sentences.text: The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average values of both sets.
sentences.text: The
sentences.text: Will
sentences.text: Rogers
sentences.text: phenomenon
sentences.text: is
sentences.text: obtained
sentences.text: when
sentences.text: moving
sentences.text: an
sentences.text: element
sentences.text: from
sentences.text: one
sentences.text: set
sentences.text: to
sentences.text: another
sentences.text: set
sentences.text: raises
sentences.text: the
sentences.text: average
sentences.text: values
sentences.text: of
sentences.text: both
sentences.text: sets
sentences.text: .
sentences.text: It is based on the following quote, attributed to comedian Will Rogers:
sentences.text: It
sentences.text: is
sentences.text: based
sentences.text: on
sentences.text: the
sentences.text: following
sentences.text: quote
sentences.text: ,
sentences.text: attributed
sentences.text: to
sentences.text: comedian
sentences.text: Will
sentences.text: Rogers
sentences.text: :
sentences.text: The effect will occur when both of these conditions are met:
sentences.text: The
sentences.text: effect
sentences.text: will
sentences.text: occur
sentences.text: when
sentences.text: both
sentences.text: of
sentences.text: these
sentences.text: conditions
sentences.text: are
sentences.text: met
sentences.text: :
sentences.text: All of this of course also works the other way around.
sentences.text: All
sentences.text: of
sentences.text: this
sentences.text: of
sentences.text: course
sentences.text: also
sentences.text: works
sentences.text: the
sentences.text: other
sentences.text: way
sentences.text: around
sentences.text: .
sentences.text: Consider the sets R and S
sentences.text: Consider
sentences.text: the
sentences.text: sets
sentences.text: R
sentences.text: and
sentences.text: S
sentences.text: The arithmetic mean of R is 2.5, and the arithmetic mean of S is 7.
sentences.text: The
sentences.text: arithmetic
sentences.text: mean
sentences.text: of
sentences.text: R
sentences.text: is
sentences.text: 2.5
sentences.text: ,
sentences.text: and
sentences.text: the
sentences.text: arithmetic
sentences.text: mean
sentences.text: of
sentences.text: S
sentences.text: is
sentences.text: 7
sentences.text: .
sentences.text: However, if 5 is moved from S to R, producing
sentences.text: However
sentences.text: ,
sentences.text: if
sentences.text: 5
sentences.text: is
sentences.text: moved
sentences.text: from
sentences.text: S
sentences.text: to
sentences.text: R
sentences.text: ,
sentences.text: producing
sentences.text: then the arithmetic mean of R increases to 3, and the arithmetic mean of S increases to 7.5.
sentences.text: then
sentences.text: the
sentences.text: arithmetic
sentences.text: mean
sentences.text: of
sentences.text: R
sentences.text: increases
sentences.text: to
sentences.text: 3
sentences.text: ,
sentences.text: and
sentences.text: the
sentences.text: arithmetic
sentences.text: mean
sentences.text: of
sentences.text: S
sentences.text: increases
sentences.text: to
sentences.text: 7.5
sentences.text: .
sentences.text: Consider this more illustrative example:
sentences.text: Consider
sentences.text: this
sentences.text: more
sentences.text: illustrative
sentences.text: example
sentences.text: :
sentences.text: with arithmetic means 1.5 and 10033.
sentences.text: with
sentences.text: arithmetic
sentences.text: means
sentences.text: 1.5
sentences.text: and
sentences.text: 10033
sentences.text: .
sentences.text: Moving 99 from S to R gives means 34 and 15000.
sentences.text: Moving
sentences.text: 99
sentences.text: from
sentences.text: S
sentences.text: to
sentences.text: R
sentences.text: gives
sentences.text: means
sentences.text: 34
sentences.text: and
sentences.text: 15000
sentences.text: .
sentences.text: 99 is orders of magnitude above 1 and 2, and orders of magnitude below 10000 and 20000.
sentences.text: 99
sentences.text: is
sentences.text: orders
sentences.text: of
sentences.text: magnitude
sentences.text: above
sentences.text: 1
sentences.text: and
sentences.text: 2
sentences.text: ,
sentences.text: and
sentences.text: orders
sentences.text: of
sentences.text: magnitude
sentences.text: below
sentences.text: 10000
sentences.text: and
sentences.text: 20000
sentences.text: .
sentences.text: It should come as no surprise that the transfer of 99 increases the mean of both R and S.
