<s>
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
(	O
often	O
cited	O
as	O
Fitts	B-General_Concept
 '	I-General_Concept
law	I-General_Concept
)	O
is	O
a	O
predictive	O
model	B-Application
of	O
human	O
movement	O
primarily	O
used	O
in	O
human	O
–	O
computer	O
interaction	O
and	O
ergonomics	O
.	O
</s>
<s>
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
is	O
used	O
to	O
model	B-Application
the	O
act	O
of	O
pointing	O
,	O
either	O
by	O
physically	O
touching	O
an	O
object	O
with	O
a	O
hand	O
or	O
finger	O
,	O
or	O
virtually	O
,	O
by	O
pointing	O
to	O
an	O
object	O
on	O
a	O
computer	B-Device
monitor	I-Device
using	O
a	O
pointing	B-Device
device	I-Device
.	O
</s>
<s>
It	O
was	O
initially	O
developed	O
by	O
Paul	O
Fitts	B-General_Concept
.	O
</s>
<s>
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
has	O
been	O
shown	O
to	O
apply	O
under	O
a	O
variety	O
of	O
conditions	O
;	O
with	O
many	O
different	O
limbs	O
(	O
hands	O
,	O
feet	O
,	O
the	O
lower	O
lip	O
,	O
head-mounted	O
sights	O
)	O
,	O
manipulanda	O
(	O
input	B-Device
devices	I-Device
)	O
,	O
physical	O
environments	O
(	O
including	O
underwater	O
)	O
,	O
and	O
user	O
populations	O
(	O
young	O
,	O
old	O
,	O
special	O
educational	O
needs	O
,	O
and	O
drugged	O
participants	O
)	O
.	O
</s>
<s>
The	O
original	O
1954	O
paper	O
by	O
Paul	O
Morris	O
Fitts	B-General_Concept
proposed	O
a	O
metric	O
to	O
quantify	O
the	O
difficulty	O
of	O
a	O
target	O
selection	O
task	O
.	O
</s>
<s>
The	O
metric	O
is	O
Fitts	B-General_Concept
's	O
index	O
of	O
difficulty	O
(	O
ID	O
,	O
in	O
bits	O
)	O
:	O
</s>
<s>
Fitts	B-General_Concept
also	O
proposed	O
an	O
index	O
of	O
performance	O
(	O
IP	O
,	O
in	O
bits	O
per	O
second	O
)	O
as	O
a	O
measure	O
of	O
human	O
performance	O
.	O
</s>
<s>
In	O
Fitts	B-General_Concept
's	O
words	O
,	O
</s>
<s>
Researchers	O
after	O
Fitts	B-General_Concept
began	O
the	O
practice	O
of	O
building	O
linear	O
regression	O
equations	O
and	O
examining	O
the	O
correlation	O
(	O
r	O
)	O
for	O
goodness	O
of	O
fit	O
.	O
</s>
<s>
a	O
and	O
b	O
are	O
constants	O
that	O
depend	O
on	O
the	O
choice	O
of	O
input	B-Device
device	I-Device
and	O
are	O
usually	O
determined	O
empirically	O
by	O
regression	O
analysis	O
.	O
</s>
<s>
Both	O
parameters	O
show	O
the	O
linear	O
dependency	O
in	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
.	O
</s>
<s>
Since	O
shorter	O
movement	O
times	O
are	O
desirable	O
for	O
a	O
given	O
task	O
,	O
the	O
value	O
of	O
the	O
b	O
parameter	O
can	O
be	O
used	O
as	O
a	O
metric	O
when	O
comparing	O
computer	O
pointing	B-Device
devices	I-Device
against	O
one	O
another	O
.	O
</s>
<s>
The	O
first	O
human	O
–	O
computer	O
interface	O
application	O
of	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
was	O
by	O
Card	O
,	O
English	O
,	O
and	O
Burr	O
,	O
who	O
used	O
the	O
index	O
of	O
performance	O
(	O
IP	O
)	O
,	O
interpreted	O
as	O
,	O
to	O
compare	O
performance	O
of	O
different	O
input	B-Device
devices	I-Device
,	O
with	O
the	O
mouse	B-Device
coming	O
out	O
on	O
top	O
compared	O
to	O
the	O
joystick	O
or	O
directional	O
movement	O
keys	O
.	O
</s>
<s>
This	O
early	O
work	O
,	O
according	O
to	O
Stuart	O
Card	O
's	O
biography	O
,	O
"	O
was	O
a	O
