Will Rogers phenomenon
Encyclopedia
The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average
values of both sets. It is based on the following quote, attributed (perhaps incorrectly) to comedian Will Rogers
:
The effect will occur when both of these conditions are met:
The arithmetic mean
of R is 2.5, and the arithmetic mean of S is 7.
However, if 5 is moved from S to R, producing
then the arithmetic mean of R increases to 3, and the arithmetic mean of S increases to 7.5.
Consider this more illustrative example:
with arithmetic means 1.5 and 10033.
Moving 99 from S to R gives means 34 and 15000. 99 is orders of magnitude above 1 and 2, and orders of magnitude below 10000 and 20000. It should come as no surprise that the transfer of 99 increases the mean of both R and S.
The element which is moved does not have to be the very lowest of its set. Consider this example:
Moving 10 from S to R will raise the mean of R from 7 to 7.375, and the mean of S from 12 to 12.333. The effect still occurs, but less dramatically.
Because these people are not healthy, removing them from the set of healthy people increases the average lifespan of the healthy group. Likewise, the migrated people are healthier than the people already in the unhealthy set, so adding them raises the average lifespan of that group as well. Both lifespans are statistically lengthened, even if early detection of a cancer does not lead to better treatment - because it is detected earlier, more time is lived in the "unhealthy" set of people.
An example of better delineation of early stages and advanced stages lung cancer by means of fluoro-deoxy-glucose PET scans shows such an effect in practice.
Average
In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....
values of both sets. It is based on the following quote, attributed (perhaps incorrectly) to comedian Will Rogers
Will Rogers
William "Will" Penn Adair Rogers was an American cowboy, comedian, humorist, social commentator, vaudeville performer, film actor, and one of the world's best-known celebrities in the 1920s and 1930s....
:
- When the OkieOkieOkie is a term dating from as early as 1907, originally denoting a resident or native of Oklahoma. It is derived from the name of the state, similar to Texan or Tex for someone from Texas, or Arkie or Arkansawyer for a native of Arkansas....
s left OklahomaOklahomaOklahoma is a state located in the South Central region of the United States of America. With an estimated 3,751,351 residents as of the 2010 census and a land area of 68,667 square miles , Oklahoma is the 28th most populous and 20th-largest state...
and moved to CaliforniaCaliforniaCalifornia is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...
, they raised the average intelligence level in both states.
The effect will occur when both of these conditions are met:
- The element being moved is below average for its current set. Removing it will, by definition, raise the average of the remaining elements.
- The element being moved is above the current average of the set it is entering. Adding it to the new set will, by definition, raise the average.
Numerical examples
Consider the sets R and S- R={1, 2, 3, 4}
- S={5, 6, 7, 8, 9}
The arithmetic mean
Arithmetic mean
In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
of R is 2.5, and the arithmetic mean of S is 7.
However, if 5 is moved from S to R, producing
- R={1, 2, 3, 4, 5}
- S={6, 7, 8, 9}
then the arithmetic mean of R increases to 3, and the arithmetic mean of S increases to 7.5.
Consider this more illustrative example:
- R={1,2}
- S={99,10000,20000}
with arithmetic means 1.5 and 10033.
Moving 99 from S to R gives means 34 and 15000. 99 is orders of magnitude above 1 and 2, and orders of magnitude below 10000 and 20000. It should come as no surprise that the transfer of 99 increases the mean of both R and S.
The element which is moved does not have to be the very lowest of its set. Consider this example:
- R={1, 3, 5, 7, 9, 11, 13}
- S={6, 8, 10, 12, 14, 16, 18}
Moving 10 from S to R will raise the mean of R from 7 to 7.375, and the mean of S from 12 to 12.333. The effect still occurs, but less dramatically.
Stage migration
One real-world example of the Will Rogers phenomenon is seen in the medical concept of stage migration. In medical stage migration, improved detection of illness leads to the movement of people from the set of healthy people to the set of unhealthy people.Because these people are not healthy, removing them from the set of healthy people increases the average lifespan of the healthy group. Likewise, the migrated people are healthier than the people already in the unhealthy set, so adding them raises the average lifespan of that group as well. Both lifespans are statistically lengthened, even if early detection of a cancer does not lead to better treatment - because it is detected earlier, more time is lived in the "unhealthy" set of people.
An example of better delineation of early stages and advanced stages lung cancer by means of fluoro-deoxy-glucose PET scans shows such an effect in practice.
External links
- “New Zealanders who emigrate to Australia raise the IQ of both countries.” – A quote by Sir Robert MuldoonRobert MuldoonSir Robert David "Rob" Muldoon, GCMG, CH served as the 31st Prime Minister of New Zealand from 1975 to 1984, as leader of the governing National Party. Muldoon had been a prominent member of the National party and MP for the Tamaki electorate for some years prior to becoming leader of the party...