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==Incorrect metrics==
As indicated by the well known aphorism, "It is not the heat, it’s the humidity," choosing the right metric is very important.  Bayesians like to clobber the incorrect metric known as p-value, as can be seen by the following table due to Freeman (Freeman PR. The role of p-values in analysing trial results. ''Statistics in Medicine''. 1993 Aug; 12(15-16): 1443-52).
<center>
{|class=wikitable border="1"
|'''Number of Patients<br> Receiving A and B''' || '''Numbers<br> Preferring A:B''' ||  '''Percent<br>Preferring A''' || ''' two-sided<br>p-value'''
|-
|20  ||  15: 5  || 75.00  || 0.04
|-
|  200  || 115: 86  || 57.50  ||0.04
|-
|  2000  || 1046: 954 || 52.30  ||0.04
|-
|2000000 ||&nbsp;1001445: 998555&nbsp;|| 50.07  || 0.04
|}
</center>
The same “statistically significant .04” appears in each row yet the practical significance is wildly different as the sample size varies, indicating that p-value as a metric is deficient.


The choice of an appropriate metric in health care is exceedingly important.  An illustration from the Wall Street Journal of March 31, 2010 shows how misleading the five-year survival rate metric can be.  A letter writer defending the U.S. against the evils of socialized medicine [http://online.wsj.com/public/page/letters.html here] replies to someone who was critical of the U.S. health care system compared to other countries:


For prostate cancer specifically, the rather astounding numbers are 92% in the U.S. versus 51% in the U.K. I am sure that the additional four out of 10 men in the U.K. who will die of prostate cancer find that to be significant, even if Dr. Krock does not.
==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.”
<div align=right>-- Donald Kennedy (former president of Stanford University), ''Academic Duty'', Harvard University Press, 1997, p.17</div>
 
----
 
"Using scientific language and measurement doesn’t prevent a researcher from conducting flawed experiments and drawing wrong conclusions — especially when they confirm preconceptions."
 
<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>


Those “astounding numbers” refer to five-year survival rates.  From [http://www.psychologicalscience.org/journals/pspi/pspi_8_2_article.pdf Gigerenzer] we learn of the misinterpretation common to patients and physicians: reliance on survival rates rather than mortality rates.  The paper begins with former New York City mayor Rudy Giuliani thanking God for being treated for prostate cancer in the capitalist U.S. where his five-year survival chances were 82% as compared to “only 44% under socialized medicine.”  Turns out that “Giuliani’s numbers, however, are meaningless” because in the U.S. prostate cancer is being diagnosed earlier, a lead-time bias, and the cancer is being over diagnosed, that is, a pseudodisease is detected,--“screening-detected abnormalities that meet the pathologic definition of cancer but will never progress to cause symptoms in the patient’s lifetime.”  When it comes to mortality rates, there are “About 26 prostate cancer deaths per 100,000 American men versus 27 per 100,000 in Britain.”  The data “suggests that many American men have been unnecessarily diagnosed (i.e., overdiagnosed) with prostate cancer during the PSA era and have undergone unnecessary surgery and radiation treatment, which often leads to impotence and/or incontinence.”  In a nutshell, “The problem is that there is no relationship between 5-year survival and mortality.”
==In progress==
[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


===Discussion===
[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


1.  The &quot;lead-time bias&quot; is due to screening, i.e., mass testing, which is much more common in the U.S. than in other countries.  Google the recent discussions regarding the efficacy of breast cancer screening in woman below the age of 50.
==Hurricane Maria deaths==
Laura Kapitula sent the following to the Isolated Statisticians e-mail list:


2. Gigarenzer’s article contains other interesting observations regarding relative risk vs. absolute risk.  It also discusses the need to present Bayes theorem in a non-confusing way so that a patient and a doctor can understand the often remarkable numerical difference between Prob(test+|diseased) and Prob(diseased|test+).
:[Why counting casualties after a hurricane is so hard]<br>
:by Jo Craven McGinty, Wall Street Journal, 7 September 2018


==Census errors==
The article is subtitled: Indirect deaths—such as those caused by gaps in medication—can occur months after a storm, complicating tallies
[http://freakonomics.blogs.nytimes.com/2010/02/02/can-you-trust-census-data/ Can you trust Census data?]<br>
by Justin Wolfers, New York Times, Freakonomics blog, 2 February 2010<br>
   
   
[http://online.wsj.com/article/SB20001424052748704533204575047241321811712.html Census Bureau obscured personal data—Too well, some say]<br>
Laura noted that
by Carl Bialik, Numbers Guy column, Wall Street Journal, 6 February 2010<br>
:[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
 
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.
 
President Trump has asserted that the actual number is
[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]
 
:[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
 
----
[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
 
[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]
 
[http://www.riskliteracy.org/]
-----
[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>
 
<math>P(E)  = {n \choose k} p^k (1-p)^{ n-k}</math>


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


These stories describe problems with the Census Bureau' [http://usa.ipums.org/usa/ IPUMS] (Integrated Public Use Mircodata Series) data, which provides subsamples of Census data to outside researchers.  In order to protect the privacy of citizens, the records are altered slightly.  For example, incomes may be rounded and ages may be tweaked by a small amount.  Ideally this would make it impossible to identify any particular individual, while at the same time not introducing any important distortion into the overall demographic profile.
<math>\hat{p}(H|HH)</math>


Unfortunately, it appears that serious distortions have resulted.  A recent [http://www.nber.org/papers/w15703.pdf NBER working paper] details the problems, which seem to be especially pronounced in data for ages 65 above.  The Freakonomics post reproduces the following graph from the paper
==Accidental insights==


<center>http://graphics8.nytimes.com/images/2010/02/02/opinion/Census-Chart/blogSpan.jpg</center>
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.
<center>[[File:BrokenTile.jpg | 400px]]</center>
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.”


showing how total population estimates based on the microdata diverge from the actual Census counts for older Americans. Breakdowns within particular age groups are also distorted. For example, The Wall Street Journal article has an [http://online.wsj.com/article/SB10001424052748704533204575047241321811712.html#project%3Dnumbguy0204%26articleTabs%3Dinteractive interactive graphic], revealing how data released in 2006 showed inexplicable fluctuations from one age year to the next in the percentage of women who were married (those errors were corrected in 2007).
<center>[[File:Montante_plot2.png | 500px]]</center>
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.
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.


As Bialik notes, &quot;The anomalies highlight how vulnerable research is to potential problems with underlying numbers supplied by other sources, even when the source is the government. And they illustrate how tricky it can be to balance privacy with accuracy.&quot;
Submitted by William Montante


Submitted by Bill Peterson
----

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

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