Re: How many Olympic Medals should Great Britain have won?

[Joe Ward]

Hi, Graham --   It's been a long time since I've heard any discussion about UNDERACHIEVERS and OVERACHIEVERS.  I've never been able to understand the discussions.   NO MATTER WHAT VALUE THE CORRELATION (SLOPE OF THE REGRESSION LINE) HAS we know that the ALGEBRAIC SUM OF THE ERRORS IS ZERO.  Now that says that the SUM OF THE ABSOLUTE VALUES OF THE POSITIVE ERRORS IS EQUAL TO THE SUM OF THE ABSOLUTE VALUES OF THE NEGATIVE ERRORS.  THEN WE WOULD EXPECT TO OBSERVE ABOUT ONE-HALF OF THE OBSERVATIONS TO HAVE POSITIVE ERRORS AND ONE-HALF TO HAVE NEGATIVE VALUES.    THEREFORE, FOR ALL CORRELATIONS (ZERO INCLUDED) WE SHOULD EXPECT TO CONCLUDE THAT ABOUT ONE-HALF OF ALL CASES WOULD BE CALLED "OVER-ACHIEVERS" AND ABOUT ONE-HALF WOULD BE CALLED "UNDER-ACHIEVERS".  DOES THAT DESIGNATION HAVE ANY OPERATIONALLY USEFUL MEANING?    --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] *************************************************