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It would be interesting to see the attachment referred to in the
original posting.
Joe Ward wrote:
> Hi, Graham -- It's been a long time since I've heard any discussion
> aboutUNDERACHIEVERS and OVERACHIEVERS. I've never been able to
> understandthe discussions. NO MATTER WHAT VALUE THE CORRELATION (SLOPE
> OF THE REGRESSION LINE) HAS weknow that the ALGEBRAIC SUM OF THE
> ERRORS IS ZERO. Now that says thatthe SUM OF THE ABSOLUTE VALUES OF
> THE POSITIVE ERRORS IS EQUAL TO THESUM OF THE ABSOLUTE VALUES OF THE
> NEGATIVE ERRORS. THEN WE WOULD EXPECTTO OBSERVE ABOUT ONE-HALF OF THE
> OBSERVATIONS TO HAVE POSITIVE ERRORS ANDONE-HALF TO HAVE NEGATIVE
> VALUES. THEREFORE, FOR ALL CORRELATIONS (ZERO INCLUDED) WE SHOULD
> EXPECT TOCONCLUDE THAT ABOUT ONE-HALF OF ALL CASESWOULD BE CALLED
> "OVER-ACHIEVERS" AND ABOUT ONE-HALF WOULD BE CALLED"UNDER-ACHIEVERS".
> DOES THAT DESIGNATION HAVE ANY OPERATIONALLY
> USEFULMEANING?
>--Joe********************************************************************************
>
> Joe Ward.........................................Health Careers High
> School
> 167 East Arrowhead Dr....................4646 Hamilton Wolfe
> San Antonio, TX 78228-2402...........San Antonio, TX 78229
> Phone: 210-433-6575.......................Phone: 210-617-5400
> Fax: 210-433-2828............................Fax: 210-617-5423
> Email: [EMAIL PROTECTED]
> http://www.ijoa.org/joeward/wardindex.html
>
> **************************************************************************
>
> ----- Original Message -----
> From: Dr Graham D Smith
> To: Edstat
> Sent: Monday, October 02, 2000 11:40 AM
> Subject: How many Olympic Medals should Great Britain have
> won?
>
> How many Olympic Medals should Great Britain have won?
>
> British Olympians won a grand total of 28 medals at the
> Sydney 2000 Games, our best medal haul for 80 years. Many
> commentators have suggested that the big improvement in
> British fortunes compared to the Atlanta 1996 Games is due
> to the use of Lottery funding to help our top sportsmen and
> sportswomen. But how many medals should Britain expect to
> win? Did we fulfil our potential or fall short of it?
>
> One important determinant of a country's Olympic success is
> the size of its population. USA, China and Russia head the
> Sydney 2000 medal table, they also have large populations.
> However, population size does not fully account for the
> number of medals won. Both India and China have much larger
> populations than USA but won fewer medals. Another important
> predictor of a nation's Olympic performance is economic
> prosperity. Richer nations often outperform poorer nations
> of the same size. Gross domestic product (GDP) is an
> economic index that reflects both economic success and
> population size.
>
> A scatterplot of the number of medals won and GDP of the 80
> medal winning countries at the 2000 Olympics shows a
> positive correlation; r = 0.595, p < 0.01 (see attached).
> GDP accounts for 35.4% of the variance of medals won. A
> regression analysis was performed on the data to estimate
> the number of medals Team GB should expect. Given that the
> UK GDP is equivalent to US$ 1.29 trillion the expected
> number of medals is 15. It seems that our Olympians did far
> better than we could have expected. Well done team GB!
>
> And well done too to Team USA, their expected medal count is
> 26.5. However, the top overachiever was Russia (followed by
> USA and Australia). The top underachiever was India.
>
>
>
> *************************************************
> Dr Graham D. Smith
> Psychology Division
> Park Campus
> University College Northampton
> Boughton Green Rd.
