Well,
thank
you
everyone
for
joining
me.
This
is
a
Discovery
Summit
2022
presentation,
courtesy
of
my
co-presenters,
Charles
Chen
and
Mason
Chen.
My
name
is
Patrick
Giuliano.
The
title
of
this
talk
is,
Box Plot A
nalysis:
Blending
Scientific
and
Artistic
Enquiry
in Uni
variate
Response
Characterization.
Here's
the
abstract.
You
can
find
this
on
the
JMP
User C
ommunity
in
the
Discovery
2022
community
page,
US D
iscovery
2022
community
page.
I'm
putting
it
here
for
reference.
I
will
provide
a
link
in
the
slides
to
the
community
page
where
the
project
will
live.
What's
the
motivation
for
this
project?
The
Box Plot
is
one
of
the
most
popular
graphical
tools
to
visualize
a
univariate
distribution
of
data.
This
project
studies
how
to
use
the
Box Plot
to
analyze
data
effectively.
Most
people
who
use
the
Box Plot
don't
use
it
necessarily
to
determine
the
shape
of
the
distribution
of
the
data.
In
fact,
many
people
use
it
wrongly
to
draw
mean
or
mean
comparison
decisions,
and
they
may
assume
normality
based
on
symmetry,
when
in
fact,
the
normality
assumption
would
actually
not
be
reasonable
if
they
were
to
take
a
closer
look
at
the
shape
of
the
data
on
a
histogram,
for
example.
The
objective
of
this
project
is
to
demonstrate
how
to
use
JMP
specifically
16,
to
interpret
information
in
a
Box Plot
and
to
improve
proficiency
in
a
global
community
of
scientists
and
engineers
that
are
really
under
a
DMEIC
or
APS,
or
Lean
type
Six
Sigma
methodology,
which
is
very
popular,
obviously,
today
and
over
the
last
few
decades.
The
interesting
thing
about
this
project
is
we
framed
it
in
the
context
of
17
quiz
questions.
This
is
a
question
and
answer
slide
deck.
And
I'm
not
going
to
go
into
too
much
detail
about
each
and
every
question,
whic
h
I
will
show
you
here.
But
what
I'd
like
to
do
is
show
you
a
little
bit
about
how
you
can
use
JMP
to
explore
the
answer
to
these
questions,
because
I
think
that's
really
the
most
interesting
and
fun
part.
The
first thing
I
wanted
to
do
is
just
quickly
go
over
what
a
Box Plot
is.
So
what
is
the
anatomy
of
a
Box Plot?
Just
as
a
refresher
for
some
of
you,
or
introduction
for
some
of
you,
the
median
is
indicated
by
the
midline,
and
it's
referred
to
as
the
second
quartile,
Q2
or
the
50th
percentile.
Then
Q1
is
referred
to
as
the
25th
percentile.
Q3
is
the
75th
percentile,
as
you
can
see
here.
The
interquartile
range,
or
IQR,
is
the
difference
between
Q3
and
Q1.
The
other
important
elements
are
we
have
what's
called
a
whisker
on
the
lower
side
and
on
the
upper
side.
Right at
the
end
of
that
whisker,
sometimes
we
refer
to
it
as
the fence
and
you'll
see
a
vertical
line
and
JMP
draws
a
vertical
line
to
indicate
that
edge.
What's
important
about
this
is
that
this
location
is
actually
Q1 minus
1.5
times
the
IQR,
which
is
represented
by
the
distance
between
this
edge and this edge.
This point
and
the
upper
fence
is
Q3 plus one
and
a
half
times
the
IQR.
So
that
defines
the
upper
edge.
Then
any
points
that
are
beyond
these
edges
or
fences
are
considered
potential
outliers.
And
they
actually
show
up
by
themselves
as
points
whereas
the
rest
of
the
data
in
the
middle
of
the
histogram
is
not
shown
for
emphasis
on
the
points
that
are
beyond
the
beyond
these
fences.
I'm
going
to
jump
right
in.
