<s>
A	O
radar	B-Application
chart	I-Application
is	O
a	O
graphical	B-Application
method	I-Application
of	O
displaying	O
multivariate	B-General_Concept
data	I-General_Concept
in	O
the	O
form	O
of	O
a	O
two-dimensional	O
chart	O
of	O
three	O
or	O
more	O
quantitative	O
variables	O
represented	O
on	O
axes	O
starting	O
from	O
the	O
same	O
point	O
.	O
</s>
<s>
The	O
relative	O
position	O
and	O
angle	O
of	O
the	O
axes	O
is	O
typically	O
uninformative	O
,	O
but	O
various	O
heuristics	O
,	O
such	O
as	O
algorithms	O
that	O
plot	B-Application
data	O
as	O
the	O
maximal	O
total	O
area	O
,	O
can	O
be	O
applied	O
to	O
sort	O
the	O
variables	O
(	O
axes	O
)	O
into	O
relative	O
positions	O
that	O
reveal	O
distinct	O
correlations	O
,	O
trade-offs	O
,	O
and	O
a	O
multitude	O
of	O
other	O
comparative	O
measures	O
.	O
</s>
<s>
The	O
radar	B-Application
chart	I-Application
is	O
also	O
known	O
as	O
web	B-Application
chart	I-Application
,	O
spider	B-Application
chart	I-Application
,	O
spider	O
graph	O
,	O
spider	O
web	B-Application
chart	I-Application
,	O
star	O
chart	O
,	O
star	B-Application
plot	I-Application
,	O
cobweb	B-Application
chart	I-Application
,	O
irregular	O
polygon	O
,	O
polar	B-Application
chart	I-Application
,	O
or	O
Kiviat	B-Application
diagram	I-Application
.	O
</s>
<s>
It	O
is	O
equivalent	O
to	O
a	O
parallel	B-Application
coordinates	I-Application
plot	B-Application
,	O
with	O
the	O
axes	O
arranged	O
radially	O
.	O
</s>
<s>
The	O
radar	B-Application
chart	I-Application
is	O
a	O
chart	O
and/or	O
plot	B-Application
that	O
consists	O
of	O
a	O
sequence	O
of	O
equi-angular	O
spokes	O
,	O
called	O
radii	O
,	O
with	O
each	O
spoke	O
representing	O
one	O
of	O
the	O
variables	O
.	O
</s>
<s>
This	O
gives	O
the	O
plot	B-Application
a	O
star-like	O
appearance	O
and	O
the	O
origin	O
of	O
one	O
of	O
the	O
popular	O
names	O
for	O
this	O
plot	B-Application
.	O
</s>
<s>
The	O
star	B-Application
plot	I-Application
can	O
be	O
used	O
to	O
answer	O
the	O
following	O
questions	O
:	O
</s>
<s>
(	O
Radar	B-Application
charts	I-Application
are	O
used	O
to	O
examine	O
the	O
relative	O
values	O
for	O
a	O
single	O
data	O
point	O
(	O
e.g.	O
,	O
point	O
3	O
is	O
large	O
for	O
variables	O
2	O
and	O
4	O
,	O
small	O
for	O
variables	O
1	O
,	O
3	O
,	O
5	O
,	O
and	O
6	O
)	O
and	O
to	O
locate	O
similar	O
points	O
or	O
dissimilar	O
points	O
.	O
)	O
</s>
<s>
Radar	B-Application
charts	I-Application
are	O
a	O
useful	O
way	O
to	O
display	O
multivariate	B-General_Concept
observations	O
with	O
an	O
arbitrary	O
number	O
of	O
variables	O
.	O
</s>
<s>
Typically	O
,	O
radar	B-Application
charts	I-Application
are	O
generated	O
in	O
a	O
multi-plot	O
format	O
with	O
many	O
stars	O
on	O
each	O
page	O
and	O
each	O
star	O
representing	O
one	O
observation	O
.	O
</s>
<s>
The	O
star	B-Application
plot	I-Application
was	O
first	O
used	O
by	O
Georg	O
von	O
Mayr	O
in	O
1877	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
differ	O
from	O
glyph	O
plots	O
in	O
that	O
all	O
variables	O
are	O
used	O
to	O
construct	O
the	O
plotted	O
star	O
figure	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