> Northampton
> NN2 7AL
>
> Tel: +44 (0) 1604 735500 Ext 2393
> E-mail: [EMAIL PROTECTED]
> *************************************************
>
>
>
>
>
> *************************************************
> Dr Graham D. Smith
> Psychology Division
> Park Campus
> University College Northampton
> Boughton Green Rd.
> Northampton
> NN2 7AL Tel: +44 (0) 1604 735500 Ext 2393
> E-mail: [EMAIL PROTECTED]
> *************************************************
>
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It would be interesting to see the attachment referred to in the original
posting.
<p>Joe Ward wrote:
<blockquote TYPE=CITE><style></style>
<font face="Courier New"><font size=-1>Hi,
Graham --</font></font> <font face="Courier New"><font size=-1>It's
been a long time since I've heard any discussion about</font></font><font
face="Courier New"><font size=-1>UNDERACHIEVERS
and OVERACHIEVERS. I've never been able to understand</font></font><font
face="Courier New"><font size=-1>the
discussions.</font></font> <font face="Courier New"><font size=-1>NO
MATTER WHAT VALUE THE CORRELATION (SLOPE OF THE REGRESSION LINE) HAS
we</font></font><font face="Courier New"><font size=-1>know
that the ALGEBRAIC SUM OF THE ERRORS IS ZERO. Now that says
that</font></font><font face="Courier New"><font size=-1>the
SUM OF THE ABSOLUTE VALUES OF THE POSITIVE ERRORS IS EQUAL TO THE</font></font><font
face="Courier New"><font size=-1>SUM
OF THE ABSOLUTE VALUES OF THE NEGATIVE ERRORS. THEN WE WOULD
EXPECT</font></font><font face="Courier New"><font size=-1>TO
OBSERVE ABOUT ONE-HALF OF THE OBSERVATIONS TO HAVE POSITIVE ERRORS
AND</font></font><font face="Courier New"><font size=-1>ONE-HALF
TO HAVE NEGATIVE VALUES.</font></font> <font face="Courier New"><font
size=-1>THEREFORE,
FOR ALL CORRELATIONS (ZERO INCLUDED) WE SHOULD EXPECT TO</font></font><font
face="Courier New"><font size=-1>CONCLUDE
THAT ABOUT ONE-HALF OF ALL CASES</font></font><font face="Courier New"><font
size=-1>WOULD
BE CALLED "OVER-ACHIEVERS" AND ABOUT ONE-HALF WOULD BE CALLED</font></font><font
face="Courier New"><font size=-1>"UNDER-ACHIEVERS".
DOES THAT DESIGNATION HAVE ANY OPERATIONALLY USEFUL</font></font><font face="Courier
New"><font size=-1>MEANING?</font></font> <font face="Courier New"><font
size=-1>--Joe</font></font><font face="Courier New"><font
size=-1>********************************************************************************</font></font>
<br><font face="Courier New"><font size=-1>Joe
Ward.........................................Health
Careers High School</font></font>
<br><font face="Courier New"><font size=-1>167 East Arrowhead
Dr....................4646
Hamilton Wolfe</font></font>
<br><font face="Courier New"><font size=-1>San Antonio, TX 78228-2402...........San
Antonio, TX 78229</font></font>
<br><font face="Courier New"><font size=-1>Phone:
210-433-6575.......................Phone:
210-617-5400</font></font>
<br><font face="Courier New"><font size=-1>Fax:
210-433-2828............................Fax:
210-617-5423</font></font>
<br><font face="Courier New"><font size=-1>Email: <a
href="mailto:[EMAIL PROTECTED]">[EMAIL PROTECTED]</a></font></font>
<br><font face="Courier New"><font size=-1><a
href="http://www.ijoa.org/joeward/wardindex.html">http://www.ijoa.org/joeward/wardindex.html</a></font></font>
<br><font face="Courier New"><font
size=-1>***************************************************************************</font></font>
<blockquote
style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px;
PADDING-LEFT: 5px; PADDING-RIGHT: 0px">
<div style="FONT: 10pt arial">----- Original Message -----</div>
<div
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><b>From:</b>
<a href="mailto:[EMAIL PROTECTED]"
title="[EMAIL PROTECTED]">Dr
Graham D Smith</a></div>
