Law of the Unconscious Statistician
Robert Israel
Unconscious Statistician", and when?
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Herman Rubin
Robert Israel <isr...@math.ubc.ca> wrote:
>This is my favourite name for a theorem. Who coined the name "Law of the
>Unconscious Statistician", and when?
I believe it was Halmos, and in the mid 1940s.
--
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
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
David Bernier
> This is my favourite name for a theorem. Who coined the name "Law of
> the Unconscious Statistician", and when?
>
It appears in Sheldon M. Ross' book "Introduction to
Probability Models", Second Edition, 1980, in Chapter 2
on Random Variables: Proposition 4.1, with the footnote:
<< This law got its name from "unconscious" statisticians
who have used it as if it were the definition
of E[g(X)]. >>
It may have appeared or been used before then.
David Bernier
Stephen J. Herschkorn
I love the name, too.
Ross dropped the name from subsequent editions due to complaints from
statisticians. I still introduce it to my classes, though.
Interesting: Berger and Casellla, in their _Statistical Inference_ (a
quite standard graduate text), make the folowing "definition::"
The _expected value_ or _mean_ of a random variable g(X) , denotef by
Eg(X), is
Eg(X) = integral(x=-infty..infty, g(x) [f_X](x)) if X is continuous,
sum(x, g(x) [f_X](x)) = sum(X, g(x) P{X = x}) if X is discrete..."
They then comment parentheticaly, "Ross 1988 refers to this as the 'law
of the unconscious statistician.' We do not find this amusing." (This
is on p. 55 of the second edition.)
However, nowhere do they note that thhis definition needs
justuifcation. The theorem we discuss here implies eaxctly that - that
if g(X) = h(Y), then integral(g dF_X) = integral(h dF_Y). Thus,
while the authors sniff at the name, they demonstrate why the theorem is
called thus.
--
Stephen J. Herschkorn sjher...@netscape.net
Math Tutor on the Internet and in Central New Jersey
Primes?
wrote:
> Math Tutor on the Internet and in Central New Jersey
The below response consists entirely of statements made prior to
original posting of this thread:
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Mar 3, 2008 ... influences spring from wells deep in both the
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Read ... 3, Read, Law of the Unconscious Statistician · Robert Israel.
7/16/09. 3, Read ...
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7.
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William Elliot
Who wrote this.
The average person uses statistics like a drunk uses a lamppost,
for support rather than illumination. Introduction of Statistics Book.
It's reputed that Mark 'Twain said
"There's lies, damn lies and statistics."
Did Mark actually say or write that?
-- Variations upon a theme.
The average politician uses statistics like a drunk uses a lamppost,
for support rather than illumination.
Corporations use statistics like a drunk uses a lamppost,
for support rather than illumination.
The government uses statistics like a drunk uses a lamppost,
for support rather than illumination.
----
David Bernier
> On Thu, 16 Jul 2009, David Bernier wrote:
>
>> Robert Israel wrote:
>>> This is my favourite name for a theorem. Who coined the name "Law of
>>> the Unconscious Statistician", and when?
>>
>> It appears in Sheldon M. Ross' book "Introduction to
>> Probability Models", Second Edition, 1980, in Chapter 2
>> on Random Variables: Proposition 4.1, with the footnote:
>>
>> << This law got its name from "unconscious" statisticians
>> who have used it as if it were the definition
>> of E[g(X)]. >>
>>
>> It may have appeared or been used before then.
>
> Who wrote this.
If you mean:
<< This law got its name from "unconscious" statisticians
who have used it as if it were the definition
of E[g(X)]. >>
I suppose it's Sheldon Ross.
There's a book on operations research that has gone through many
editions:
by Gerald J. Lieberman (deceased) and
Frederick S. Hillier
In
"Introduction to the techniques of operations research"
by Hillier only, page 67 (printed in 1965)
(according to Google Books):
"In section kB we introduced the Theorem of the
Unconscious Statistician, and pointed out"
David Bernier
Musatov
> On Thu, 16 Jul 2009, David Bernier wrote:
> > Robert Israel wrote:
> >> This is my favourite name for a theorem. Who coined the name "Law of the
> >> Unconscious Statistician", and when?
>
> > It appears in Sheldon M. Ross' book "Introduction to
> > Probability Models", Second Edition, 1980, in Chapter 2
> > on Random Variables: Proposition 4.1, with the footnote:
>
> > << This law got its name from "unconscious" statisticians
> > who have used it as if it were the definition
> > of E[g(X)]. >>
>
> > It may have appeared or been used before then.