How
did
we
explore
and
develop
the
answers
to
these
questions,
and
in
some
cases,
even
refine
the
questions
themselves?
Well,
we
created
a
simulated
data
table in
JMP
16,
where
we
constructed
100
rows
of
data,
and
we
constructed
data,
first from
a
normal
distribution,
and
then
applied
some
transformation
to
that
data.
We
see
that
we
have
a
normally
distributed
data
drawn
from
a
population
the
mean
of
zero
and
a
standard deviation
of
one.
Then we
have
uniformly
distributed
data.
Then
we
have
data
that's
peaked,
i.e
has
a
positive
Kurtosis.
Then
we
have
data
that's
right
skewed,
has
two
modes,
has
some
outliers
about
3
%
on
average
and
then
integers.
In
all
the
cases,
with
the
exception
of
the
bimodal,
we
just
based
the
simulated
formula,
on
the
original
normal
column.
The
way
that
we
put
all
the
data
on
the
same
scale
is
we
use
the
column
standardized
function
so
that
we
could
compare
all
the
data
relative
to
each
other
in
the
distribution
platform.
This
is
just
a
preview
of
that.
I'll
jump
over
to
JMP
and
show
you
that.
But
again,
all
of
this
data
is
centered
at a mean of
approximately
zero
and
a
standard
deviation,
approximately
one.
We
covered
the
first question.
Why i
s
a
Box Plot,
sometimes
referred
to
as
a
five-
point
plot?
Well,
there
are
five
main
points
.
There's
Q1,
there's
Q2
in
the
middle,
there's
Q3,
and
then
there
are
the
whiskers,
the
upper
and
lower
.
Next
question.
What
are
the
two
ways
that
the
Box Plot
can
determine
whe
ther the
distribution
is
skewed?
Well,
we
can
look
at
the
width
of
the
box
itself.
We
can
also
look
at
the
width
of
the
whiskers.
In
this
right
skewed
example,
you
can
see
that
upper
whisker
is
much
longer
than
the
lower
one.
So
that
would
imply
that
the
data
is
right
skewed.
In
other
words,
that
the
tail
in
the
data,
if
you
were
to
imagine
that
distribution,
is
pointing
to
the
right.
Third, why
does
the
Box Plot include
the
median
and
not
the
mean?
Well,
a
Box Plot
uses
the
median
to
determine
or
gauge
skewness.
So
if
the
distribution
is
normal,
then
the
mean
is
equal
to
the
median.
And
in
fact,
what
you
would
see
here
is
that
this
median
line
in
the
middle
would
line
up
exactly
with
the
edges
of
this
diamond,
the
middle
of
this
diamond.
In
that
case,
you
would
effectively
have
a
situation
where
you're
not
really
losing
any
information
because
the
distribution is symmetric.
The
median
in
general,
then
might
be
considered
better,
regardless
of
whether
the
distribution
is
normal
or
non-normal.
Fourth,
why
is
the
Box
Plot
the
most
powerful
visualization
tool,
or
one
of
the
most
powerful
tools
to
separate
skewness
and
outlier
problems?
When
we
talked
about
this
idea
that
because
the
Box Plot
uses
this
Q1
minus
one
and
half
times
IQR
and
Q3 plus one
and
a
half
times
IQR
methodology,
it
really
allows
us
to
separate
potential
outliers
from
the
main
data.
It
also
gives
us
a
framework
by
which
to
judge
whether
the
upper
whisker
is
larger
or
smaller
than
a
lower
whisker.
So
those
two
components
of
the
plot
really
help
us,
rather,
see
if
we're
trained
skewness
and
potential
outlying
this.
This is
a
unique
feature
of
the
Box Plot.
The
fifth question
is
a
little
more
interesting.
What's
the
relationship
between
the
interquartile
range,
that
distance
between
Q1
and
Q3,
and
the
standard
deviation,
which
we
can
calculate
for
any
data
set,
regardless
of
how
it's
distributed?
If
the
data
is
normal,
what
about
if
the
data
is
skewed
or
non-normal
or
peaked
or
any
other
shape?
