(ROOT (S (NP (DT The) (NML (NNP Will) (NNP Rogers)) (NN phenomenon)) (VP (VBZ is) (VP (VBN obtained) (SBAR (WHADVP (WRB when)) (S (S (VP (VBG moving) (NP (DT an) (NN element)) (PP (IN from) (NP (CD one) (NN set))) (PP (IN to) (NP (DT another) (NN set))))) (VP (VBZ raises) (NP (NP (DT the) (JJ average) (NNS values)) (PP (IN of) (NP (DT both) (NNS sets))))))))) (. .)))
The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average values of both sets.
det
Definite=Def|PronType=Art
the
The
DET
DT
compound
Number=Sing
Will
Will
PROPN
NNP
flat
Number=Sing
Rogers
Rogers
PROPN
NNP
nsubj:pass
Number=Sing
phenomenon
phenomenon
NOUN
NN
aux:pass
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
root
Tense=Past|VerbForm=Part|Voice=Pass
obtain
obtained
VERB
VBN
advmod
PronType=Int
when
when
ADV
WRB
csubj
VerbForm=Ger
move
moving
VERB
VBG
det
Definite=Ind|PronType=Art
a
an
DET
DT
obj
Number=Sing
element
element
NOUN
NN
case
from
from
ADP
IN
nummod
NumForm=Word|NumType=Card
one
one
NUM
CD
obl
Number=Sing
set
set
NOUN
NN
case
to
to
ADP
IN
det
another
another
DET
DT
nmod
Number=Sing
set
set
NOUN
NN
advcl
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
raise
raises
VERB
VBZ
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
average
average
ADJ
JJ
obj
Number=Plur
value
values
NOUN
NNS
case
of
of
ADP
IN
det
both
both
DET
DT
nmod
Number=Plur
set
sets
NOUN
NNS
punct
.
.
PUNCT
.
(ROOT (S (NP (PRP It)) (VP (VBZ is) (VP (VBN based) (PP (IN on) (NP (NP (DT the) (VBG following) (NN quote)) (, ,) (VP (VBN attributed) (PP (IN to) (NP (NN comedian) (NNP Will) (NNP Rogers)))))))) (: :)))
It is based on the following quote, attributed to comedian Will Rogers:
nsubj
Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs
it
It
PRON
PRP
cop
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
case
Tense=Past|VerbForm=Part|Voice=Pass
base
based
VERB
VBN
case
on
on
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
VerbForm=Ger
follow
following
VERB
VBG
root
Number=Sing
quote
quote
NOUN
NN
punct
,
,
PUNCT
,
acl
Tense=Past|VerbForm=Part
attribute
attributed
VERB
VBN
case
to
to
ADP
IN
obl
Number=Sing
comedian
comedian
NOUN
NN
flat
Number=Sing
Will
Will
PROPN
NNP
flat
Number=Sing
Rogers
Rogers
PROPN
NNP
punct
:
:
PUNCT
:
(ROOT (S (NP (DT The) (NN effect)) (VP (MD will) (VP (VB occur) (SBAR (WHADVP (WRB when)) (S (NP (NP (DT both)) (PP (IN of) (NP (DT these) (NNS conditions)))) (VP (VBP are) (VP (VBN met))))))) (: :)))
The effect will occur when both of these conditions are met:
det
Definite=Def|PronType=Art
the
The
DET
DT
nsubj
Number=Sing
effect
effect
NOUN
NN
aux
VerbForm=Fin
will
will
AUX
MD
root
VerbForm=Inf
occur
occur
VERB
VB
advmod
PronType=Int
when
when
ADV
WRB
nsubj:pass
both
both
DET
DT
case
of
of
ADP
IN
det
Number=Plur|PronType=Dem
this
these
DET
DT
nmod
Number=Plur
condition
conditions
NOUN
NNS
aux:pass
Mood=Ind|Number=Plur|Person=3|Tense=Pres|VerbForm=Fin
be
are
AUX
VBP
advcl
Tense=Past|VerbForm=Part|Voice=Pass
meet
met
VERB
VBN
punct
:
:
PUNCT
:
(ROOT (S (NP (NP (DT All)) (PP (IN of) (NP (DT this))) (PP (IN of) (NP (NN course)))) (ADVP (RB also)) (VP (VBZ works) (NP (DT the) (JJ other) (NN way) (RB around))) (. .)))
