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| Gary... |
 Posted: Mon Aug 24, 2009 11:37 am |
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See:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition
Some results of real coin tossing experiments:
A. The French naturalist Count Buffon (1707-1788) tossed a coin 4040
times. Results: 2048 heads, or proportion 2048/4040 = 0.5069 for
heads.
B. Around 1900, the English statistician Karl Pearson heroically
tossed a coin 24,000 times. Result: 12,012 heads, a proportion of
0.5005.
C. While imprisoned by the Germans during World War II, the South
African mathematician John Kerrich tossed a coin 10,000 times. Result:
5067 heads, a proportion of 0.5067. |
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| Gary... |
| Posted: Tue Sep 01, 2009 12:01 pm |
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On Sep 1, 8:32 pm, "Kenneth M. Lin" <kenm... at (no spam) aol.com> wrote:
[quote:ff32dda7ae]"Gary" <lanceg... at (no spam) gmail.com> wrote in message
news:f1fe2ca4-06fd-480e-9503-df0f1de417a3 at (no spam) g10g2000yqh.googlegroups.com...
See:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-...
Some results of real coin tossing experiments:
A. The French naturalist Count Buffon (1707-1788) tossed a coin 4040
times. Results: 2048 heads, or proportion 2048/4040 = 0.5069 for
heads.
B. Around 1900, the English statistician Karl Pearson heroically
tossed a coin 24,000 times. Result: 12,012 heads, a proportion of
0.5005.
C. While imprisoned by the Germans during World War II, the South
African mathematician John Kerrich tossed a coin 10,000 times. Result:
5067 heads, a proportion of 0.5067.
I am sure that no coins are "unbiased" because face and tail aren't designed
to balance 100%. However, you'd notice that the bias is so slight to be of
no advantage in a short run.
[/quote:ff32dda7ae]
The article referenced at the top suggests that the face (head or
tail) that is uppermost when a coin is tossed will have a slight
advantage. I don't think this is to do with the balance of the coin
but rather with the number of times a coin will turn in the air after
it is tossed. I added the counts from real coin tossing experiments
because they suggest (to me) that the bias is very slight. But of
course the people who tossed the coins didn't note which side faced
upwards so that we could use their data to check the claim of the
article referenced above.
Lance |
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| Kenneth M. Lin... |
| Posted: Tue Sep 01, 2009 12:32 pm |
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Guest
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"Gary" <lancegary at (no spam) gmail.com> wrote in message
news:f1fe2ca4-06fd-480e-9503-df0f1de417a3 at (no spam) g10g2000yqh.googlegroups.com...
[quote:4e8c5fdf78]See:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition
Some results of real coin tossing experiments:
A. The French naturalist Count Buffon (1707-1788) tossed a coin 4040
times. Results: 2048 heads, or proportion 2048/4040 = 0.5069 for
heads.
B. Around 1900, the English statistician Karl Pearson heroically
tossed a coin 24,000 times. Result: 12,012 heads, a proportion of
0.5005.
C. While imprisoned by the Germans during World War II, the South
African mathematician John Kerrich tossed a coin 10,000 times. Result:
5067 heads, a proportion of 0.5067.
[/quote:4e8c5fdf78]
I am sure that no coins are "unbiased" because face and tail aren't designed
to balance 100%. However, you'd notice that the bias is so slight to be of
no advantage in a short run. |
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| Philipp Pagel... |
| Posted: Tue Sep 01, 2009 11:20 pm |
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Gary <lancegary at (no spam) gmail.com> wrote:
[quote:0b9f5ecfd6]http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition
[/quote:0b9f5ecfd6]
To me it seems that the most important aspect of the bias describe in the text
is the fact that the coin flip is made as reproducible as possible by using a
mechanical flipping device. I doubt that the bias can be maintained by a human
coin-flipper. Of course one could practice to throw a coin in a particular way
to get more consistent results but I don't believe that this would be possible
with the traditional "rapidly spinning in the air" method.
Interestingly, other researchers claim you cannot even load a coin:
www.stat.berkeley.edu/~nolan/Papers/dice.pdf
cu
Philipp
--
Dr. Philipp Pagel
Lehrstuhl f. Genomorientierte Bioinformatik
Technische Universität München
http://webclu.bio.wzw.tum.de/~pagel/ |
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| illywhacker... |
| Posted: Tue Sep 01, 2009 11:37 pm |
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Guest
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On 2 Sep, 11:20, Philipp Pagel <pDOTpa... at (no spam) wzw.tum.de> wrote:
[quote:540083a859]Gary <lanceg... at (no spam) gmail.com> wrote:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-...