Well,
we
know,
based
on
theory,
that
the
ratio
of
the
IQR,
to the standard deviation
is
1.35
for
normal
data.
What
would
that
ratio
look
like
if
the
data
wasn't
normal?
Well,
we
can
explore
that
in
JMP,
and
I'm
going
to
show
you
that
really
quickly.
Here's
the
data
set.
I'm
also
going
to
post
this
on
the
community
.
The
first thing
I'm
going
to
do
is
go
ahead
and
show
you
how
I
get
to
a
visual
state
where
we
can
see
all
the
Box Plots
together,
without
the
distributions.
This
is
interesting,
but
I'm
going
to
go
ahead
and
start
from
the
beginning.
I'm
going
to
analyze
distribution.
I'm going to
show
you
how
I
got
there.
I'm
actually
going
to
click
everything,
and
JMP
is
going
to
give
me
a
histogram
and
a
Box Plot
together.
A
t
the
end
of
the
presentation,
we're
going
to
summarize
why
that's
important.
But
what
I'm
going
to
do
here
is
I'm
going
to
go
ahead
and
turn
off
the
histogram,
I
can
go
ahead
and
customize
the
width
here
of
the
lines.
I
can
copy
this
customization
over,
which
is
really
nice.
I'm
going
to
hold
down
the
control
key
because
I'm
on
a
PC.
I'm
going
to
right
click
and
then
I'm
going
to
hit
Edit,
Copy, P
aste C
ustomizations,
and
that's
going
to
bring
them
all
over.
I'm
actually
going
to
hold
down
the
control
key
again
and
resize
this
so that I
can
resize
them
all
together.
Now
I'm
going
to
minimize
the
quantile
section,
because
I'm
going
to
get
the
information
that
I
need
from
the
summary
statistics
section.
I
actually
have
the
IQR
and
a
standard
deviation
shown
here.
A
lthough
I
could
customize
this,
either
here
or
in
the
properties,
which
I
can
access
under
File,
Preferences
and
under
the
distribution
platform
group.
What
I'm
going
to
do
is
I'm
actually
going
to
make
this
information
into
a
data
table
and
I'm
going
to
right-
click
and
select,
Make
Combined
Data
Table
to
do
that.
Now
I
only
need
the
IQR
and the
standard
deviation.
I'm
really
only
interested
in
that.
So
I'm
actually
going
to
select,
one
of
the
standard
deviations,
one
of
the
IQRs.
I'm
going
to
move
my
cursor
over
here
and
select
Matching
on
all
of
the
rows
that
have
these
values
in
them.
I'm
going
to
go
ahead
and
invert
the
selection,
delete
the
rows
that
I
don't
want,
and
I'm
left
with
this.
Now
I'm
just
going
to
go
ahead
and
restructure
the
data
so
that
I
can
calculate
the
ratio
of
the
IQR
to
the
standard
deviation.
So
I'm
just
going
to
use
Table
Split
for
that.
I'm
going
to
go
ahead
and
split
by
column 1
put
column
2
in
here,
put
these
in
a
group.
I'm going
to
click
OK.
I
have
the
data
how
I
want.
This
shows
me
from
which
distribution
this statistics
came
from,
I'm
going
to
go
ahead
and
do
a
New
Formula C
olumn,
Combine,
Ratio.
There
you
go.
This
looks
a
little
bit
hard
to
interpret
for
me.
I'm
going
to
go
ahead
and
change
it
so
that
I
can
only
see
two
decimals.
I've
got
numbers
which
are
very
similar,
it
should
be,
anyway,
very
similar
to
what
I
have
in
the
slide here
detailing
the
ratio
of
the
IQR
to
the
standard
deviation.
Of course,
they're
going
to
be
different
because
there's
sampling
error.
This
table
is
only
one
sampling
experiment.
But
this
is
how
I
can
quickly
and
interactively
extract
this
information
and
really
understand,
what
does
this
ratio
look
like
if
my
data
is
not
normal
in
a
particular
way?