major	O
factor	O
leading	O
to	O
the	O
mouse	B-Device
's	O
commercial	O
introduction	O
by	O
Xerox	O
"	O
.	O
</s>
<s>
Many	O
experiments	O
testing	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
apply	O
the	O
model	B-Application
to	O
a	O
dataset	O
in	O
which	O
either	O
distance	O
or	O
width	O
,	O
but	O
not	O
both	O
,	O
are	O
varied	O
.	O
</s>
<s>
The	O
model	B-Application
's	O
predictive	O
power	O
deteriorates	O
when	O
both	O
are	O
varied	O
over	O
a	O
significant	O
range	O
.	O
</s>
<s>
Notice	O
that	O
because	O
the	O
ID	O
term	O
depends	O
only	O
on	O
the	O
ratio	O
of	O
distance	O
to	O
width	O
,	O
the	O
model	B-Application
implies	O
that	O
a	O
target	O
distance	O
and	O
width	O
combination	O
can	O
be	O
re-scaled	O
arbitrarily	O
without	O
affecting	O
movement	O
time	O
,	O
which	O
is	O
impossible	O
.	O
</s>
<s>
Despite	O
its	O
flaws	O
,	O
this	O
form	O
of	O
the	O
model	B-Application
does	O
possess	O
remarkable	O
predictive	O
power	O
across	O
a	O
range	O
of	O
computer	O
interface	O
modalities	O
and	O
motor	O
tasks	O
,	O
and	O
has	O
provided	O
many	O
insights	O
into	O
user	O
interface	O
design	O
principles	O
.	O
</s>
<s>
A	O
movement	O
during	O
a	O
single	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
task	O
can	O
be	O
split	O
into	O
two	O
phases	O
:	O
</s>
<s>
Often	O
it	O
is	O
cited	O
that	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
can	O
be	O
applied	O
to	O
eye	B-General_Concept
tracking	I-General_Concept
.	O
</s>
<s>
During	O
a	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
task	O
the	O
user	O
consciously	O
acquires	O
its	O
target	O
and	O
can	O
actually	O
see	O
it	O
,	O
making	O
these	O
two	O
types	O
of	O
interaction	O
not	O
comparable	O
.	O
</s>
<s>
The	O
formulation	O
of	O
Fitts	B-General_Concept
's	O
index	O
of	O
difficulty	O
most	O
frequently	O
used	O
in	O
the	O
human	O
–	O
computer	O
interaction	O
community	O
is	O
called	O
the	O
Shannon	O
formulation	O
:	O
</s>
<s>
In	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
,	O
the	O
distance	O
represents	O
signal	O
strength	O
,	O
while	O
target	O
width	O
is	O
noise	O
.	O
</s>
<s>
Using	O
this	O
form	O
of	O
the	O
model	B-Application
,	O
the	O
difficulty	O
of	O
a	O
pointing	O
task	O
was	O
equated	O
to	O
a	O
quantity	O
of	O
information	O
transmitted	O
(	O
in	O
units	O
of	O
bits	O
)	O
by	O
performing	O
the	O
task	O
.	O
</s>
<s>
Although	O
no	O
formal	O
mathematical	O
connection	O
was	O
established	O
between	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
and	O
the	O
Shannon-Hartley	O
theorem	O
it	O
was	O
inspired	O
by	O
,	O
the	O
Shannon	O
form	O
of	O
the	O
law	O
has	O
been	O
used	O
extensively	O
,	O
likely	O
due	O
to	O
the	O
appeal	O
of	O
quantifying	O
motor	O
actions	O
using	O
information	O
theory	O
.	O
</s>
<s>
In	O
2002	O
the	O
ISO	O
9241	O
was	O
published	O
,	O
providing	O
standards	O
for	O
human	O
–	O
computer	O
interface	O
testing	O
,	O
including	O
the	O
use	O
of	O
the	O
Shannon	O
form	O
of	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
.	O
</s>
<s>
The	O
Shannon-Entropy	O
results	O
in	O
a	O
different	O
information	O
value	O
than	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
.	O
</s>
<s>
If	O
the	O
observed	O
error	O
rate	O
