Human Factors and Fitts’ Law
Ken Goldberg, IEOR and EECS, UC Berkeley
What is Ergonomics?
Prof. Wojciech Jastrzebowski
in Poland in 1857:
From two Greek words
Ergon meaning work
and
Nomos meaning principles or laws
Ergonomics = The Science of Work
What is Ergonomics?
Common Definitions
“Ergonomics is essentially fitting the workplace to
the worker. The better the fit the higher the
level of safety and worker efficiency.” Fitting the
Task to the Human ~ Grandjean 1990
“Ergonomics removes barriers to quality,
productivity and human performance by fitting
products, tasks, and environments to people.”
ErgoWeb.com
Human Factors
What Is Human Factors?
The following definition was adopted by the
International Ergonomics Association in August
2000:
Ergonomics (or human factors) is the scientific
discipline concerned with the understanding of
interactions among humans and other elements of a
system, and the profession that applies theory,
principles, data, and other methods to design in
order to optimize human well-being and overall
system performance.
Human Factors and Ergonomics
• Britain - The Ergonomic Society was formed in
1952 with people from psychology, biology,
physiology, and design.
• United States - The Human Factors Society
was formed in 1957. In the US "human factors
engineering" was emphasized by the US military
with concentration on human engineering and
engineering psychology.
from Mike Mandel, Making Good Time (CMP Bulletin vol. 8 no. 2,
California Museum of Photography, UC California, Riverside, 1989)
Gilbreth Video
Hawthorne Effect
Worker Study (1927 - 1932) of the Hawthorne Plant
of the Western Electric Company in Cicero, Illinois.
Led by Harvard Business School professor Elton
Mayo: Effect of varying light levels on Productivity.
Measure of Man, Henry Dreyfuss, 1960
Occupational Safety and Health Administration,
(OSHA, 1970, www.osha.gov)
Neutral Posture for Computer
Use
Position the monitor about an
arm’s length away directly in
front of you. The top of the
screen no higher than eye
level (Unless the user wears
bi-focal glasses)
Use a document
holder close to the
monitor rather than
laying papers flat
Mouse should be next to keyboard
both at a height equivalent to the
user’s seated elbow height
Knees comfortably bent with
feet resting on the floor. If the
chair is raised so the keyboard
height equals elbow height, use
a footrest .
Adjust the seat height
so upper arms hang
vertically, elbows bent
about 90 degrees,
shoulders relaxed and
wrists fairly straight
Adjust
the back
rest to
provide
firm
support
to the
small of
the back
Paul M. Fitts, 1954
Fitts connected the speed-accuracy
tradeoff of choice reaction times to
reaching movement tasks
Fitts’ “Law”
A
W
•
T = a + b log2( A )
W
ID
Parameters a, b experimentally determined
Alternative: Square-root Law
• Fitts’ Logarithmic Law is not derived using
biomechanics and kinematics
• We derive a “Square-root” Law:
based on 2 simple assumptions
Assumption 1
Acceleration
Acceleration ( x ) is piecewise constant
s = T /2
Time
T
Assumption 2
Acceleration is proportional to target width
Wider targets are easier to reach
 larger accelerations possible
Optimal Control
• Given a bound on | x | ,
Fastest way to reach a target is to use
“bang-bang” control
T/2
T
Optimal Bang-Bang Control Velocity
s = T/2
Position at time T:
T
Optimal Bang-Bang Control Position
A
A
2
s = T/2
T
Optimal Binary Acceleration Model
• Use Assumption 2 to specify a single
formula that relates A, W, and T
• Assumption 2 Hypothesis:
Maximal acceleration set by the human is
proportional to target width
(Wider targets permit larger accelerations)
Optimal Binary Acceleration Model
• Assume:
• Optimal bang-bang model:
• Add reaction time a:
• Parameters a,b set from experimental data
First Mouse (Douglas Engelbart and
William English, 1964)
First Mouse Patent (Engelbart)
(Shumin Zhai, IBM Almaden Research Center)
Modern Input Devices
Fitts’ Law Java Applet
Experimental Tests
Homogeneous
Cursor Motions
Fixed
Rectangle Test
Heterogeneous
Cursor Motions
Variable
Rectangle Test
Circle Test
Available Data
• Original data set:
–
–
–
–
–
2232 users for fixed rectangle tests
2466 users for variable rectangle tests
1897 users for circle test
User did not complete all trials  Removed
User has outlier points  Removed
• Final data set:
– 1640 users for fixed rectangle tests
– 1996 users for variable rectangle tests
– 1561 users for circle tests
Model Parameters
• Parameter set using least-squares linear
regression for each user
• Average parameters over all users:
Typical User
Models
with
Lowest
RMS Error
Effect Size
Square-root
Law better
Logarithmic
Law better
• Mean signed difference in RMS errors between
the Square-root Law and Fitts’ Logarithmic Law,
as a percent of the mean RMS error for Fitts’
Logarithmic Law, with 95% confidence intervals
Web-Based Fitts’ Law Demo
www.tele-actor.net/fitts/
Human Factors and Ergonomics
• Britain - The Ergonomic Society was
formed in 1952
• United States - The Human Factors
Society was formed in 1957.