We
can
see
here,
that
the
values
that
tend
to
be
lower
at
the
peak
distribution
of
the
one
with
outliers,
the
values
that
tend
to
be
higher
than
the
typical
or
the
expected
theoretical
1, 3, 5
normal,
are
going
to
be
the
uniform,
the
right
skewed
and bimodal.
Next
question,
what's
the
ideal
outlier
percent
if
the
distribution
is
perfectly
normal?
Well,
it
turns
out
that
if
we
look
in
the
textbooks
or
reduce
simulation,
on
average,
we
should
see
about
0.7%
of
the
points
beyond
the
fences,
in
a
normal
distribution,
or
at
least
perhaps
not
beyond
the
fences,
but
if
we
were
to
do
a
control
chart,
we
would
certainly
see
about,
which
is
under
the
assumption
of
normality.
For
example,
if
we
were
to
do
an
individual
moving
range
chart,
we
would
see
around
0.7%
of
the
points
on
average
being
outside
the
limits.
Although
for
practical
purposes,
we
could
probably
say,
if
we
saw
about
3
%
or
less
of
the
distribution
beyond
the
limits,
we
would
consider
it
approximately
normal.
Why
is
that
question
important?
Well,
we
can
use
the
proportion
of
the
points
beyond
the
fences
in
a
Box Plot
when
the
sample
size
is
small
to
determine
whether
or
not
we
have
some
evidence
of
normality
on
the
basis
of
outliers.
Although
if
our
sample
size
is
too
big,
then
we're
going
to
see
lots
and
lots
of
points
beyond
those
fences.
So
it's
really
important
that
we
consider
a
"
reasonable
sample
size."
And
that's
part
of
the
reason
why
we
only
considered
100
rows
in
our
project.
Next
question,
what's
the
difference
between
a
quartile
range
and
a
quantile
range
Box Plot?
Well,
in
a
practical
context,
anyway,
we
can
talk
about
the
Explore Outlier
utility
in
JMP
16,
which
a
llows
us
to
adjust
the
Q,
which
is
the
multiplier
on
the
IQR
and
the
tail
quantile,
which
is
essentially
how
the
data
is
divided
up.
We
can
customize
that
range.
I'm
just
going
to
show
you
what
that
looks
like
real
quickly.
I'm
going
to
go
into
Analyze,
I'm
going
to
go
to
Screening,
Explore
Outliers.
I'm
going
to
do
this
on
my
raw
data.
I'm
actually
going
to
close
this.
I'm
going
to
go
back
to
the
raw
data
table.
I'll
just
pick
a
couple
of
these.
I'll
actually
pick
the
ones
that
I
have
in
my
slides
to
peak
in
the
outliers.
I'm
going
to
go
ahead
and
use
the
quantile
range
outliers.
I'm
going
to
adjust
this
to
what
the
Box Plot uses: 0.25
and
1.5.
I'm
going
to
click
Rescan
and
JMP's going to
identify
potential
outliers
here.
How
does
this
connect
to
the
distribution
platform?
Well,
if
we
go
over
here,
we
look
at
this,
what
we're
going
to
see,
is
there
are
a
number
of
outliers
here.
I'm
actually
going
to
select
the
rows,
I'm
going
to
go
over
here.
Well,
lo
and
behold,
it's
these
values.
So
you
got
1, 2, 3, 4, 5, 6,7.
There's
seven
outliers.
1, 2, 3, 4, 5, 6,7.
That
squares
up.
That's
exactly
what
we
would
expect.
Similarly,
we've
got
1, 2, 3, 4,
and
if
we
scroll
over
here,
and
under
the
outliers,
see
if we're over
here
are
to
four.
Great.
Going
back
to
the
slides
here,
we
can
customize
this
.
And
that's
actually
what
we
get
into
in
subsequent
Question
10.
How
do
we
determine
whether
outliers
are
marginal
or
extreme?
Well,
and
why
is
it
important?
Well,
we
can
adjust
the
sensitivity
of
the
outlier
detection
based
on
the
multiplier
on
the
IQR
while
keeping
the
tail
quantile
the
same.