To me it seems that the most important aspect of the bias describe in the text
is the fact that the coin flip is made as reproducible as possible by using a
mechanical flipping device. I doubt that the bias can be maintained by a human
coin-flipper. Of course one could practice to throw a coin in a particular way
to get more consistent results but I don't believe that this would be possible
with the traditional "rapidly spinning in the air" method.
Interestingly, other researchers claim you cannot even load a coin:
www.stat.berkeley.edu/~nolan/Papers/dice.pdf
[/quote:540083a859]
Yes - except:
1) the range of biases mentioned in this paper ('According to Peterson
(1990), "A look at the spread in the way real people flip real coins
indicates <...> a slight bias would begin to show up after millions of
tosses. The proportion of, say, heads would settle at a number such as
0.503 or 0.497..." ') are consistent with the web page cited by the
OP.
And indeed the web page says:
"The 51% figure in Premise 1 is a bit curious and, when I first saw
it, I assumed it was a minor bias introduced by the fact that the
"heads" side of the coin has more decoration than the "tails" side,
making it heavier. But it turns out that this sort of imbalance has
virtually no effect unless you spin the coin on its edge, in which
case you'll see a huge bias."
So it seems they agree.
illywhacker; |
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| Stan Brown... |
| Posted: Wed Sep 02, 2009 6:53 pm |
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Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenmlin at (no spam) aol.com>:
[quote:509b59ed25]
"Gary" <lancegary at (no spam) gmail.com> wrote in message
news:f1fe2ca4-06fd-480e-9503-df0f1de417a3 at (no spam) g10g2000yqh.googlegroups.com...
See:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition
Some results of real coin tossing experiments:
A. The French naturalist Count Buffon (1707-1788) tossed a coin 4040
times. Results: 2048 heads, or proportion 2048/4040 = 0.5069 for
heads.
B. Around 1900, the English statistician Karl Pearson heroically
tossed a coin 24,000 times. Result: 12,012 heads, a proportion of
0.5005.
C. While imprisoned by the Germans during World War II, the South
African mathematician John Kerrich tossed a coin 10,000 times. Result:
5067 heads, a proportion of 0.5067.
I am sure that no coins are "unbiased" because face and tail aren't designed
to balance 100%. However, you'd notice that the bias is so slight to be of
no advantage in a short run.
[/quote:509b59ed25]
It is important to note that a 95% confidence interval for any of
those includes 0.50000. That is, their results are not inconsistent
with a perfectly fair coin.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com
Shikata ga nai... |
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| illywhacker... |
| Posted: Wed Sep 02, 2009 9:58 pm |
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Guest
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On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
[quote:b46e2e92c0]Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
"Gary" <lanceg... at (no spam) gmail.com> wrote in message
news:f1fe2ca4-06fd-480e-9503-df0f1de417a3 at (no spam) g10g2000yqh.googlegroups.com....
See:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-....
Some results of real coin tossing experiments:
A. The French naturalist Count Buffon (1707-1788) tossed a coin 4040
times. Results: 2048 heads, or proportion 2048/4040 = 0.5069 for
heads.
B. Around 1900, the English statistician Karl Pearson heroically
tossed a coin 24,000 times. Result: 12,012 heads, a proportion of
0.5005.
C. While imprisoned by the Germans during World War II, the South
African mathematician John Kerrich tossed a coin 10,000 times. Result:
5067 heads, a proportion of 0.5067.
I am sure that no coins are "unbiased" because face and tail aren't designed
to balance 100%. However, you'd notice that the bias is so slight to be of
no advantage in a short run.
It is important to note that a 95% confidence interval for any of
those includes 0.50000. That is, their results are not inconsistent
with a perfectly fair coin.
[/quote:b46e2e92c0]
Nevertheless, the most likely interpretation is that the coin (or
rather the whole coin tossing system) is biased.
illywhacker; |
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| Jussi Piitulainen... |
| Posted: Thu Sep 03, 2009 4:05 am |
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Guest
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illywhacker writes:
[quote:77209654e2]On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
"Gary" <lanceg... at (no spam) gmail.com> wrote in message
news:f1fe2ca4-06fd-480e-9503-df0f1de417a3 at (no spam) g10g2000yqh.googlegroups.com...
See:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-...
Some results of real coin tossing experiments:
A. The French naturalist Count Buffon (1707-1788) tossed
a coin 4040 times. Results: 2048 heads, or proportion
2048/4040 = 0.5069 for heads.
