

We sat in on an internal Google meeting where they talked about changing the search algorithm — here's what we learned


Reading , Writing and Risk Literacy

[1]


Today is the deadliest day of the year for car wrecks in the U.S.

Some math doodles

<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>

<math>P(E) = {n \choose k} p^k (1-p)^{ n-k}</math>

<math>\hat{p}(H|H)</math>

<math>\hat{p}(H|HH)</math>

Accidental insights

My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end. I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics. But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.

While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash.

BrokenTile.jpg

As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.” Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.

Piece Sq. Inches % of Total
1 43.25 31.9%
2 35.25 26.0%
3 23.25 17.2%
4 14.10 10.4%
5 7.10 5.2%
6 4.70 3.5%
7 3.60 2.7%
8 3.03 2.2%
9 0.66 0.5%
10 0.61 0.5%
Montante plot1.png

The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line. I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect? What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head: “On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use” and “Chance favors only the prepared mind.”

Montante plot2.png

My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from Nature News on research by Hans Herrmann, et. al. Shattered eggs reveal secrets of explosions. As described there, researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. Bill also provided a link to a vignette from CRAN describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.

Submitted by William Montante