You
might
intuitively
expect
that
if
you
were
to
take
Qâ plus a
larger
number
times
the
IQR,
it's
going
to
extend
the
whisker
length
and similarly,
on
the
lower
side.
That's
going
to
mean
that
more
points
are
going
to
fall
inside.
So
less
outlier
would
be
detected.
We
should
be
able
to
see
that
and
test
that
in JMP.
So
if
I
were
to
increase
this
to
two
and
click
Rescan,
we
see
a
few
outliers
become
part
of
the
Box Plot,
or
we
can
imagine
a
situation
where
that's
the
case.
I'll
increase
this
to
three,
I'll
hit
Re
scan
we
see
even fewer
outliers
being
identified
still.
A
s
I
go
up
to
Q equal to
five,
now
I
only
have
one
outlier
detected
in
the
peak
column
of
data.
So
the
idea
here
is
that
we
can
develop
criteria
for
Q,
for
example,
we
might
situate
it
with
three,
a situation
where
data
might
be
considered
a
typographical
error,
where
it
might
be
an
extreme
or
more extreme outlier.
We
might
set
Q
equal
1.5 if, for example,
we think that the potential outlier
might
be
associated
with
variability
due to
the
measurement
system
or special
process
variation.
We
can
do
some
simulation
based on
our
application
and decide on what the
value
of
Q
should be in
these
particular
scenarios.
In connection
with
that,
in
Question
10,
we
touched
a
little
bit
on
GRR
or
measurement
system
variability.
Question
8
talks
a
little
bit about,
it goes
a
little
bit
deeper
into
this
and
brings
together
some
ideas.
The
idea
here
is
that
we
might actually consider
the
distance
between
the
upper
fence
and
the
first outlier
or
the
first potential
outlier
series
of
outliers.
We
may
extend
that
upper
fence
by
a
distance
of
two times the Sigma
due
to
the
measurement
system
variability.
In
this
way, we're actually considering
the
variability
due to
the
measurement
system.
And
we're
asking
ourselves,
is
this
potential
value
within
the
noise
of
the
measurement
system
or
not?
We're
creating
a
graphical
way, a blended graphical means
of
determining
whether
the
value
is
reasonable
under the
expectation
tha
t
there's measurement
system
variability.
I
have
here
the
distance
between
the
marginal
outlier and the whisker
should
be
compared
to
the
GRR
noise
standard
deviation.
If
it's
within
two
standard
deviations,
we
don't
have
95
%
confidence
to conclude this
marginal
outlier
is different
from
the
whisker.
This
is
just
a
graphical
version
of
a
one-
sample
T-
test
in
effect.
We
could
actually
construct
a
one-
sample
T-
test
using this red line as our
target
and
the
observed
value,
or
rather
assumed
series
of
values, this black dot,
as
our
distribution
relative
to
that
target.
The
next
question,
how
many
points
do we
need
really
to
produce
a
Box Plot
if
we're
sample
size
limited?
Well,
we
might
need
at
least
seven
points,
and our simulation
in
this
particular
sampling
experiment
shows
that.
What's
happening
here?
Well,
each
of
these
three
data
sets
have
the
same
median.
You
can
see
in
this
data
set,
there
are
six
observations.
In
this
one
there
are
seven,
and
then
this
one
there
are
eight.
Let's
start
on
the
left,
actually,
and
we
have
eight
observations,
one
out
here
around
15.
What
if
we
reduce
the
number of observations to seven
and
we
actually
included
the
same observation here,
but
we
reduce
one
of
the
others?
What
if
we
reduce
it
further
while
maintaining
the
same
median?
Then
what
we
see
is
that
this outlier 15,
which
is
still
in
the
data
set,
no
longer
becomes
an
outlier.
In
essence,
it
becomes
absorbed
into the whisker
itself.
The
other
thing
that's
interesting
about this simple experiment,
is
that
the
IQR
becomes
inflated when we go from seven to six.