sentences.text: It
sentences.text: should
sentences.text: come
sentences.text: as
sentences.text: no
sentences.text: surprise
sentences.text: that
sentences.text: the
sentences.text: transfer
sentences.text: of
sentences.text: 99
sentences.text: increases
sentences.text: the
sentences.text: mean
sentences.text: of
sentences.text: both
sentences.text: R
sentences.text: and
sentences.text: S
sentences.text: .
sentences.text: The element which is moved does not have to be the very lowest of its set.
sentences.text: The
sentences.text: element
sentences.text: which
sentences.text: is
sentences.text: moved
sentences.text: does
sentences.text: not
sentences.text: have
sentences.text: to
sentences.text: be
sentences.text: the
sentences.text: very
sentences.text: lowest
sentences.text: of
sentences.text: its
sentences.text: set
sentences.text: .
sentences.text: Consider this example:
sentences.text: Consider
sentences.text: this
sentences.text: example
sentences.text: :
sentences.text: 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.
sentences.text: Moving
sentences.text: 10
sentences.text: from
sentences.text: S
sentences.text: to
sentences.text: R
sentences.text: will
sentences.text: raise
sentences.text: the
sentences.text: mean
sentences.text: of
sentences.text: R
sentences.text: from
sentences.text: 7
sentences.text: to
sentences.text: 7.375
sentences.text: ,
sentences.text: and
sentences.text: the
sentences.text: mean
sentences.text: of
sentences.text: S
sentences.text: from
sentences.text: 12
sentences.text: to
sentences.text: 12.333
sentences.text: .
sentences.text: The effect still occurs, but less dramatically.
sentences.text: The
sentences.text: effect
sentences.text: still
sentences.text: occurs
sentences.text: ,
sentences.text: but
sentences.text: less
sentences.text: dramatically
sentences.text: .
sentences.text: One real-world example of the Will Rogers phenomenon is seen in the medical concept of stage migration.
sentences.text: One
sentences.text: real-world
sentences.text: example
sentences.text: of
sentences.text: the
sentences.text: Will
sentences.text: Rogers
sentences.text: phenomenon
sentences.text: is
sentences.text: seen
sentences.text: in
sentences.text: the
sentences.text: medical
sentences.text: concept
sentences.text: of
sentences.text: stage
sentences.text: migration
sentences.text: .
sentences.text: 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.
sentences.text: In
sentences.text: medical
sentences.text: stage
sentences.text: migration
sentences.text: ,
sentences.text: improved
sentences.text: detection
sentences.text: of
sentences.text: illness
sentences.text: leads
sentences.text: to
sentences.text: the
sentences.text: movement
sentences.text: of
sentences.text: people
sentences.text: from
sentences.text: the
sentences.text: set
sentences.text: of
sentences.text: healthy
sentences.text: people
sentences.text: to
sentences.text: the
sentences.text: set
sentences.text: of
sentences.text: unhealthy
sentences.text: people
sentences.text: .
sentences.text: Because these people are not healthy, removing them from the set of healthy people increases the average lifespan of the healthy group.
sentences.text: Because
sentences.text: these
sentences.text: people
sentences.text: are
sentences.text: not
sentences.text: healthy
sentences.text: ,
sentences.text: removing
sentences.text: them
sentences.text: from
sentences.text: the
sentences.text: set
sentences.text: of
sentences.text: healthy
sentences.text: people
sentences.text: increases
sentences.text: the
sentences.text: average
sentences.text: lifespan
sentences.text: of
sentences.text: the
sentences.text: healthy
sentences.text: group
sentences.text: .
sentences.text: Likewise, the migrated people are more healthy than the people already in the unhealthy set, so adding them raises the average lifespan of that group as well.
sentences.text: Likewise
sentences.text: ,
sentences.text: the
sentences.text: migrated
sentences.text: people
sentences.text: are
sentences.text: more
sentences.text: healthy
sentences.text: than
sentences.text: the
sentences.text: people
sentences.text: already
sentences.text: in
sentences.text: the
sentences.text: unhealthy
sentences.text: set
sentences.text: ,
sentences.text: so
sentences.text: adding
sentences.text: them
sentences.text: raises
sentences.text: the
sentences.text: average
sentences.text: lifespan
sentences.text: of
sentences.text: that
sentences.text: group
sentences.text: as
sentences.text: well
sentences.text: .
text: 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 to comedian Will Rogers: The effect will occur when both of these conditions are met: All of this of course also works the other way around. Consider the sets R and S 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. 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 more healthy than the people already in the unhealthy set, so adding them raises the average lifespan of that group as well.