B. Around 1900, the English statistician Karl Pearson
heroically tossed a coin 24,000 times. Result: 12,012
heads, a proportion of 0.5005.
C. While imprisoned by the Germans during World War II,
the South African mathematician John Kerrich tossed a
coin 10,000 times. Result: 5067 heads, a proportion of
0.5067.
I am sure that no coins are "unbiased" because face and
tail aren't designed to balance 100%. However, you'd
notice that the bias is so slight to be of no advantage in
a short run.
It is important to note that a 95% confidence interval for
any of those includes 0.50000. That is, their results are
not inconsistent with a perfectly fair coin.
Nevertheless, the most likely interpretation is that the coin
(or rather the whole coin tossing system) is biased.
[/quote:77209654e2]
I wonder why it should always be biased in favour of heads.
Those are three different coins, most likely, and three
different tossers, and all get more heads than tails. |
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| illywhacker... |
| Posted: Thu Sep 03, 2009 5:55 am |
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Guest
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On 3 Sep, 12:05, Jussi Piitulainen <jpiit... at (no spam) ling.helsinki.fi> wrote:
[quote:0405c632ea]illywhacker writes:
On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
"Gary" <lanceg... at (no spam) gmail.com> wrote in message
news:f1fe2ca4-06fd-480e-9503-df0f1de417a3 at (no spam) g10g2000yqh.googlegroups.com...
See:
http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-...
Some results of real coin tossing experiments:
A. The French naturalist Count Buffon (1707-1788) tossed
a coin 4040 times. Results: 2048 heads, or proportion
2048/4040 = 0.5069 for heads.
B. Around 1900, the English statistician Karl Pearson
heroically tossed a coin 24,000 times. Result: 12,012
heads, a proportion of 0.5005.
C. While imprisoned by the Germans during World War II,
the South African mathematician John Kerrich tossed a
coin 10,000 times. Result: 5067 heads, a proportion of
0.5067.
I am sure that no coins are "unbiased" because face and
tail aren't designed to balance 100%. However, you'd
notice that the bias is so slight to be of no advantage in
a short run.
It is important to note that a 95% confidence interval for
any of those includes 0.50000. That is, their results are
not inconsistent with a perfectly fair coin.
Nevertheless, the most likely interpretation is that the coin
(or rather the whole coin tossing system) is biased.
I wonder why it should always be biased in favour of heads.
Those are three different coins, most likely, and three
different tossers, and all get more heads than tails.- Hide quoted text -
[/quote:0405c632ea]
I suggest you read the article.
illywhacker; |
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| Stan Brown... |
| Posted: Thu Sep 03, 2009 7:12 pm |
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Guest
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Thu, 3 Sep 2009 00:58:44 -0700 (PDT) from illywhacker
<illywacker at (no spam) gmail.com>:
[quote:427a43a221]
On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
It is important to note that a 95% confidence interval for any of
those includes 0.50000. That is, their results are not inconsistent
with a perfectly fair coin.
Nevertheless, the most likely interpretation is that the coin (or
rather the whole coin tossing system) is biased.
[/quote:427a43a221]
That's a very common error in interpreting confidence intervals.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com
Shikata ga nai... |
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| illywhacker... |
| Posted: Thu Sep 03, 2009 11:01 pm |
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Guest
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On 4 Sep, 03:12, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
[quote:e0e12fcefe]Thu, 3 Sep 2009 00:58:44 -0700 (PDT) from illywhacker
illywac... at (no spam) gmail.com>:
On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
It is important to note that a 95% confidence interval for any of
those includes 0.50000. That is, their results are not inconsistent
with a perfectly fair coin.
Nevertheless, the most likely interpretation is that the coin (or
rather the whole coin tossing system) is biased.
That's a very common error in interpreting confidence intervals.
[/quote:e0e12fcefe]
I am not intepreting confidence intervals. Confidence intervals are a
radically flawed method
(cf http://bayes.wustl.edu/etj/articles/confidence.pdf)
based on an untenable (and, more importantly, extremely limiting) view
of probability and statistics. You will say: 'So how come CIs are
still taught everywhere?' I would ask exactly the same question.
Rather, I am adopting a Bayesian point of view based on an
uninformative prior, and my statement is correct.
illywhacker; |
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| illywhacker... |
| Posted: Sun Sep 06, 2009 5:56 am |
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On Sep 6, 2:53 pm, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
[quote:8126a2629f]Fri, 4 Sep 2009 02:01:26 -0700 (PDT) from illywhacker
illywac... at (no spam) gmail.com>:
On 4 Sep, 03:12, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Thu, 3 Sep 2009 00:58:44 -0700 (PDT) from illywhacker
illywac... at (no spam) gmail.com>:
On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
It is important to note that a 95% confidence interval for any of
those includes 0.50000. That is, their results are not inconsistent
with a perfectly fair coin.