All of this of course also works the other way around.
nsubj
all
All
DET
DT
case
of
of
ADP
IN
nmod
Number=Sing|PronType=Dem
this
this
PRON
DT
advmod
ExtPos=ADV
of
of
ADP
IN
fixed
Number=Sing
course
course
NOUN
NN
advmod
also
also
ADV
RB
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
work
works
VERB
VBZ
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
other
other
ADJ
JJ
obl:npmod
Number=Sing
way
way
NOUN
NN
advmod
around
around
ADV
RB
punct
.
.
PUNCT
.
(ROOT (S (VP (VB Consider) (NP (NP (DT the) (NNS sets)) (NP (NNP R) (CC and) (NNP S))))))
Consider the sets R and S
root
Mood=Imp|VerbForm=Fin
consider
Consider
VERB
VB
det
Definite=Def|PronType=Art
the
the
DET
DT
obj
Number=Plur
set
sets
NOUN
NNS
appos
Number=Sing
R
R
PROPN
NNP
cc
and
and
CCONJ
CC
conj
Number=Sing
S
S
PROPN
NNP
(ROOT (S (S (NP (DT The) (NN arithmetic)) (VP (VBP mean) (PP (IN of) (S (NP (NNP R)) (VP (VBZ is) (NP (CD 2.5))))))) (, ,) (CC and) (S (S (NP (DT the) (NN arithmetic)) (VP (VBP mean) (PP (IN of) (NP (NNP S))))) (VP (VBZ is) (NP (CD 7)))) (. .)))
The arithmetic mean of R is 2.5, and the arithmetic mean of S is 7.
det
Definite=Def|PronType=Art
the
The
DET
DT
nsubj
Number=Sing
arithmetic
arithmetic
NOUN
NN
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
mean
mean
VERB
VBP
case
of
of
ADP
IN
obl
Number=Sing
R
R
PROPN
NNP
cop
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
ccomp
NumForm=Digit|NumType=Frac
2.5
2.5
NUM
CD
punct
,
,
PUNCT
,
cc
and
and
CCONJ
CC
det
Definite=Def|PronType=Art
the
the
DET
DT
nsubj
Number=Sing
arithmetic
arithmetic
NOUN
NN
acl
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
mean
mean
VERB
VBP
case
of
of
ADP
IN
obl
Number=Sing
S
S
PROPN
NNP
cop
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
conj
NumForm=Digit|NumType=Card
7
7
NUM
CD
punct
.
.
PUNCT
.
(ROOT (S (ADVP (RB However)) (, ,) (SBAR (IN if) (S (NP (CD 5)) (VP (VBZ is) (VP (VBN moved) (PP (PP (IN from) (NP (NNP S))) (PP (IN to) (NP (NNP R)))))))) (, ,) (VP (VBG producing))))
However, if 5 is moved from S to R, producing
advmod
however
However
ADV
RB
punct
,
,
PUNCT
,
mark
if
if
SCONJ
IN
nsubj:pass
NumForm=Digit|NumType=Card
5
5
NUM
CD
aux:pass
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
root
Tense=Past|VerbForm=Part|Voice=Pass
move
moved
VERB
VBN
case
from
from
ADP
IN
obl
Number=Sing
S
S
PROPN
NNP
case
to
to
ADP
IN
obl
Number=Sing
R
R
PROPN
NNP
punct
,
,
PUNCT
,
advcl
VerbForm=Ger
produce
producing
VERB
VBG
(ROOT (S (ADVP (RB then)) (S (NP (DT the) (NN arithmetic)) (VP (VBP mean) (PP (IN of) (NP (NN R)))) (VP (VBZ increases) (PP (IN to) (NP (CD 3))))) (, ,) (CC and) (S (NP (NP (DT the) (NN arithmetic) (NN mean)) (PP (IN of) (NP (NN S)))) (VP (VBZ increases) (PP (IN to) (NP (CD 7.5))))) (. .)))
then the arithmetic mean of R increases to 3, and the arithmetic mean of S increases to 7.5.
advmod
PronType=Dem
then
then
ADV
RB
det
Definite=Def|PronType=Art
the
the
DET
DT
nsubj
Number=Sing
arithmetic
arithmetic
NOUN
NN
nsubj
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
mean
mean
VERB
VBP
case
of
of
ADP
IN
obl
Number=Sing
R
R
NOUN
NN
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
increase
increases
VERB
VBZ
case
to
to
ADP
IN
obl
NumForm=Digit|NumType=Card
3
3
NUM
CD
punct
,
,
PUNCT
,
cc
and
and
CCONJ
CC
det
Definite=Def|PronType=Art
the
the
DET
DT
compound
Number=Sing
arithmetic
arithmetic
NOUN
NN
nsubj
Number=Sing
mean
mean
NOUN
NN
case
of
of
ADP
IN
nmod
Number=Sing
S
S
NOUN
NN
conj
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
increase
increases
VERB
VBZ
case
to
to
ADP
IN
obl
NumForm=Digit|NumType=Frac
7.5
7.5
NUM
CD
punct
.
