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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? .

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Human Factors and Fitts’ Law Ken Goldberg, IEOR and EECS, UC Berkeley

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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)

Adjust the seat height so upper arms hang vertically, elbows bent about 90 degrees, shoulders relaxed and wrists fairly straight

Use a document holder close to the monitor rather than laying papers flat

Adjust the back rest to provide firm support to the small of the back

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 .


Paul M. Fitts, 1954

Fitts connected the speed-accuracy tradeoff of choice reaction times to reaching movement tasks


A

W

ID

A

W

Fitts’ “Law”

  • T = a + b log2( )

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

T

Position at time T:


A

A

2

Optimal Bang-Bang Control Position

T

s = T/2


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

Heterogeneous Cursor Motions

Fixed Rectangle Test

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

  • 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

Square-root Law better

Logarithmic Law better


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


1

2

3

4

5

6

7

8

Choice Reaction Time Task

Stimulus: 1,…,N Response: 1,…,N

J. Merkel, 1885: Stimuli 1,…,N equally likely.

TR = a + b log2N

4


Information Theory

  • Base 2 logarithm of the number of alternatives is a measure of information

    Number of bits = log2N

    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


1

2

3

4

5

6

7

8

Information Transmitted

7-8

  • # possibilities before event: 8

  • # possibilities after event: 2

  • Information transmitted: -log2(2/8) = 2 bits

  • Uncertainty: 1 bit

000

001

010

011

100

101

110

111


1

2

3

4

5

6

7

8

Discrete vs. Continuous Choice

000

001

010

011

100

101

110

111

Target

StartPosition

Width W

Amplitude A


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

StartPosition

Width W

Amplitude A


Shannon Formulation of Fitts’ Task

  • Formulation based on Shannon’s Theorem[I. Scott MacKenzie 1992]

  • Shannon Formulation for Fitts’ Task:

  • C = Information capacity of communication channel

  • B = channel bandwidth

  • S = signal strength

  • N = noise power


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

  • Velocity profiles are asymmetric

  • Asymmetry increases as target width decreases

  • Amplitude has relatively little effect on asymmetry

[ ]

C.L. MacKenzie et al,1987


Asymmetric Binary Acceleration Model

Assume: Percent time accelerating increases with W

Asymmetric velocity profile:

Acceleration is constant a

Deceleration set so distanceA reached at time T

s

T


s

T

Asymmetric Velocity Profile


s

T

Asymmetric Model Position


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


Optimal Binary Acceleration Model

Velocity v

a

Movement Time T


Asymmetric Binary Acceleration Model

s

Velocity v

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


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