<div style="FONT: 10pt arial"><b>To:</b> <a href="mailto:[EMAIL PROTECTED]"
title="[EMAIL PROTECTED]">Edstat</a></div>
<div style="FONT: 10pt arial"><b>Sent:</b> Monday, October 02, 2000 11:40
AM</div>
<div style="FONT: 10pt arial"><b>Subject:</b> How many Olympic Medals should
Great Britain have won?</div>
<center><font face="Arial"><font size=+4>How many Olympic Medals should
Great Britain have won?</font></font></center>
<p><font face="Arial">British Olympians won a grand total of 28 medals
at the Sydney 2000 Games, our best medal haul for 80 years. Many commentators
have suggested that the big improvement in British fortunes compared to
the Atlanta 1996 Games is due to the use of Lottery funding to help our
top sportsmen and sportswomen. But how many medals should Britain expect
to win? Did we fulfil our potential or fall short of it?</font>
<p><font face="Arial">One important determinant of a country's Olympic
success is the size of its population. USA, China and Russia head the Sydney
2000 medal table, they also have large populations. However, population
size does not fully account for the number of medals won. Both India and
China have much larger populations than USA but won fewer medals. Another
important predictor of a nation's Olympic performance is economic prosperity.
Richer nations often outperform poorer nations of the same size. Gross
domestic product (GDP) is an economic index that reflects both economic
success and population size.</font>
<p><font face="Arial">A scatterplot of the number of medals won and GDP
of the 80 medal winning countries at the 2000 Olympics shows a positive
correlation; <i>r</i> = 0.595, <i>p</i> < 0.01 (see attached). GDP accounts
for 35.4% of the variance of medals won. A regression analysis was performed
on the data to estimate the number of medals Team GB should expect. Given
that the UK GDP is equivalent to US$ 1.29 trillion the expected number
of medals is 15. It seems that our Olympians did far better than we could
have expected. Well done team GB!</font>
<p><font face="Arial">And well done too to Team USA, their expected medal
count is 26.5. However, the top overachiever was Russia (followed by USA
and Australia). The top underachiever was India.</font>
<br>
<br>
<p><font face="Arial"><font
size=-1>*************************************************</font></font>
<br><font face="Arial"><font size=-1>Dr Graham D. Smith</font></font>
<br><font face="Arial"><font size=-1>Psychology Division</font></font>
<br><font face="Arial"><font size=-1>Park Campus</font></font>
<br><font face="Arial"><font size=-1>University College Northampton</font></font>
<br><font face="Arial"><font size=-1>Boughton Green Rd.</font></font>
<br><font face="Arial"><font size=-1>Northampton</font></font>
<br><font face="Arial"><font size=-1>NN2 7AL</font></font>
<p><font face="Arial"><font size=-1>Tel: +44 (0) 1604 735500 Ext 2393</font></font>
<br><font face="Arial"><font size=-1>E-mail: <a
href="mailto:[EMAIL PROTECTED]">[EMAIL PROTECTED]</a></font></font>
<br><font face="Arial"><font
size=-1>*************************************************</font></font>
<br>
<br>
<br>
<br>
<br>
<br> <font size=-1>*************************************************</font>
<br><font size=-1>Dr Graham D. Smith</font>
<br><font size=-1>Psychology Division</font>
<br><font size=-1>Park Campus</font>
<br><font size=-1>University College Northampton</font>
<br><font size=-1>Boughton Green Rd.</font>
<br><font size=-1>Northampton</font>
<br><font size=-1>NN2 7AL</font> <font size=-1>Tel: +44 (0) 1604 735500
Ext 2393</font>
<br><font size=-1>E-mail: <a
href="mailto:[EMAIL PROTECTED]">[EMAIL PROTECTED]</a></font>
<br><font size=-1>*************************************************</font></blockquote>
</blockquote>
</body>
</html>
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