was	O
4%	O
in	O
the	O
sequence	O
of	O
trials	O
,	O
then	O
We	O
=	O
W	O
.	O
If	O
the	O
error	O
rate	O
was	O
greater	O
than	O
4%	O
,	O
We	O
>	O
W	O
,	O
and	O
if	O
the	O
error	O
rate	O
was	O
less	O
than	O
4%	O
,	O
We	O
<	O
W	O
.	O
By	O
using	O
We	O
,	O
a	O
Fitts	B-General_Concept
 '	I-General_Concept
law	I-General_Concept
model	B-Application
more	O
closely	O
reflects	O
what	O
users	O
actually	O
did	O
,	O
rather	O
than	O
what	O
they	O
were	O
asked	O
to	O
do	O
.	O
</s>
<s>
With	O
the	O
adjustment	O
for	O
accuracy	O
,	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
more	O
truly	O
encompasses	O
the	O
speed-accuracy	O
tradeoff	O
.	O
</s>
<s>
Not	O
long	O
after	O
the	O
original	O
model	B-Application
was	O
proposed	O
,	O
a	O
2-factor	O
variation	O
was	O
proposed	O
under	O
the	O
intuition	O
that	O
target	O
distance	O
and	O
width	O
have	O
separate	O
effects	O
on	O
movement	O
time	O
.	O
</s>
<s>
Welford	O
's	O
model	B-Application
,	O
proposed	O
in	O
1968	O
,	O
separated	O
the	O
influence	O
of	O
target	O
distance	O
and	O
width	O
into	O
separate	O
terms	O
,	O
and	O
provided	O
improved	O
predictive	O
power	O
:	O
</s>
<s>
This	O
model	B-Application
has	O
an	O
additional	O
parameter	O
,	O
so	O
its	O
predictive	O
accuracy	O
cannot	O
be	O
directly	O
compared	O
with	O
1-factor	O
forms	O
of	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
.	O
</s>
<s>
However	O
,	O
a	O
variation	O
on	O
Welford	O
's	O
model	B-Application
inspired	O
by	O
the	O
Shannon	O
formulation	O
,	O
</s>
<s>
The	O
additional	O
parameter	O
k	O
allows	O
the	O
introduction	O
of	O
angles	O
into	O
the	O
model	B-Application
.	O
</s>
<s>
Therefore	O
,	O
this	O
model	B-Application
can	O
be	O
directly	O
compared	O
against	O
the	O
Shannon	O
form	O
of	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
using	O
the	O
F-test	B-General_Concept
of	O
nested	O
models	O
.	O
</s>
<s>
This	O
comparison	O
reveals	O
that	O
not	O
only	O
does	O
the	O
Shannon	O
form	O
of	O
Welford	O
's	O
model	B-Application
better	O
predict	O
movement	O
times	O
,	O
but	O
it	O
is	O
also	O
more	O
robust	O
when	O
control-display	O
gain	O
(	O
the	O
ratio	O
between	O
e.g.	O
</s>
<s>
Consequently	O
,	O
although	O
the	O
Shannon	O
model	B-Application
is	O
slightly	O
more	O
complex	O
and	O
less	O
intuitive	O
,	O
it	O
is	O
empirically	O
the	O
best	O
model	B-Application
to	O
use	O
for	O
virtual	O
pointing	O
tasks	O
.	O
</s>
<s>
In	O
its	O
original	O
form	O
,	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
is	O
meant	O
to	O
apply	O
only	O
to	O
one-dimensional	O
tasks	O
.	O
</s>
<s>
A	O
major	O
application	O
for	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
is	O
2D	O
virtual	O
pointing	O
tasks	O
on	O
computer	B-Device
screens	I-Device
,	O
in	O
which	O
targets	O
have	O
bounded	O
sizes	O
in	O
both	O
dimensions	O
.	O
</s>
<s>
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
has	O
been	O
extended	O
to	O
two-dimensional	O
tasks	O
in	O
two	O
different	O
ways	O
.	O
</s>
<s>
hierarchical	O
pull-down	O
menus	O
,	O
the	O
user	O
must	O
generate	O
a	O
trajectory	O
with	O
the	O
pointing	B-Device
device	I-Device
that	O
is	O
constrained	O
by	O
the	O
menu	O
geometry	O
;	O
for	O
this	O
application	O
the	O