can	O
be	O
used	O
in	O
sports	O
to	O
chart	O
players	O
 '	O
strengths	O
and	O
weaknesses	O
by	O
calculating	O
various	O
statistics	O
related	O
to	O
the	O
player	O
that	O
can	O
tracked	O
along	O
the	O
central	O
axis	O
of	O
the	O
chart	O
.	O
</s>
<s>
The	O
results	O
of	O
the	O
radar	B-Application
chart	I-Application
can	O
also	O
be	O
useful	O
in	O
situational	O
play	O
.	O
</s>
<s>
Another	O
application	O
of	O
radar	B-Application
charts	I-Application
is	O
the	O
control	O
of	O
quality	O
improvement	O
to	O
display	O
the	O
performance	O
metrics	O
various	O
objects	O
including	O
computer	O
programs	O
,	O
computers	O
,	O
phones	O
,	O
vehicles	O
,	O
and	O
more	O
.	O
</s>
<s>
An	O
example	O
of	O
this	O
where	O
radar	B-Application
charts	I-Application
may	O
be	O
useful	O
is	O
the	O
performance	O
analysis	O
of	O
various	O
sorting	O
algorithms	O
.	O
</s>
<s>
A	O
programmer	O
could	O
gather	O
up	O
several	O
different	O
sorting	O
algorithms	O
such	O
as	O
selection	O
,	O
bubble	O
,	O
and	O
quick	O
,	O
then	O
analyze	O
the	O
performance	O
of	O
these	O
algorithms	O
by	O
measuring	O
their	O
speed	O
,	O
memory	O
usage	O
,	O
and	O
power	O
usage	O
,	O
then	O
graph	O
these	O
on	O
a	O
radar	B-Application
chart	I-Application
to	O
see	O
how	O
each	O
sort	O
performs	O
under	O
various	O
sizes	O
of	O
data	O
.	O
</s>
<s>
Then	O
after	O
using	O
a	O
radar	B-Application
chart	I-Application
to	O
visualize	O
the	O
data	O
,	O
they	O
could	O
decide	O
on	O
what	O
car	O
is	O
best	O
for	O
them	O
based	O
on	O
the	O
results	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
can	O
be	O
used	O
in	O
life	O
sciences	O
to	O
display	O
the	O
strengths	O
and	O
weakness	O
of	O
drugs	O
and	O
other	O
medications	O
.	O
</s>
<s>
They	O
could	O
then	O
graph	O
the	O
results	O
using	O
a	O
radar	B-Application
chart	I-Application
to	O
see	O
the	O
spread	O
of	O
variables	O
and	O
find	O
how	O
the	O
differ	O
,	O
such	O
as	O
one	O
anti-depressant	O
being	O
cheaper	O
and	O
quicker	O
acting	O
,	O
but	O
not	O
having	O
great	O
relief	O
over	O
time	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
can	O
be	O
used	O
to	O
graph	O
the	O
variables	O
of	O
life	O
affecting	O
a	O
person	O
's	O
wellness	O
,	O
and	O
then	O
be	O
analyzed	O
to	O
help	O
them	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
are	O
primarily	O
suited	O
for	O
strikingly	O
showing	O
outliers	O
and	O
commonality	O
,	O
or	O
when	O
one	O
chart	O
is	O
greater	O
in	O
every	O
variable	O
than	O
another	O
,	O
and	O
primarily	O
used	O
for	O
ordinal	O
measurements	O
–	O
where	O
each	O
variable	O
corresponds	O
to	O
"	O
better	O
"	O
in	O
some	O
respect	O
,	O
and	O
all	O
variables	O
on	O
the	O
same	O
scale	O
.	O
</s>
<s>
Conversely	O
,	O
radar	B-Application
charts	I-Application
have	O
been	O
criticized	O
as	O
poorly	O
suited	O
for	O
making	O
trade-off	O
decisions	O
–	O
when	O
one	O
chart	O
is	O
greater	O
than	O
another	O
on	O
some	O
variables	O
,	O
but	O
less	O
on	O
others	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
can	O
distort	O
data	O
to	O
some	O
extent	O
,	O
especially	O
when	O
areas	O
are	O
filled	O
in	O
,	O
because	O