.
PUNCT
.
(ROOT (S (VP (VB Consider) (NP (DT this) (ADJP (RBR more) (JJ illustrative)) (NN example))) (: :)))
Consider this more illustrative example:
root
Mood=Imp|Person=2|VerbForm=Fin
consider
Consider
VERB
VB
det
Number=Sing|PronType=Dem
this
this
DET
DT
advmod
Degree=Cmp
more
more
ADV
RBR
amod
Degree=Pos
illustrative
illustrative
ADJ
JJ
obj
Number=Sing
example
example
NOUN
NN
punct
:
:
PUNCT
:
(ROOT (S (PP (IN with) (NP (NN arithmetic))) (VP (VBZ means)) (NP (CD 1.5) (CC and) (CD 10033)) (. .)))
with arithmetic means 1.5 and 10033.
case
with
with
ADP
IN
obl
Number=Sing
arithmetic
arithmetic
NOUN
NN
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
mean
means
VERB
VBZ
obj
NumForm=Digit|NumType=Frac
1.5
1.5
NUM
CD
cc
and
and
CCONJ
CC
conj
NumForm=Digit|NumType=Card
10033
10033
NUM
CD
punct
.
.
PUNCT
.
(ROOT (S (S (VP (VBG Moving) (NP (CD 99)) (PP (IN from) (NP (NN S))) (PP (IN to) (NP (NNP R))))) (VP (VBZ gives) (NP (NNS means) (CD 34) (CC and) (CD 15000))) (. .)))
Moving 99 from S to R gives means 34 and 15000.
csubj
VerbForm=Ger
move
Moving
VERB
VBG
obj
NumForm=Digit|NumType=Card
99
99
NUM
CD
case
from
from
ADP
IN
obl
Number=Sing
S
S
NOUN
NN
case
to
to
ADP
IN
obl
Number=Sing
R
R
PROPN
NNP
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
give
gives
VERB
VBZ
obj
Number=Plur
means
means
NOUN
NNS
nummod
NumForm=Digit|NumType=Card
34
34
NUM
CD
cc
and
and
CCONJ
CC
conj
NumForm=Digit|NumType=Card
15000
15000
NUM
CD
punct
.
.
PUNCT
.
(ROOT (S (NP (CD 99)) (VP (VBZ is) (NP (NP (NNS orders)) (PP (IN of) (NP (NP (NP (NN magnitude)) (PP (IN above) (NP (CD 1) (CC and) (CD 2)))) (, ,) (CC and) (NP (NP (NNS orders)) (PP (IN of) (NP (NP (NN magnitude)) (PP (IN below) (NP (CD 10000) (CC and) (CD 20000)))))))))) (. .)))
99 is orders of magnitude above 1 and 2, and orders of magnitude below 10000 and 20000.
root
NumForm=Digit|NumType=Card
99
99
NUM
CD
cop
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
appos
Number=Plur
order
orders
NOUN
NNS
case
of
of
ADP
IN
nmod
Number=Sing
magnitude
magnitude
NOUN
NN
case
above
above
ADP
IN
nmod
NumForm=Digit|NumType=Card
1
1
NUM
CD
cc
and
and
CCONJ
CC
conj
NumForm=Digit|NumType=Card
2
2
NUM
CD
punct
,
,
PUNCT
,
cc
and
and
CCONJ
CC
conj
Number=Plur
order
orders
NOUN
NNS
case
of
of
ADP
IN
nmod
Number=Sing
magnitude
magnitude
NOUN
NN
case
below
below
ADP
IN
nmod
NumForm=Digit|NumType=Card
10000
10000
NUM
CD
cc
and
and
CCONJ
CC
conj
NumForm=Digit|NumType=Card
20000
20000
NUM
CD
punct
.
.
PUNCT
.