We
can
see
that
visually
as that
the width of this box from Q1 to Q3
becomes
much
wider.
We
can
also
see
that
numerically
here.
I
actually
want
to
show
you
how
we
might
explore
that
in
JMP.
Here's
some
data.
It's
not
the
same
data,
but
here's
some
data.
I
just
created
a
column
that
ranks
the
data.
A
gain,
I
just
use
an
instant
column
formula.
I
can
do
that
by
selecting
one of these options,
so
I
believe
it's
under
distributional.
Now,
what
I'm
going
to
do
is I'm going
to
go
ahead
and
just
clock
this
data.
I'm
going
to
turn
the
histogram
on
its
side.
I'm
actually
going
to
invoke
the
local data filter.
I'm
going
to
bring
in
that
rank
column
that
I'm
going
to
make it ordinal first,
so
that
I
can
select
data
individually
rather
than
under
the
assumption
of
the
continuous
distribution.
I'm
going
to
select
everything.
Now,
let's
see,
if
I
go
back
to
the
data
table,
I
know
that
8
represents
the
highest,
the
largest
value.
I'll
keep
8
in
there,
and
I'll
just
start
reducing
some
of
the lower values
by
holding
down
my
control
key
and
clicking
that,
which
will
effectively
remove
that
point
dynamically
from
this
analysis.
I
got
the
control
key
down
and
clicked
again,
click again.
You
saw
it
there,
that one outlier at the low side,
anyway,
in
this
case,
just
disappeared.
There's
a
relationship
among
the
distance
between the
fences
and
the
points,
which
is
calculated
on
the
basis
of
the
data
where the median and the quartiles
are
calculated
based
on
the
data
that's
in
the
analysis.
This
gives
you
a
better
means
of
appreciating
how
the
Box Plot
is changing as
a
function
of
data
that's either
in
or
out
of
the
analysis.
This
is
a
really
super
cool
feature
that I really
like
to
use
a
lot
in
many
contexts.
What's
the
advantage
of a Robust Fit Outlier
algorithm,
which
is
a
JMP
16
algorithm?
It
gives
us
another
means
of
detecting
outlyingness
.
We
have
the
ability
to
use
a
Cauchy
method
which
often
avoids
the
impact of skewness,
which
can
be
useful
for
practical
situations.
We
can
also
use
a
3-s
igma
or a K-sigma multiplier
in
order
to
help
detect
outlyingness
.
All
of
these
methods
really
help
us
separate potential outliers from real outliers
and
help
us
create
a
reasonable
signal detection and
methodology
in a similar way that we might
do
if
we
were
to
use
control
charting
and build a control chart with
limits
for
our
particular
experimental
or
manufacturing
application.
13.
Can
we
include
the
sample
size
information
in
the
Box
Plot?
Well, this
is
where
the
Box
Plot
starts
to
present
a
clear
limitation.
There
isn't
any
sample
size
information
explicitly
in
the
Box Plot.
A
lthough,
we
do
have
the
ability in graph builder
to create a notch Box Plot,
which
gives
you
something
like a
confidence
interval
on
the
median,
the
edges
indicate
a
confidence
interval
on the
median.
We
also
have
the
ability
in
graph
builder to invoke the caption box
which is a very useful
feature
for
summarization
of
data
graphically
without
needing
to
provide
an
additional
tabular
data
output.
But
of
course,
that
information
is
completely
hidden
to
the
Box Plot
itself.
Connected
to
that
is,
can
we
make
any
decision
with any level of
statistical
confidence
if
we're
just
looking
at
the
Box Plot?
The
answer
is
no.
In
this
particular
example, we actually designed it
so
the
medians
were
slightly
different
on
average.
And
so
we're
getting
some
separation
among
the
medians
between
the
groups.
We
used
to
fit
Y by
X
in
this
context.
What
this
shows
is
that
the
mean
[inaudible 00:29:27]
represents the
mean,
the mean diamonds
are
non-
overlapping.
