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==Data-mining birth month and disease==
==More on the hot hand==
[http://www.minnpost.com/second-opinion/2015/06/season-and-month-birth-linked-risk-disease-study-has-lots-caveats Season and month of birth linked to risk of disease, but study has lots of caveats]<br>
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. 
by Susan Perry, ''Minneapolis Post'', 11 June 2015


The article reports that
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.
<blockquote>
The season — and even the specific month — in which we are born is associated with certain disease risks later in life,
according to a [https://en.wikipedia.org/wiki/Data_mining data-mining] [http://jamia.oxfordjournals.org/content/jaminfo/early/2015/06/01/jamia.ocv046.full.pdf study [PDF]] published this week in the [http://jamia.oxfordjournals.org/about Journal of the American Medical Informatics Association].
The study found, for example, that people born in early spring are at the highest risk of developing heart disease, while those born in early fall are most likely to develop respiratory illnesses.
Reproductive and neurological illnesses, on the other hand, were found to occur most often among people born during the early winter months.
As for individual birth months, the ones tied with the highest risk of disease were October and November, while May had the lowest risk.
</blockquote>


Perry cautions against over-interpreting the results, which show an association between birth-month and disease but do not prove a causal link.  Furthermore,
:{| class="wikitable" style="text-align:center"
<blockquote>
|-
...as [https://systemsbiology.columbia.edu/faculty/nicholas-tatonetti Nicholas Tatonetti], a co-author of the study and an assistant professor of biomedical informatics at Columbia University, noted in [http://newsroom.cumc.columbia.edu/blog/2015/06/08/data-scientists-find-connections-between-birth-month-and-health/ a released statement], “Even though we found significant associations, the overall disease risk is not that great. The risk related to birth month is relatively minor when compared to more influential variables like diet and exercise.
| TTHT  || Heads follows heads 0 time.
</blockquote>
|-
Later, we read,
| THTT  || Heads follows heads 0 times
<blockquote>
|-
Here — with all of the caveats mentioned above — are some of those 16 medical conditions and the birth months associated with their highest and lowest risk:
| HTTT  || Heads follows heads 0 times
* Atrial fibrillation (irregular heart beat): March (high), October (low)
|-
* Essential hypertension (high blood pressure with no identifiable cause): January (high), October (low)
| TTHH  || Heads follows heads 1 time
* Congestive heart failure: March (high) October (low)
|-
* Acute upper respiratory infection: October (high), May (low)
| THTH  || Heads follows heads 0 times
* Prostate cancer: February (high), October (low)
|-
* Overlapping cancer of the bronchus and lung: February (high), November (low)
| HTTH  || Heads follows heads 0 times
* Bruising: December (high), April (low)
|}
</blockquote> 


Perry's article contains a video of Tatonetti as well as an incomprehensible chart taken from Tatonetti.  The technical article's  Abstract says the results are based on data mining of
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.
<blockquote>
1 749 400 individuals and found 55 diseases that were significantly dependent on birth month. Of these 19 were previously reported in the literature (p-value < .001) 20 were for conditions with close relationships to those reported and 16 were previously unreported. We found distinct incidence patterns across disease categories.
<br><br>
Conclusions: Lifetime disease risk is affected by birth month.  Seasonally dependent early development mechanisms may play a role in increasing lifetime risk of disease.
</blockquote>
Presumably readers of the journal are expected to respect the association/causation distinction--avoiding the slippery slope from "Lifetime disease risk is affected by birth month" to "Lifetime disease risk is caused by birth month."--and to interpret the P=values with appropriate caution.  Perry has certainly done a good job! 


Interestingly, the final summary section of the paper seems more carefully worded:
:{| class="wikitable" style="text-align:center"
<blockquote>
|-
We discovered 16 associations with birth month that have never been explicitly studied previously. Nine of these associations were related to cardiovascular conditions strengthening the link between cardiac conditions, early development, and Vitamin D. Seasonally-dependent early developmental mechanisms might play a role in increasing lifetime disease risk.
| THHT  || Heads follows heads 1 time
</blockquote>
|-
| 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
|}


Submitted by Paul Alper
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.