Nevertheless, the most likely interpretation is that the coin (or
rather the whole coin tossing system) is biased.
That's a very common error in interpreting confidence intervals.
I am not intepreting confidence intervals. Confidence intervals are a
radically flawed method
(cfhttp://bayes.wustl.edu/etj/articles/confidence.pdf)
based on an untenable (and, more importantly, extremely limiting) view
of probability and statistics. You will say: 'So how come CIs are
still taught everywhere?' I would ask exactly the same question.
Rather, I am adopting a Bayesian point of view based on an
uninformative prior, and my statement is correct.
Well, so much for 120 years of development of statistics, then.
[/quote:8126a2629f]
Indeed. Arguments from authority like the one you just deployed have
alas carried the day in much of statistics for all that time, and
frequently continue to do so; a testimony to how unthinking and
incurious (since the alternative has been there all the time) most
people are, even ones that are supposed to be smart.
illywhacker |
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| Stan Brown... |
| Posted: Sun Sep 06, 2009 6:53 am |
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Guest
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Fri, 4 Sep 2009 02:01:26 -0700 (PDT) from illywhacker
<illywacker at (no spam) gmail.com>:
[quote:87a2037bcd]
On 4 Sep, 03:12, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Thu, 3 Sep 2009 00:58:44 -0700 (PDT) from illywhacker
illywac... at (no spam) gmail.com>:
On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
It is important to note that a 95% confidence interval for any of
those includes 0.50000. That is, their results are not inconsistent
with a perfectly fair coin.
Nevertheless, the most likely interpretation is that the coin (or
rather the whole coin tossing system) is biased.
That's a very common error in interpreting confidence intervals.
I am not intepreting confidence intervals. Confidence intervals are a
radically flawed method
(cf http://bayes.wustl.edu/etj/articles/confidence.pdf)
based on an untenable (and, more importantly, extremely limiting) view
of probability and statistics. You will say: 'So how come CIs are
still taught everywhere?' I would ask exactly the same question.
Rather, I am adopting a Bayesian point of view based on an
uninformative prior, and my statement is correct.
[/quote:87a2037bcd]
Well, so much for 120 years of development of statistics, then.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com
Shikata ga nai... |
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| Herman Rubin... |
| Posted: Sun Sep 06, 2009 12:43 pm |
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Guest
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In article <MPG.250d7ae430157f0298bc0b at (no spam) news.individual.net>,
Stan Brown <the_stan_brown at (no spam) fastmail.fm> wrote:
[quote:0ec221b4ba]Fri, 4 Sep 2009 02:01:26 -0700 (PDT) from illywhacker
illywacker at (no spam) gmail.com>:
On 4 Sep, 03:12, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Thu, 3 Sep 2009 00:58:44 -0700 (PDT) from illywhacker
illywac... at (no spam) gmail.com>:
On 3 Sep, 02:53, Stan Brown <the_stan_br... at (no spam) fastmail.fm> wrote:
Tue, 1 Sep 2009 11:32:51 -0700 from Kenneth M. Lin <kenm... at (no spam) aol.com>:
It is important to note that a 95% confidence interval for any of
those includes 0.50000. That is, their results are not inconsistent
with a perfectly fair coin.
Nevertheless, the most likely interpretation is that the coin (or
rather the whole coin tossing system) is biased.
That's a very common error in interpreting confidence intervals.
I am not intepreting confidence intervals. Confidence intervals are a
radically flawed method
(cf http://bayes.wustl.edu/etj/articles/confidence.pdf)
based on an untenable (and, more importantly, extremely limiting) view
of probability and statistics. You will say: 'So how come CIs are
still taught everywhere?' I would ask exactly the same question.
Rather, I am adopting a Bayesian point of view based on an
uninformative prior, and my statement is correct.
Well, so much for 120 years of development of statistics, then.
[/quote:0ec221b4ba]
The last 60 show that there are major misconceptions in the
preceding years. Self consistency requires a prior Bayes
approach; this can even be done in the absence of computable
posteriors.
One can consider interval estimates; put down your loss
function. For example, if the loss is the probability
of noncoverage plus a multiple of the length of the interval,
for normal observations with known variance the coverage
probability depends heavily on the variance. Notice that
I have used no Bayesian ideas, just getting invariant
solutions to this simple problem, and it is easily computed.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin at (no spam) stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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