Human Factors and Fitts Law Ken Goldberg IEOR

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. ” Ergo. Web. 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 log 2( 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 ( ) is piecewise constant

Assumption 2 Acceleration is proportional to target width Wider targets are easier to reach larger accelerations possible

Optimal Control • Given a bound on , 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 log 2 N

Information Theory • Base 2 logarithm of the number of alternatives is a measure of information Number of bits = log 2 N Corresponds to the average number of yes/no questions required to identify correct stimulus • In example: log 2 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: -log 2(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: 2 A Information transmitted = Index of Difficulty

$Weber Fraction Formulation of Fitts’ Task • Welford, 1968 • Weber fraction: W/(A+0. 5$

Weber Fraction Formulation of Fitts’ Task • Welford, 1968 • Weber fraction: W/(A+0. 5 W) Target Start Position Amplitude A Width W

Shannon Formulation of Fitts’ Task • Formulation based on Shannon’s Theorem [I. Scott Mac. Kenzie 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

Velocity Profiles of Fitts’ Task [ ] 1. 2. 3. C. L. Mac. Kenzie 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