==Bogus statistics==
:{| class="wikitable" style="text-align:center"
[How To Spot a Bogus Statistic]<br>
|-
by Geoffrey James, Inc.com, 30 May 2015
| HHHT  || Heads follows heads 2 times
|-
| HHHH || Heads follows heads 3 times
|}


The article begins by citing Bill Gates recent [http://www.gatesnotes.com/About-Bill-Gates/6-Books-I-Recommended-for-TED-2015 recommendation] that everyone should read the Darrell Huff classic ''How to Lie With Statistics''.
An unweighted average of the 14 sequences gives
<center>
[(6 &times; 1/6) + (6 &times; 1/2) + (2 &times; 5/6)] / 14 = [17/3] / 14 = 0.405,
</center>


As an object lesson, James considers efforts to dispute the scientific consensus on anthropogenic climate change.  
which is what Miller and Sanjurjo report.
A weighted average of the 14 sequences gives
<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


Submitted by Bill Peterson
===Comment===
<center>
{| class="wikitable" style="text-align:center"
|-
! 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
|-
|  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==
==Predicting GOP debate participants==
Line 60: Line 108:
:by Kevin Quealy and Amanda Cox , "Upshot" blog ''New York Times'', 21 July 2015
:by Kevin Quealy and Amanda Cox , "Upshot" blog ''New York Times'', 21 July 2015


==Sleeping beauties==
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]
Doulas Rogers sent a link to the following:
<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.
 
</blockquote>
:[http://www.nytimes.com/2015/05/20/sports/football/nfl-explores-making-the-2-point-conversion-more-tempting.html Defining and identifying Sleeping Beauties in science]<br>
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.
:by Qing Ke, et. al., ''PNAS'' (vol. 112 no. 24), 2015.
 
[http://www.psmag.com/books-and-culture/sleeping-beauties-of-science The sleeping beauties of science]<br>
by Nathan Collins, ''Pacific Standard'', 28 May 2015
 
Cites a [http://www.tandfonline.com/doi/abs/10.1080/14786440109462720?journalCode=tphm17#.VagU4aYYeVg 1901 paper] by Karl Pearson


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.


==Some math doodles==
==Some math doodles==
Line 76: Line 119:


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


==Accidental insights==
==Accidental insights==

Revision as of 15:35, 31 July 2015

More on the hot hand

In Chance News 105, the last item was titled 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.

TTHT Heads follows heads 0 time.
THTT Heads follows heads 0 times
HTTT Heads follows heads 0 times
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.

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.

HHHT Heads follows heads 2 times
HHHH Heads follows heads 3 times

An unweighted average of the 14 sequences gives

[(6 × 1/6) + (6 × 1/2) + (2 × 5/6)] / 14 = [17/3] / 14 = 0.405,

which is what Miller and Sanjurjo report. A weighted average of the 14 sequences gives

[(1)(6 × 1/6) + (2)(6 × 1/2) + (3)(2 × 5/6)] / [(1×6) + (2 × 6) + (3 × 2)]
= [1 + 6 + 5] / [6 + 12 + 6] = 12/24 = 0.50.

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

Comment

Sequence
of tosses
Number of H
in first 3 tosses
Number of H
followed by H
Number of HH
in first 3 tosses
Number of HH
followed by H
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

Predicting GOP debate participants

Ethan Brown posted this following link on the Isolated Statisticians list:

The first G.O.P. debate: Who’s in, who’s out and the role of chance
by Kevin Quealy and Amanda Cox , "Upshot" blog New York Times, 21 July 2015

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 following criterion

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.

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 State of the debate widget that updates the current top 10 based on the most recent polling results.

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>\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


The p-value ban

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