Human Factors and Fitts’ Law
Ken Goldberg, IEOR and EECS, UC Berkeley
Cupstacking Video
Outline
• Fitts’ Law Introduction
• Kinematics Models of Fitts’ Task
– Symmetric Binary Acceleration Model
– Asymmetric Binary Acceleration Model
• Fitts’ Task in HCI
• Web-based Experiments
Choice Reaction Time Task
Stimulus: 1,…,N
Response: 1,…,N
4
1
2
3
4
5
6
7
8
J. Merkel, 1885: Stimuli 1,…,N equally likely.
TR = a + b log2 N
Information Theory
• Base 2 logarithm of the number of
alternatives is a measure of information
Number of bits = log2 N
Corresponds to the average number of yes/no
questions required to identify correct stimulus
• In example:
log2 8 = 3 bits
Fitts’ Information Theory Approach
• Define “information” encoded in a reaching
moving task
• Information transmitted I in a response is a
measure of the reduction in uncertainty
Information Transmitted
7-8
1
2
3
4
5
6
7
8
000
001
010
011
100
101
110
111
•
•
•
•
# possibilities before event: 8
# possibilities after event: 2
Information transmitted: -log2(2/8) = 2 bits
Uncertainty: 1 bit
Discrete vs. Continuous Choice
1
2
3
4
5
6
7
8
000
001
010
011
100
101
110
111
Target
Start
Position
Amplitude A Width W
Fitts’ Formulation
Number of possibilities after response: W
Number of possibilities before response: 2A
Information transmitted = Index of Difficulty
Weber Fraction Formulation of
Fitts’ Task
• Welford, 1968
• Weber fraction: W/(A+0.5W)
Target
Start
Position
Amplitude A Width W
Shannon Formulation of Fitts’ Task
• Formulation based on Shannon’s Theorem
[I. Scott MacKenzie 1992]
C = Information capacity of
communication channel
B = channel bandwidth
S = signal strength
N = noise power
• Shannon Formulation for Fitts’ Task:
Outline
• Fitts’ Law Introduction
• Kinematics Models of Fitts’ Task
– Symmetric Binary Acceleration Model
– Asymmetric Binary Acceleration Model
• Fitts’ Task in HCI
• Web-based Experiments
Outline
• Fitts’ Law Introduction
• Kinematics Models of Fitts’ Task
– Symmetric Binary Acceleration Model
– Asymmetric Binary Acceleration Model
• Fitts’ Task in HCI
• Web-based Experiments
Velocity Profiles of Fitts’ Task
[ ]
1.
2.
3.
C.L. MacKenzie et al,
1987
Velocity profiles are asymmetric
Asymmetry increases as target width decreases
Amplitude has relatively little effect on asymmetry
Asymmetric Binary Acceleration Model
Assume:
Percent time accelerating increases with W
Asymmetric velocity profile:
Acceleration is constant a
Deceleration set so distance
A reached at time T
s
T
Asymmetric Velocity Profile
s
T
Asymmetric Model Position
s
T
Asymmetric Binary Acceleration Model
• Add reaction time a:
• Parameters a,b set from experimental data
• Same formula as Optimal Binary
Acceleration Model;
Different assumptions and derivations
Velocity v
Optimal Binary Acceleration Model
a
Movement Time T
Asymmetric Binary Acceleration Model
Velocity v
s
Movement Time T
Outline
• Fitts’ Law Introduction
• Kinematics Models of Fitts’ Task
– Symmetric Binary Acceleration Model
– Asymmetric Binary Acceleration Model
• Fitts’ Task in HCI
• Web-based Experiments
Mouse
• First mouse (1964):
Douglas Engelbart and William English