the	O
area	O
contained	O
becomes	O
proportional	O
to	O
the	O
square	O
of	O
the	O
linear	O
measures	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
can	O
also	O
become	O
hard	O
to	O
visually	O
compare	O
between	O
different	O
samples	O
on	O
the	O
chart	O
when	O
their	O
values	O
are	O
close	O
as	O
their	O
lines	O
or	O
areas	O
bleed	O
into	O
each	O
other	O
,	O
as	O
shown	O
in	O
Figure	O
5	O
.	O
</s>
<s>
Radar	B-Application
charts	I-Application
impose	O
several	O
structures	O
on	O
data	O
,	O
which	O
are	O
often	O
artificial	O
:	O
</s>
<s>
Relatedness	O
of	O
neighbors	O
–	O
radar	B-Application
charts	I-Application
are	O
often	O
used	O
when	O
neighboring	O
variables	O
are	O
unrelated	O
,	O
creating	O
spurious	O
connections	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
alternating	O
data	O
9	O
,	O
1	O
,	O
9	O
,	O
1	O
,	O
9	O
,	O
1	O
yields	O
a	O
spiking	O
radar	B-Application
chart	I-Application
(	O
which	O
goes	O
in	O
and	O
out	O
)	O
,	O
while	O
reordering	O
the	O
data	O
as	O
9	O
,	O
9	O
,	O
9	O
,	O
1	O
,	O
1	O
,	O
1	O
instead	O
yields	O
two	O
distinct	O
wedges	O
(	O
sectors	O
)	O
.	O
</s>
<s>
In	O
some	O
cases	O
there	O
is	O
a	O
natural	O
structure	O
,	O
and	O
radar	B-Application
charts	I-Application
can	O
be	O
well-suited	O
.	O
</s>
<s>
For	O
example	O
,	O
for	O
diagrams	O
of	O
data	O
that	O
vary	O
over	O
a	O
24-hour	O
cycle	O
,	O
the	O
hourly	O
data	O
is	O
naturally	O
related	O
to	O
its	O
neighbor	O
,	O
and	O
has	O
a	O
cyclic	O
structure	O
,	O
so	O
it	O
can	O
naturally	O
be	O
displayed	O
as	O
a	O
radar	B-Application
chart	I-Application
.	O
</s>
<s>
One	O
set	O
of	O
guidelines	O
on	O
the	O
use	O
of	O
radar	B-Application
charts	I-Application
(	O
or	O
rather	O
the	O
closely	O
related	O
"	O
polar	O
area	O
graph	O
"	O
)	O
is	O
:	O
</s>
<s>
Radar	B-Application
charts	I-Application
are	O
helpful	O
for	O
small-to-moderate-sized	O
multivariate	B-General_Concept
data	I-General_Concept
sets	O
.	O
</s>
<s>
Their	O
primary	O
weakness	O
is	O
that	O
their	O
effectiveness	O
is	O
limited	O
to	O
data	B-General_Concept
sets	I-General_Concept
with	O
less	O
than	O
a	O
few	O
hundred	O
points	O
.	O
</s>
<s>
Further	O
,	O
when	O
using	O
radar	B-Application
charts	I-Application
with	O
multiple	O
dimensions	O
or	O
samples	O
,	O
the	O
radar	B-Application
chart	I-Application
may	O
become	O
cluttered	O
and	O
harder	O
to	O
interpret	O
as	O
the	O
number	O
of	O
samples	O
grows	O
.	O
</s>
<s>
We	O
will	O
use	O
this	O
table	O
below	O
to	O
create	O
Radar	B-Application
charts	I-Application
comparing	O
the	O
2021	O
MVP	O
batting	O
stats	O
to	O
the	O
league	O
averages	O
for	O
Designated	O
Hitters	O
and	O
regular	O
batters	O
,	O
in	O
an	O
attempt	O
to	O
visualize	O
performance	O
metrics	O
and	O
visually	O
come	O
to	O
a	O
conclusion	O
that	O
Shohei	O
out	O
performed	O
the	O
average	O
player	O
.	O
</s>
<s>
Next	O
we	O
will	O
include	O
additional	O
samples	O
into	O
the	O
Radar	B-Application
chart	I-Application
,	O
using	O
Hall	O
of	O
Fame	O
players	O
Jackie	O
Robinson	O
,	O
Jim	O
Thome	O
,	O
and	O
Frank	O
Thomas	O
to	O
compare	O
Shohei	O
to	O
a	O
few	O
of	O
the	O