It
looks
like
all
across
all
four groups being compared,
which
indicates
that
there's
some evidence
that
there's
a
difference
in
the
means
between
the
groups.
We
can
also
see
the
difference
in
the
medians.
We
can
do
a
non-
parametric
test.
In
this
case,
we're
using
a
non-
parametric steel test with control,
where
the
control
is
just
the
Z
normal.
We're
seeing
some
evidence of separation,
statistical
separation
among
the
medians in this particular instance.
It's
hard
for
us
to
detect
that
and
see that in the Box Plot.
In
fact,
it
really
isn't
that
clear
at
all.
How
can
we
tell
if
we
have
any
concern
with
respect
to
Kurt
osis
?
What's
Kurtosis?
Kurtosis is
basically
the
idea
that
if it were a
positive
Kurtosis,
you
would
have
data
that's
concentrated
in
the
middle,
your
data
that's
squished
together
into
the
middle
of
the
distribution.
That's
this
example
in
the
right.
If
you
had
an
idealized
case
of extreme negative
Kurtosis,
you'd
have
a
uniform
distribution
where
the
data
is
really
spread
out.
What
you
can
see
in
these
graphs
relative
to
the
normal
distribution,
is
that
the
50
%
dense
zone,
indicated
by
this
red
bar,
is
basically
about
as
long
as
the distance between
Q1
and
Q3
here,
but
it's
on
one
side
of
the
median,
on
one
side
of
the
median
and
the
uniform
case.
It's
about
as
long
as
this
box
width
then
it's
also
on
one
side
of
the
median.
That's
a
unique
characteristic
feature
of
this
uniform
distribution
shape.
If
we
look
at
the
peak
situation,
we
see
that
the
box
width
is much
more
compressed
and the shortest half width
is also
about the same as
the
box width,
the shortest half is the
most
dense
region
rather
as
centered
about
the
median.
That's
similar
to
what
you
would
see for the normal distribution case,
where
the
50
%
dense
region
will
be
about centered
on
the
mean
or
the
median
and
about
the
same
width
as
the
box.
Clearly,
the
differentiator
here
is that
the
distances
are
reduced
quite
a
bit.
Really
the
takeaway
here,
though,
is
that
this
type
of
interpretation
is
really
difficult.
And
it
would
be
easier
for
us
to rely on
the
shape that's evinced by the histogram
than
to
try
to
look
at
the
Box Plots
separately.
Question
16
is
very
similar to 15.
What
about
in
the
context
of
data
that
has
more
than
one
mode?
What
about
a
bimodal
distribution?
Well,
I
just
took
the
Box Plots
and
pulled
them
out on the left,
they're
from
the
pictures
on
the
right.
We
can't
really
see
a
whole
lot
of
difference
among
these.
It's
difficult
for
us
to
interpret
this.
But
once
we
put
the
histograms, we can see
clearly
if
we
fit
a
two-
peak distribution
that
there's
two
modes
in
this
data,
and
there's
maybe
one
mode,
maybe
a
small
mode,
but
really
essentially
one
mode
in
the
data
on
the
left.
The
Box Plot
isn't
particularly good
at
detecting
that
presence
of
multiple
modes.
The
last
question
is,
how
many
"normality violation failure modes"
can
we
detect
with
the
Box Plot?
This
question
brings
all
the
other
ones
together.
Well,
if
we
have
skewness,
we've
shown
that
we
have
a
strong
ability
to
detect
that.
If
we
have
potential
outliers,
we
definitely
have
a
strong
ability
to
detect
that.
If
we
have
Kurtosis,
which
is
really
related
to
the
shape
as is
if
there
are
multiple
modes,
then
we
really
don't
have
a
strong
ability
to
detect
that.
If
we're
considering
hypothesis
testing,
we definitely don't have an
ability
to detect that
either
with
the
Box Plot.
What's
the
takeaways?
Well,
the
Box Plot
is
definitely a powerful visualization tool.
It's
a
great
introductory
tool,
and it
has
a
wonderful
ability
to
separate skewness
from
potential
outlying
ness.
But
it
has
its
limitations.
