Sandbox: Difference between revisions

From ChanceWiki
Jump to navigation Jump to search
 
(461 intermediate revisions by the same user not shown)
Line 1: Line 1:
==More on the hot hand==
In Chance News 105, the last item was titled [https://www.causeweb.org/wiki/chance/index.php/Chance_News_105#Does_selection_bias_explain_the_.22hot_hand.22.3F Does Selection bias explain the hot hand?].  It described how in their July 6 article, Miller and Sanjurjo assert that a way to determine the probability of a heads following a heads in a fixed sequence, you may calculate the proportion of times a head is followed by a head for each possible sequence and then compute the average proportion, giving each sequence an equal weighting on the grounds that each possible sequence is equally likely to occur.  I agree that each possible sequence is equally likely to occur.  But I assert that it is illegitimate to weight each sequence equally because some sequences have more chances for a head to follow a second head than others. 


Let us assume, as Miller and Sanjurjo do, that we are considering the 14 possible sequences of four flips containing at least one head in the first three flips.  A head is followed by another head in only one of the six sequences (see below) that contain only one head that could be followed by another, making the probability of a head being followed by another 1/6 for this set of six sequences.


:{| class="wikitable" style="text-align:center"
==Forsooth==
|-
 
| TTHT  || Heads follows heads 0 time.
==Quotations==
|-
“We know that people tend to overestimate the frequency of well-publicized, spectacular
| THTT  || Heads follows heads 0 times
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,
| HTTT  || Heads follows heads 0 times
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>
| TTHH  || Heads follows heads 1 time
|-
| THTH  || Heads follows heads 0 times
|-
| HTTH  || Heads follows heads 0 times
|}


A head is followed by another head six times in the six sequences (see below) that contain two heads that could be followed by another head, making the probability of a head being followed by another 6/12 = 1/2 for this set of six sequences.
----


:{| class="wikitable" style="text-align:center"
"Using scientific language and measurement doesn’t prevent a researcher from conducting flawed experiments and drawing wrong conclusions — especially when they confirm preconceptions."
|-
| THHT  || Heads follows heads 1 time
|-
| HTHT  || Heads follows heads 0 times
|-
| HHTT  || Heads follows heads 1 time
|-
| THHH  || Heads follows heads 2 times
|-
| HTHH  || Heads follows heads 1 time
|-
| HHTH  || Heads follows heads 1 time
|}


A head is followed by another head five times in the six sequences (see below) that contain three heads that could be followed by another head, making the probability of a head being followed by another 5/6 this set of two sequences.
<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>


:{| class="wikitable" style="text-align:center"
==In progress==
|-
[https://www.nytimes.com/2018/11/07/magazine/placebo-effect-medicine.html What if the Placebo Effect Isn’t a Trick?]<br>
| HHHT  || Heads follows heads 2 times
by Gary Greenberg, ''New York Times Magazine'', 7 November 2018
|-
| HHHH || Heads follows heads 3 times
|}


An unweighted average of the 14 sequences gives
[https://www.nytimes.com/2019/07/17/opinion/pretrial-ai.html The Problems With Risk Assessment Tools]<br>
<center>
by Chelsea Barabas, Karthik Dinakar and Colin Doyle, ''New York Times'', 17 July 2019
[(6 &times; 1/6) + (6 &times; 1/2) + (2 &times; 5/6)] / 14 = [17/3] / 14 = 0.405,
</center>


which is what Miller and Sanjurjo report.
==Hurricane Maria deaths==
A weighted average of the 14 sequences gives
Laura Kapitula sent the following to the Isolated Statisticians e-mail list:
<center>
[(1)(6 &times; 1/6) + (2)(6  &times; 1/2) + (3)(2 &times; 5/6)] / [(1&times;6) + (2 &times; 6) + (3 &times; 2)] <br>
= [1 + 6 + 5] / [6 + 12 + 6] = 12/24 = 0.50.
</center>
Using an unweighted average instead of a weighted average is the pattern of reasoning underlying the statistical artifact known as Simpson’s paradox.  And as is the case with Simpson’s paradox, it leads to faulty conclusions about how the world works.   