(ROOT (S (NP (NP (PRP It))) (VP (MD should) (VP (VB come) (PP (IN as) (NP (DT no) (NN surprise))) (SBAR (IN that) (S (NP (NP (DT the) (NN transfer)) (PP (IN of) (NP (CD 99)))) (VP (VBZ increases) (NP (NP (DT the) (NN mean)) (PP (IN of) (NP (CC both) (NNP R) (CC and) (NNP S))))))))) (. .)))
It should come as no surprise that the transfer of 99 increases the mean of both R and S.
expl
Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs
it
It
PRON
PRP
aux
VerbForm=Fin
should
should
AUX
MD
root
VerbForm=Inf
come
come
VERB
VB
case
as
as
ADP
IN
det
no
no
DET
DT
obl
Number=Sing
surprise
surprise
NOUN
NN
mark
that
that
SCONJ
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
nsubj
Number=Sing
transfer
transfer
NOUN
NN
case
of
of
ADP
IN
nmod
NumForm=Digit|NumType=Card
99
99
NUM
CD
acl
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
increase
increases
VERB
VBZ
det
Definite=Def|PronType=Art
the
the
DET
DT
obj
Number=Sing
mean
mean
NOUN
NN
case
of
of
ADP
IN
cc:preconj
both
both
CCONJ
CC
nmod
Number=Sing
R
R
PROPN
NNP
cc
and
and
CCONJ
CC
conj
Number=Sing
S
S
PROPN
NNP
punct
.
.
PUNCT
.
(ROOT (S (NP (NP (DT The) (NN element)) (SBAR (WHNP (WDT which)) (S (VP (VBZ is) (VP (VBN moved)))))) (VP (VBZ does) (RB not) (VP (VB have) (S (VP (TO to) (VP (VB be) (NP (NP (DT the) (ADJP (JJ very) (JJS lowest))) (PP (IN of) (NP (PRP$ its) (NN set))))))))) (. .)))
The element which is moved does not have to be the very lowest of its set.
det
Definite=Def|PronType=Art
the
The
DET
DT
nsubj
Number=Sing
element
element
NOUN
NN
nsubj:pass
PronType=Rel
which
which
PRON
WDT
aux:pass
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
acl:relcl
Tense=Past|VerbForm=Part|Voice=Pass
move
moved
VERB
VBN
aux
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
do
does
AUX
VBZ
advmod
not
not
PART
RB
root
VerbForm=Inf
have
have
VERB
VB
mark
to
to
PART
TO
cop
VerbForm=Inf
be
be
AUX
VB
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
very
very
ADJ
JJ
xcomp
Degree=Sup
low
lowest
ADJ
JJS
case
of
of
ADP
IN
nmod:poss
Case=Gen|Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs
its
its
PRON
PRP$
obl
Number=Sing
set
set
NOUN
NN
punct
.
.
PUNCT
.
(ROOT (S (VP (VB Consider) (NP (DT this) (NN example))) (: :)))
Consider this example:
root
Mood=Imp|Person=2|VerbForm=Fin
consider
Consider
VERB
VB
det
Number=Sing|PronType=Dem
this
this
DET
DT
obj
Number=Sing
example
example
NOUN
NN
punct
:
:
PUNCT
:
(ROOT (S (S (VP (VBG Moving) (NP (CD 10)) (PP (IN from) (NP (NN S))) (PP (IN to) (NP (NNP R))))) (VP (MD will) (VP (VP (VB raise) (NP (NP (DT the) (NN mean)) (PP (IN of) (NP (NNP R)))) (PP (IN from) (NP (CD 7))) (PP (IN to) (NP (CD 7.375)))) (, ,) (CC and) (NP (NP (DT the) (NN mean)) (PP (IN of) (NP (NN S))) (PP (PP (IN from) (NP (CD 12))) (PP (IN to) (NP (CD 12.333))))))) (. .)))