Accot-Zhai	B-General_Concept
steering	I-General_Concept
law	I-General_Concept
was	O
derived	O
.	O
</s>
<s>
For	O
simply	O
pointing	O
to	O
targets	O
in	O
a	O
two-dimensional	O
space	O
,	O
the	O
model	B-Application
generally	O
holds	O
as-is	O
but	O
requires	O
adjustments	O
to	O
capture	O
target	O
geometry	O
and	O
quantify	O
targeting	O
errors	O
in	O
a	O
logically	O
consistent	O
way	O
.	O
</s>
<s>
Overall	O
the	O
W-model	O
represents	O
the	O
state-of-the-art	O
measurement	O
.	O
</s>
<s>
The	O
a	O
parameter	O
is	O
typically	O
positive	O
and	O
close	O
to	O
zero	O
,	O
and	O
sometimes	O
ignored	O
in	O
characterizing	O
average	O
performance	O
,	O
as	O
in	O
Fitts	B-General_Concept
 '	I-General_Concept
original	O
experiment	O
.	O
</s>
<s>
If	O
the	O
latter	O
are	O
not	O
incorporated	O
into	O
the	O
model	B-Application
,	O
then	O
average	O
movement	O
times	O
can	O
be	O
artificially	O
decreased	O
.	O
</s>
<s>
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
deals	O
only	O
with	O
targets	O
defined	O
in	O
space	O
.	O
</s>
<s>
The	O
model	B-Application
for	O
temporal	O
pointing	O
was	O
first	O
presented	O
to	O
the	O
human	O
–	O
computer	O
interaction	O
field	O
in	O
2016	O
.	O
</s>
<s>
The	O
model	B-Application
predicts	O
the	O
error	O
rate	O
,	O
the	O
human	O
performance	O
in	O
temporal	O
pointing	O
,	O
as	O
a	O
function	O
of	O
temporal	O
index	O
of	O
difficulty	O
(	O
IDt	O
)	O
:	O
</s>
<s>
Multiple	O
design	O
guidelines	O
for	O
GUIs	B-Application
can	O
be	O
derived	O
from	O
the	O
implications	O
of	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
.	O
</s>
<s>
In	O
its	O
basic	O
form	O
,	O
Fitts	B-General_Concept
's	I-General_Concept
law	I-General_Concept
says	O
that	O
targets	O
a	O
user	O
has	O
to	O
hit	O
should	O
be	O
as	O
big	O
as	O
possible	O
.	O
</s>
<s>
Since	O
the	O
pointer	O
will	O
always	O
stop	O
at	O
the	O
edge	O
,	O
the	O
user	O
can	O
move	O
the	O
mouse	B-Device
with	O
the	O
greatest	O
possible	O
speed	O
and	O
still	O
hit	O
the	O
target	O
.	O
</s>
<s>
The	O
use	O
of	O
this	O
rule	O
can	O
be	O
seen	O
for	O
example	O
in	O
MacOS	B-Application
,	O
which	O
always	O
places	O
the	O
menu	O
bar	O
on	O
the	O
top	O
left	O
edge	O
of	O
the	O
screen	O
instead	O
of	O
the	O
current	O
program	O
's	O
windowframe	O
.	O
</s>
<s>
Microsoft	B-Application
Windows	I-Application
(	O
prior	O
to	O
Windows	B-Application
11	I-Application
)	O
places	O
its	O
"	O
Start	O
"	O
button	O
in	O
the	O
lower	O
left	O
corner	O
and	O
Microsoft	B-Application
Office	I-Application
2007	O
uses	O
the	O
upper	O
left	O
corner	O
for	O
its	O
"	O
Office	O
"	O
menu	O
.	O
</s>
<s>
MacOS	B-Application
places	O
the	O
close	O
button	O
on	O
the	O
upper	O
left	O
side	O
of	O
the	O
program	O
window	O
and	O
the	O
menu	O
bar	O
fills	O
out	O
the	O
magic	O
corner	O
with	O
another	O
button	O
.	O
</s>
<s>
The	O
user	O
can	O
continue	O
interaction	O
right	O
from	O
the	O
current	O
mouse	B-Device
position	O
and	O
does	O
n't	O
have	O
to	O
move	O
to	O
a	O
different	O
preset	O
area	O
.	O
</s>
<s>
The	O
research	O
suggests	O
that	O
in	O
practical	O
implementations	O
the	O
direction	O
in	O
which	O
a	O
user	O
has	O
to	O
move	O
their	O
mouse	B-Device
has	O
also	O
to	O
be	O
accounted	O
for	O
.	O
</s>