Submitted by Jeff Eiseman, University of Massachusetts
:[Why counting casualties after a hurricane is so hard]<br>
:by Jo Craven McGinty, Wall Street Journal, 7 September 2018


===Comment===
The article is subtitled: Indirect deaths—such as those caused by gaps in medication—can occur months after a storm, complicating tallies
<center>
   
{| class="wikitable" style="text-align:center"
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>
! Sequence<br> of tosses !! Number of H <br> in first 3 tosses !! Number of H <br> followed by H !! Number of HH <br> in first 3 tosses!! Number of HH <br> followed by H
:by Glenn Kessler, ''Washington Post'', 1 June 2018
|-
|  TTTT || 0 || 0  || 0 || 0
|-
| TTTH      || 0  || 0 || 0 || 0
|-
| TTHT || 1  || 0  || 0 || 0
|-
| THTT || 1  || 0  || 0 || 0
|-
| HTTT || 1  || 0  || 0 || 0
|-
| TTHH || 1  || 1  || 0 || 0
|-
| THTH || 1  || 0  || 0 || 0
|-
| THHT || 2  || 1  || 1 || 0
|-
| HTTH || 1  || 0  || 0 || 0
|-
| HTHT || 2  || 0  || 0 || 0
|-
| HHTT || 2  || 1  || 1 || 0
|-
| THHH || 2  || 2  || 1 || 1
|-
| HTHH || 2  || 1  || 0 || 0
|-
| HHTH || 2  || 1  || 1 || 0
|-
| HHHT || 3  || 2 || 2 || 1
|-
| HHHH || 3  || 3 || 2 || 2
|-
! Total || 24  || 12  || 8 || 4  
|}
</center>


==Predicting GOP debate participants==
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.
Ethan Brown posted this following link on the Isolated Statisticians list:


:[http://www.nytimes.com/interactive/2015/07/21/upshot/election-2015-the-first-gop-debate-and-the-role-of-chance.html The first G.O.P. debate: Who’s in, who’s out and the role of chance]<br>
President Trump has asserted that the actual number is
:by Kevin Quealy and Amanda Cox , "Upshot" blog ''New York Times'', 21 July 2015
[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]


Because of the large number of declared candidates (16 and growing at the time of the article), Fox News has limited participation in its August 6 debate to those who meet the [http://press.foxnews.com/2015/05/fox-news-and-facebook-partner-to-host-first-republican-presidential-primary-debate-of-2016-election/ following criterion]
:[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>
<blockquote>Must place in the top 10 of an average of the five most recent national polls, as recognized by FOX News leading up to August 4th at 5 PM/ET. Such polling must be conducted by major, nationally recognized organizations that use standard methodological techniques.
:by Carl Bialik, FiveThirtyEight, 26 August 2015
</blockquote>
Polls are of course subject to sampling error.  The ''NYT'' article uses simulation to illustrate how this could affect participation.  Supposing the latest polling averages represent the "correct" values, they simulate 5 additional polls (as Ethan noted, this is a bootstrapping approach).  The results show that this can affect who's in and who's out as well as the order on the stage of those who do make the cut.


The ''Washington Post'' maintains a [http://www.washingtonpost.com/blogs/the-fix/wp/2015/06/02/whos-in-and-whos-out-in-the-first-republican-debate/?tid=trending_strip_1 State of the debate] widget that updates the current top 10 based on the most recent polling results.
----
[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


===Update===
[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.nytimes.com/2015/08/04/upshot/2016-presidential-election-who-gets-into-the-republican-debate-rounding-could-decide.html?hp&action=click&pgtype=Homepage&module=first-column-region&region=top-news&WT.nav=top-news&abt=0002&abg=0 Who gets into the Republican debate: Rounding could decide]<br>
----
by Kevin Quealy, "Upshot" blog, ''New York Times'', 3 August 2015
[http://www.wyso.org/post/stats-stories-reading-writing-and-risk-literacy Reading , Writing and Risk Literacy]


The article points out that Fox has not specified if or how it will round the polling figures.  For example, the 9th, 10th and 11th places in the earlier post above are Chris Christie (3.3%), John Kasich (2.7%) and Rick Perry (2.3%).  These are all within a one percentage point range, with Christie and Kasich currently in, but Perry out.  But more recent data have Kasich at 3.3% and Perry at 2.7%, a tie if both are rounded to 3%.
[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==
==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 \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|H)</math>


<math>\hat{p}(H|HH)</math>
<math>\hat{p}(H|HH)</math>
Line 175: Line 119:


----
----
==The p-value ban==
http://www.statslife.org.uk/opinion/2114-journal-s-ban-on-null-hypothesis-significance-testing-reactions-from-the-statistical-arena

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

Retrieved from "https://www.causeweb.org/wiki/chance/index.php?title=Sandbox&oldid=22455"