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.
csubj
VerbForm=Ger
move
Moving
VERB
VBG
obj
NumForm=Digit|NumType=Card
10
10
NUM
CD
case
from
from
ADP
IN
obl
Number=Sing
S
S
NOUN
NN
case
to
to
ADP
IN
obl
Number=Sing
R
R
PROPN
NNP
aux
VerbForm=Fin
will
will
AUX
MD
root
VerbForm=Inf
raise
raise
VERB
VB
det
Definite=Def|PronType=Art
the
the
DET
DT
obj
Number=Sing
mean
mean
NOUN
NN
case
of
of
ADP
IN
nmod
Number=Sing
R
R
PROPN
NNP
case
from
from
ADP
IN
obl
NumForm=Digit|NumType=Card
7
7
NUM
CD
case
to
to
ADP
IN
obl
NumForm=Digit|NumType=Card
7.375
7.375
NUM
CD
punct
,
,
PUNCT
,
cc
and
and
CCONJ
CC
det
Definite=Def|PronType=Art
the
the
DET
DT
conj
Number=Sing
mean
mean
NOUN
NN
case
of
of
ADP
IN
nmod
Number=Sing
S
S
NOUN
NN
case
from
from
ADP
IN
nmod
NumForm=Digit|NumType=Card
12
12
NUM
CD
case
to
to
ADP
IN
nmod
NumForm=Digit|NumType=Card
12.333
12.333
NUM
CD
punct
.
.
PUNCT
.
(ROOT (S (NP (DT The) (NN effect)) (ADVP (RB still)) (VP (VP (VBZ occurs)) (, ,) (CC but) (ADVP (RBR less) (RB dramatically))) (. .)))
The effect still occurs, but less dramatically.
det
Definite=Def|PronType=Art
the
The
DET
DT
nsubj
Number=Sing
effect
effect
NOUN
NN
advmod
still
still
ADV
RB
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
occur
occurs
VERB
VBZ
punct
,
,
PUNCT
,
cc
but
but
CCONJ
CC
advmod
Degree=Cmp
less
less
ADV
RBR
conj
dramatically
dramatically
ADV
RB
punct
.
.
PUNCT
.
(ROOT (S (NP (NP (CD One) (JJ real-world) (NN example)) (PP (IN of) (NP (DT the) (NML (NNP Will) (NNP Rogers)) (NN phenomenon)))) (VP (VBZ is) (VP (VBN seen) (PP (IN in) (NP (NP (DT the) (JJ medical) (NN concept)) (PP (IN of) (NP (NN stage) (NN migration))))))) (. .)))
One real-world example of the Will Rogers phenomenon is seen in the medical concept of stage migration.
nummod
NumForm=Word|NumType=Card
one
One
NUM
CD
amod
Degree=Pos
real-world
real-world
ADJ
JJ
nsubj:pass
Number=Sing
example
example
NOUN
NN
case
of
of
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
compound
Number=Sing
Will
Will
PROPN
NNP
flat
Number=Sing
Rogers
Rogers
PROPN
NNP
nmod
Number=Sing
phenomenon
phenomenon
NOUN
NN
aux:pass
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
root
Tense=Past|VerbForm=Part|Voice=Pass
see
seen
VERB
VBN
case
in
in
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
medical
medical
ADJ
JJ
obl
Number=Sing
concept
concept
NOUN
NN
case
of
of
ADP
IN
compound
Number=Sing
stage
stage
NOUN
NN
nmod
Number=Sing
migration
migration
NOUN
NN
punct
.
.
PUNCT
.
(ROOT (S (PP (IN In) (NP (NML (JJ medical) (NN stage)) (NN migration))) (, ,) (NP (NP (VBN improved) (NN detection)) (PP (IN of) (NP (NN illness)))) (VP (VBZ leads) (PP (IN to) (NP (NP (DT the) (NN movement)) (PP (PP (IN of) (NP (NP (NNS people)) (PP (IN from) (NP (NP (DT the) (NN set)) (PP (IN of) (NP (JJ healthy) (NNS people))))))) (PP (IN to) (NP (NP (DT the) (NN set)) (PP (IN of) (NP (JJ unhealthy) (NNS people))))))))) (. .)))
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.
case
in
In
ADP
IN
amod
Degree=Pos
medical
medical
ADJ
JJ
compound
Number=Sing
stage
stage
NOUN
NN
obl
Number=Sing
migration
migration
NOUN
NN
punct
,
,
PUNCT
,
amod
Tense=Past|VerbForm=Part
improve
improved
VERB
VBN
nsubj
Number=Sing
detection
detection
NOUN
NN
case
of
of
ADP
IN
nmod
Number=Sing
illness
illness
NOUN
NN
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
lead
leads
VERB
VBZ
case
to
to
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
obl
Number=Sing
movement
movement
NOUN
NN
case
of
of
ADP
IN
nmod
Number=Plur
person
people
NOUN
NNS
case
from
from
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
nmod
Number=Sing
set
set
NOUN
NN
case
of
of
ADP
IN
amod
Degree=Pos
healthy
healthy
ADJ
JJ
nmod
Number=Plur
person
people
NOUN
NNS
case
to
to
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
obl
Number=Sing
set
set
NOUN
NN
case
of
of
ADP
IN
amod
Degree=Pos
unhealthy
unhealthy
ADJ
JJ
nmod
Number=Plur
person
people
NOUN
NNS
punct
.