In
cases
where
we're
looking
at
Kurtotic
shape
or
a
bimodality
or multimodality,
the
histogram
is
definitely
a
better
choice.
That's
really
probably
why
JMP
uses both the Histogram and the Box Plot together
in
the
distribution
platform to visualize how the data is behaving,
if
you
will.
Of
course,
adding
descriptive
statistics
helps us really
round
up
the
picture
where we
have
a
graphical
first approach.
This
is
just,
again,
a
summarization
of
what
we've
discussed.
But the
last
couple
of
minutes,
I
just
want
to
show
you
a
couple
more
things
about
the
data
set
itself.
Because
I
think
this
is
perhaps
the
most
useful
aspect
of
the
project.
How
might
we
set
up
a
data
set
like
this?
All
we
really
have
to
do
to
simulate
data in JMP
is
just
create
some
rows
and then create
a
function,
a random
normal
function.
The
process
that
we
did, one way
you
could
do
this
is
you
could say,
okay,
you
can
go
into
a
column
formulaâ¦
Let me
just
show
you
this.
You
can
just
double-
click
into
it,
and
you
can
click
Formula,
you
can
edit
the
formula.
You
can
go
over
here
to
these
random functions,
you
can
click
it
in,
and
then
you
can
specify
a
population
mean in Sigma.
Zero
and
one
by
default,
click
OK,
and
then
I
can
add
a
bunch
of
rows.
I'll
go
ahead
and
add
100
rows.
What
about
these
other
distributions?
A uniform
distribution is,
we
can
use
the
random
uniform
function.
And
then
we
can
specify
a
Min
and
Max
value.
In
this
case,
I
just
specified
the
minimum
of this
column,
this
normally
distributed
data
column,
and
the
Max is
the
maximum.
And
then
finally,
as
I
mentioned,
I
standardized
the
column
so
that
it was
on
the
same
numeric
scale.
This
standardize
this
column,
standardized
feature
is
common
to
all
of
these
columns.
Now,
the
last
thing
I
want
to
talk about real quick
is,
well,
what
about
peak?
What
about
right
skewed,
and
even
bi
modal?
Well,
one
of
the
things
we
can
do, which I really think is cool,
is
we
can
use
the
distribution
calculator in JMP
to
help
us
understand
what certain
distribution
types
look
like.
I'm
just
going
to
go
into
it
here.
I'm
going
to
just
drive
down
in
here.
I'll
share
with
you
the
location
here
of
this
script.
It's
going
to
be
under
Calculator. It's not.
It's
going
to
be
under Distribution.
Generator.
Distribution
calculator,
on the calculators,
yes.
How
might
I
create
a
distribution
that's
right
skewed?
Which
random
function
would
I
use?
Well,
I
have
the
ability
to
look
at some of
these
distributions and see
for
example,
if
I
specify
a
random
F
and
I
specify these parameters,
then
I'm
getting
a
distribution
with
this
kind of skewness.
And
then
I
can
say,
well,
what
happens
if
I
change
these
parameters
a
little
bit?
How
is
that
going
to
change
the
distribution?
I
can
use
this
insight
to
specify the parameters
for
the
random distributions
that
I
specify
in
my
data
set.
In
fact,
that's
what
I
did
here.
What
did
I
do
for
the
peaked
one?
Well,
if
I
look
at
the
T
distribution,
and
I
reduce
the
degrees
of
freedom,
I'm
going
to
get
a
distribution
that's
relatively
peak.
I'm
going
to
see a
positive
Kurtosis
in
that.
That's
one
way
I
can
understand
the shape of these distributions
so
that
I
can
use them to my advantage
to
do
different
what
if
analysis
in JMP.
I'm
just
going
to
quickly
go
back
to
my
slides.
Thank
you
very
much
for
listening.
If
you
have
any
questions,
I
look
forward
to
receiving
them
on
the
user
community.
As I
mentioned,
this
project
will
be
posted
there,
and
the
summary
abstract
is posted
at
this
link
here.
Thank
you again.
