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Statistics
are
persuasive
So much so that
people
organizations
and
whole
countries
Base
some of
their
most
important
decisions
on
organized
data
But
there's
a
problem
with
that
Any
set
of
statistics
might
have
something
lurking
inside
it
Something
that
can
turn
the
results
completely
upside down
For
example
imagine
you
need
to
choose
between
two
hospitals
For
an
elderly
relative's
surgery
Out of
each
hospital's
last
1000
patient's
900
survived
at
Hospital
A
While
only
800
survived
at
Hospital
B
So
it
looks
like
Hospital
A
is
the
better
choice
But
before
you
make your decision
Remember
that
not
all
patients
arrive
at
the
hospital
With
the
same
level
of
health
And
if
we
divide
each
hospital's
last
1000
patients
Into
those
who
arrived
in good health
and
those
Who
arrived
in poor health
The
picture
starts
to
look
very
different
Hospital
A
had
only
100
patients
who
arrived
in poor health
Of which
30
survived
But
Hospital
B
had
400
and
they
were
able
to
save
210
So
Hospital
B
is
the
better
choice
For
patients
who
arrive
at
hospital
in poor health
With
a
survival
rate
of
525%
And
what
if
your
relative's
health
is
good
When
she
arrives
at
the
hospital?
Strangely enough
Hospital
B
is
still
the
better
choice
With
a
survival
rate
of
over
98%
So
how
can
Hospital
A
have
a
better
overall
survival
rate
If
Hospital
B
has
better
survival
rates
for
patients
In
each
of
the
two
groups
?
What
we've
stumbled upon
is
a
case of
Simpson's
paradox
Where
the
same
set
of
data
can
appear
to
show
opposite
trends
Depending
on
how
it's
grouped
This
often
occurs
when
aggregated
data
hides
a
conditional
variable
Sometimes
known as
a
lurking
variable
Which is a
hidden
additional
factor
that significantly influences
results
Here
the
hidden
factor
is
the
relative
proportion
of
patients
Who
arrive
in
good
or
poor health
Simpson's
paradox
isn't
just
a
hypothetical
scenario
It
pops
up
from time to time
in
the
real
world
Sometimes
in
important
contexts
One
study
in
the
UK
appeared to
show
That
smokers
had
a
higher
survival
rate
than
nonsmokers
Over
a
twenty-year
time period
That is
until
dividing
the
participants
by
age
group
Showed
that
the
nonsmokers
were
significantly
older
on average
And
thus
more likely to
die
during
the
trial
period
Precisely
because
they
were
living
longer
in general
Here
the
age
groups
are
the
lurking
variable
And
are
vital
to
correctly
interpret
the
data
In
another
example
An
analysis
of
Florida's
death penalty
cases
Seemed
to
reveal
no
racial
disparity
in
sentencing
Between
black
and
white
defendants
convicted
of
murder
But
dividing
the
cases
by
the
race
of
the
victim
told
a
different
story
In
either
situation
Black
defendants
were
more likely to
be
sentenced
to
death
The
slightly
higher
overall
sentencing
rate
for
white
defendants
Was
due to the fact that
cases
with
white
victims
Were
more likely to
elicit
a
death
sentence
Than
cases
where
the
victim
was
black
And
most
murders
occurred
between
people
of
the
same
race
So
how
do
we
avoid
falling for
the
paradox?
Unfortunately
there's
no one-size-fits-all
answer
Data
can
be
grouped
and
divided
in
any
number
of
ways
And
overall
numbers
may
sometimes
give
a
more
accurate
picture
Than
data
divided
into
misleading
or
arbitrary
categories
All
we
can
do
is
carefully
study
the
actual
situations
The
statistics
describe
And
consider
whether lurking variables
may
be
present
Otherwise
we
leave
ourselves
vulnerable to
those
who
would
use
data
To
manipulate
others
and
promote
their
own
agendas