.
PUNCT
.
(ROOT (S (SBAR (IN Because) (S (NP (DT these) (NNS people)) (VP (VBP are) (RB not) (ADJP (JJ healthy))))) (, ,) (S (VP (VBG removing) (NP (PRP them)) (PP (IN from) (NP (NP (DT the) (NN set)) (PP (IN of) (NP (JJ healthy) (NNS people))))))) (VP (VBZ increases) (NP (NP (DT the) (JJ average) (NN lifespan)) (PP (IN of) (NP (DT the) (JJ healthy) (NN group))))) (. .)))
Because these people are not healthy, removing them from the set of healthy people increases the average lifespan of the healthy group.
mark
because
Because
SCONJ
IN
det
Number=Plur|PronType=Dem
this
these
DET
DT
nsubj
Number=Plur
person
people
NOUN
NNS
cop
Mood=Ind|Number=Plur|Person=3|Tense=Pres|VerbForm=Fin
be
are
AUX
VBP
advmod
not
not
PART
RB
advcl
Degree=Pos
healthy
healthy
ADJ
JJ
punct
,
,
PUNCT
,
csubj
VerbForm=Ger
remove
removing
VERB
VBG
obj
Case=Acc|Number=Plur|Person=3|PronType=Prs
they
them
PRON
PRP
case
from
from
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
obl
Number=Sing
set
set
NOUN
NN
case
of
of
ADP
IN
amod
Degree=Pos
healthy
healthy
ADJ
JJ
nmod
Number=Plur
person
people
NOUN
NNS
root
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
increase
increases
VERB
VBZ
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
average
average
ADJ
JJ
obj
Number=Sing
lifespan
lifespan
NOUN
NN
case
of
of
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
healthy
healthy
ADJ
JJ
nmod
Number=Sing
group
group
NOUN
NN
punct
.
.
PUNCT
.
(ROOT (S (ADVP (RB Likewise)) (, ,) (NP (DT the) (VBN migrated) (NNS people)) (VP (VBP are) (ADJP (ADJP (RBR more) (JJ healthy)) (PP (IN than) (NP (NP (DT the) (NNS people)) (ADVP (RB already)) (PP (IN in) (NP (DT the) (JJ unhealthy) (NN set)))))) (, ,) (RB so) (S (VP (VBG adding) (SBAR (S (NP (PRP them)) (VP (VBZ raises) (NP (NP (DT the) (JJ average) (NN lifespan)) (PP (IN of) (NP (DT that) (NN group)))) (ADVP (RB as) (RB well)))))))) (. .)))
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.
advmod
likewise
Likewise
ADV
RB
punct
,
,
PUNCT
,
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Tense=Past|VerbForm=Part
migrate
migrated
VERB
VBN
nsubj
Number=Plur
person
people
NOUN
NNS
cop
Mood=Ind|Number=Plur|Person=3|Tense=Pres|VerbForm=Fin
be
are
AUX
VBP
advmod
Degree=Cmp
more
more
ADV
RBR
root
Degree=Pos
healthy
healthy
ADJ
JJ
case
than
than
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
obl
Number=Plur
person
people
NOUN
NNS
advmod
already
already
ADV
RB
case
in
in
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
unhealthy
unhealthy
ADJ
JJ
nmod
Number=Sing
set
set
NOUN
NN
punct
,
,
PUNCT
,
advmod
so
so
ADV
RB
csubj
VerbForm=Ger
add
adding
VERB
VBG
obj
Case=Acc|Number=Plur|Person=3|PronType=Prs
they
them
PRON
PRP
parataxis
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
raise
raises
VERB
VBZ
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
average
average
ADJ
JJ
obj
Number=Sing
lifespan
lifespan
NOUN
NN
case
of
of
ADP
IN
det
Number=Sing|PronType=Dem
that
that
DET
DT
nmod
Number=Sing
group
group
NOUN
NN
advmod
as
as
ADV
RB
fixed
Degree=Pos
well
well
ADV
RB
punct
.
.
PUNCT
.
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.