>
> Who wrote this.
>
> The average person uses statistics like a drunk uses a lamppost,
> for support rather than illumination. Introduction of Statistics Book.
>
> It's reputed that Mark 'Twain said
> "There's lies, damn lies and statistics."
>
> Did Mark actually say or write that?
>
Figures often beguile me, particularly when I have the arranging of
them myself; in which case the remark attributed to Disraeli would
often apply with justice and force: "There are three kinds of lies:
lies, damned lies and statistics."
- Mark Twain's Own Autobiography: The Chapters from the North American
Review
Further background on this quote is provided by Stephen Goranson who
writes on the Mark Twain Forum in a post dated 31 July 2002: Twain's
Autobiography attribution of a remark about lies and statistics to
Disraeli is generally not accepted. Evidence is now available to
conclude that the phrase originally appeared in 1895 in an article by
Leonard H. Courtney. So Disraeli is not the source, nor any pre-1895
person; merely Courtney. The 1895 article is now available online at:
http://www.york.ac.uk/depts/maths/histstat/lies.htm Courtney may have
read Carlyle on statistics (also quoted at this site); certainly,
misuse of statistics was complained about before 1895.
http://www.twainquotes.com/Statistics.html
> -- Variations upon a theme.
>
> The average politician uses statistics like a drunk uses a lamppost,
> for support rather than illumination.
>
> Corporations use statistics like a drunk uses a lamppost,
> for support rather than illumination.
>
> The government uses statistics like a drunk uses a lamppost,
> for support rather than illumination.
>
> ----
Other finds I found interesting:
Lies, damn lies, and college rankings « Politics, Technology,
and ...We know there's lies, damn lies, and statistics. Sarah Lawrence
College is tired of the lies, and they're not going to participate any
more. ...
Mark Twain: "There are three kinds of lies: lies, damned lies, and
statistics."
Musatov: "Hmmm... what are the other two types of lies per Twain?"
Twain. "There are lies, damn lies and statistics." -- Samuel Clemens.
Musatov cited: "Twain also wrote, 'Liberty lies in the hearts of
men...', wait did he mean 'lies' or 'lies'?
G. A. Edgar
<ma...@rdrop.remove.com> wrote:
> It's reputed that Mark 'Twain said
> "There's lies, damn lies and statistics."
>
> Did Mark actually say or write that?
perhaps Twain was quoting Disraeli ...
http://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
Herman Rubin
>> Robert Israel wrote:
>>> This is my favourite name for a theorem. Who coined the name "Law of the
>>> Unconscious Statistician", and when?
>> It appears in Sheldon M. Ross' book "Introduction to
>> Probability Models", Second Edition, 1980, in Chapter 2
>> on Random Variables: Proposition 4.1, with the footnote:
>> << This law got its name from "unconscious" statisticians
>> who have used it as if it were the definition
>> of E[g(X)]. >>
>> It may have appeared or been used before then.
It is my personal recollection that Halmos used this
in 1946 or 1947. As "Fundamental Theorem" rather than
"Law", I believe it stresses the important point that
an expectation (or integral) can be computed on any
appropriate probability space to represent the random
variable, and this makes it useful. The proof is
rather trivial and enlightening.
>Who wrote this.
>The average person uses statistics like a drunk uses a lamppost,
>for support rather than illumination. Introduction of Statistics Book.
>It's reputed that Mark 'Twain said
>"There's lies, damn lies and statistics."
It is reputed that Disraeli said this.
>Did Mark actually say or write that?
>-- Variations upon a theme.
>The average politician uses statistics like a drunk uses a lamppost,
>for support rather than illumination.
>Corporations use statistics like a drunk uses a lamppost,
>for support rather than illumination.
>The government uses statistics like a drunk uses a lamppost,
>for support rather than illumination.
There was an article entitled, "Statistics; the
Religion of Medicine." It is misused that way.
It is needed wherever there are uncertain observations,
or uncertainty in the theory. But as it is used, it
is a loaded gun in the hands of the idiot in industry,
politics, government, and medicine.
Musatov
wrote:
> In article <20090717005029.I36...@agora.rdrop.com>, William Elliot
Was he? I am not sure. It is possible. Is it not?
--
Musatov