greatest	O
batters	O
of	O
all	O
time	O
.	O
</s>
<s>
This	O
Radar	B-Application
chart	I-Application
not	O
only	O
can	O
give	O
us	O
intuition	O
of	O
how	O
Shohei	O
compares	O
to	O
the	O
top	O
historical	O
players	O
,	O
but	O
will	O
also	O
serve	O
a	O
purpose	O
in	O
showing	O
the	O
limitations	O
of	O
having	O
too	O
many	O
samples	O
in	O
a	O
Radar	B-Application
chart	I-Application
.	O
</s>
<s>
We	O
can	O
see	O
in	O
Figure	O
10	O
how	O
a	O
radar	B-Application
chart	I-Application
can	O
be	O
easily	O
interpreted	O
when	O
the	O
number	O
of	O
spokes	O
and	O
samples	O
is	O
relatively	O
small	O
.	O
</s>
<s>
When	O
we	O
compare	O
more	O
samples	O
in	O
Figure	O
11	O
,	O
even	O
without	O
an	O
area	O
fill	O
on	O
the	O
radar	B-Application
chart	I-Application
,	O
it	O
becomes	O
apparent	O
how	O
difficult	O
it	O
can	O
become	O
to	O
interpret	O
or	O
make	O
trade-off	O
decisions	O
.	O
</s>
<s>
The	O
chart	O
on	O
the	O
right	O
contains	O
the	O
star	B-Application
plots	I-Application
of	O
15	O
cars	O
.	O
</s>
<s>
The	O
variable	O
list	O
for	O
the	O
sample	O
star	B-Application
plot	I-Application
is	O
:	O
</s>
<s>
For	O
example	O
,	O
we	O
can	O
look	O
at	O
the	O
star	B-Application
plot	I-Application
of	O
the	O
Cadillac	B-Application
Seville	O
(	O
the	O
last	O
one	O
on	O
the	O
image	O
)	O
and	O
see	O
that	O
it	O
is	O
one	O
of	O
the	O
most	O
expensive	O
cars	O
,	O
gets	O
below	O
average	O
(	O
but	O
not	O
among	O
the	O
worst	O
)	O
gas	O
mileage	O
,	O
has	O
an	O
average	O
repair	O
record	O
,	O
and	O
has	O
average-to-above-average	O
roominess	O
and	O
size	O
.	O
</s>
<s>
We	O
can	O
then	O
compare	O
the	O
Cadillac	B-Application
models	O
(	O
the	O
last	O
three	O
plots	O
)	O
with	O
the	O
AMC	O
models	O
(	O
the	O
first	O
three	O
plots	O
)	O
.	O
</s>
<s>
The	O
Cadillac	B-Application
models	O
are	O
expensive	O
,	O
have	O
poor	O
gas	O
mileage	O
,	O
and	O
are	O
large	O
in	O
both	O
size	O
and	O
roominess	O
.	O
</s>
<s>
One	O
may	O
use	O
line	O
graphs	O
for	O
time	O
series	O
and	O
other	O
data	O
,	O
in	O
the	O
form	O
of	O
parallel	B-Application
coordinates	I-Application
.	O
</s>
<s>
Comparison	O
in	O
Harvey	O
balls	O
(	O
and	O
radar	B-Application
charts	I-Application
)	O
may	O
be	O
significantly	O
aided	O
by	O
ordering	O
the	O
variables	O
algorithmically	O
to	O
add	O
order	O
.	O
</s>
<s>
An	O
excellent	O
way	O
for	O
visualising	O
structures	O
within	O
multivariate	B-General_Concept
data	I-General_Concept
is	O
offered	O
by	O
principal	B-Application
component	I-Application
analysis	I-Application
(	O
PCA	O
)	O
.	O
</s>
<s>
Another	O
alternative	O
is	O
to	O
use	O
small	O
,	O
inline	O
bar	O
charts	O
,	O
which	O
may	O
be	O
compared	O
to	O
sparklines	B-Application
.	O
</s>
<s>
Although	O
radar	O
and	O
polar	B-Application
charts	I-Application
are	O
often	O
described	O
as	O
the	O
same	O
chart	O
types	O
,	O
some	O
sources	O
make	O
a	O
difference	O
between	O
them	O
and	O
even	O
consider	O
the	O
radar	B-Application
chart	I-Application
to	O
be	O
a	O
polar	B-Application
chart	I-Application
's	O
variation	O
that	O
does	O
not	O
display	O
data	O
in	O
terms	O
of	O
polar	O
coordinate	O
.	O
</s>
