steven c. seow 2009571002 이 봉 근 user interface lab department of information management...

Steven C. Seow

2009571002 이 봉 근User Interface LabDepartment of Information Management Engineering

Human Computer Interaction, Vol. 20, 2005

Information Theoretic Models of HCI:A Comparison of the Hick-Hyman Law and Fitts’ Law

1. Introduction

2. Psychology and HCI

3. Information theory

4. The Hick-Hyman law

5. Fitts’ law

6. Integration of the laws

7. The Hick-Hyman law and HCI

8. Conclusion

User Interface LabDepartment of Information Management Engineering

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Contents

Background Two surviving human performance principles based on Information Theory.

Hick-Hyman Law and Fitts’ Law A search of the current HCI literature will reveal that

Hick-Hyman Law failed to gain momentum in the field of HCI,

Whereas Fitts’ Law received, and continues to receive, substantial attention.

Objective This article reviews each law with respects to

Its origins, theoretical formulation, theoretical development, research, and ap-plication

And discusses the possible contributing factors responsible for

The failure of Hick-Hyman Law to gain momentum in the field.


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1. Introduction

The relationship between psychology and HCI Hard science (computer science) would drive out soft science (psychology).

The solution psychologists proposed was to “harden” psychology, that is, to improve the scientific caliber of the discipline to prevent its displacement

Three possible roles for psychology

A. Primary professionals in HCI, as they are in some fields like mental health and counseling

B. Specialists working with the primary professionals (the system designers)

C. The system designers could apply psychology themselves.


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2. Psychology and HCI

3.1. The Communication System The classical Information Theory is essentially a communication engineering

theory based on the transmission of electrical signals for telegraphic comm. The two laws are based on analogies of this general model of comm system. channel capacity (C)

The amount of information that a communication channel transmits in a fixed amount of time• Physical limitations and different capacities

This leads to an important distinction between the classical Information The-ory and the psychological ones based on it.


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3. Information Theory

Figure 1. Schematic diagram of a general model of communication system

3.1. The communication system (cont’) Engineers can calculate the theoretical channel capacity by knowing the physical

specification of the hardware (bandwidth, transmitter, type of cable, etc.).

What psychologists can do, however, is to measure information processing performance to infer the information capacity of the psychological system.• This is the index of performance (IP) in Fitts (1954) and • The rate of gain of information in Hick (1952).


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Figure 2. Hypothetical data showing the concept of the reciprocal of the slope as information capacity.

3.2. Quantifying Information Information is formally defined in Information Theory as a reduction in uncer-

tainty and quantified in units of bit. The Shannon-Weiner measure of information,

The amount of uncertainty is called the entropy (H)• This is only applicable when the alternatives are equiprobable.

• Unequal probabilities: The amount of information or uncertainty is maxi-mal when all elements are equiprobable.

Transmitted amount of information• Received info’ = transmitted info’ - (loss + noise info’)


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The Hick-Hyman Law was built upon prior findings of a systematic relationship be-tween number of alternate stimuli and choice-reaction times.


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4. The Hick-Hyman Law

Figure 3. Schematic diagram of a general model of communication system

First reported by Donders(1686), Merkel(1885)

Merkel discovered that it takes longer to response to a large set of stimuli than that of small set

This regularity caught the atten-tion of psychologists

4.1. Hick (1952) original experiments William Edmund Hick was probably the first to apply Information Theory to

psychological problems (Hick, 1953). Experiments

Apparatus

Task • To depress the correct key for a lighting of a particular lamp.

Goal • The goal of the experiment was to determine the empirical relationship be-

tween choice reaction time and stimulus information content


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Figure B-1. Author’s impression of the apparatus in Hick (1952).

4.1. Hick (1952) original experiments


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Figure 4. data of subject A (Hick him-self) in experiment I in Hick (1952)

The data are fitted with a loga-rithm function of 0.518 log10 (n +

1)

Figure 5. Data of subject B in exper-iments II and III in Hick

The data are fitted with a loga-rithm function of

RT = –0.042 + 0.519 log10 (ne + 1)

Hick characterized the relationships between RT and n or ne as logarithmic and concluded that “the amount of information extracted is proportional to the time taken to extract it, on the average”

4.2. Hyman (1953) original experiments Ray Hyman may be the first to articulate the linearity between the two variables. Experiments

Apparatus

Task • To responded by calling out the designated name of the light.

Goal • Exploiting the fact that entropy is maximal when the stimuli are equiproba-

ble.


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Figure C-1. Author’s impression of the apparatus in Hyman (1953).

4.2. Hyman (1953) original experiments With the extension of Hyman (1953), Hick’s Law was consequently accepted by

many as the Hick-Hyman Law. Essentially, the law predicts a linear relationship between reaction time and transmitted information:

RT is reaction time, a and b are empirically determined constants, and HT is the transmitted information. The reciprocal of b is what Hick referred to as the rate of gain of information or the information capacity.


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Figure 6. data of subject FP in Hy-man

The data points of all three experiments are fitted with a linear function of 180 + 215HT

4.3. Theoretical developments Longstreth et al. : Power curve model

H-H law is little increase of RT when the stimuli are familiar letters or digits and when the responses are verbal identification.

They submitted a power curve as a replacement for fitting the data:

Laming et al. : Parallel exhaustive process models

These models suggested as replacement of Hick’s serial process models.• Usher and McClelland’s (2001) Leaky, Competing Accumulator Model.

※ (a) information is accrued in a gradual process and

(b) the accumulated information is subject to random fluctuations


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4.4. Research and applications Speed-Accuracy Tradeoff

speed up performance, faster responses are produced at the expense of accu-racy. The converse is true.

※Using payoff and feedback appears to be effective in motivating participants

to focus on speed or accuracy. Stimulus-Response Compatibility

An increase in SRC has been found to diminish the slope of the RT Psychometrics

Roth (1964) is commonly cited as one of the first to investigate the RT-IQ re-lationship

HCI applications

Applications of Hick-Hyman Law are scarce in the HCI literature.• Laudauer and Nachbar (1985): touchscreen menu design

※ H-H law was unable to proffer any practical (menu) design.


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Fitts’ law The law states a linear relationship between task difficulty and movement time

T = a + b ID, ID=log2(2A/W)

T is the average time to reach a target, a and b are constant

ID is the index of difficulty, A is the amplitude of the pointing movement and W is the width of the target

5.1. Fitts original experiments the reciprocal tapping, disk transfer, and pin transfer tasks.


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5. Fitts’ Law

5.2. Theoretical developments There are significant theoretical modifications to the original Fitts’ equation.

Welford (1960)

MacKenzie (1992)

Meyer et al. (1988)

deterministic iterative-corrections model • Single rapid aimed movement → a series of submovement

stochastic optimized-submovement model• Single rapid aimed movement → primary and secondary submovement

ISO 9241-9: Throughput, effective target width (We)


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5. Fitts’ Law

5.3. Research and applications Speed-Accuracy Tradeoff

Fitts assumed that the motor system has a fixed information capacity and that making participants perform beyond this capacity will result in systematic variability in responses.

Psychometrics

HCI applications

Pointing

Angle of approach

Semantic pointing: display-control ratio

Text entry on soft keyboards

Navigation: multi-scale pointing (e.g. panning, zooming)


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5. Fitts’ Law

If a certain stimuli were provided

Choice which reaction have to be Corre-

sponded(choice-reaction time)

Selecting or aiming the target

(Movement time)

Attempt to combine two laws


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6. Integration of the Laws

• Aim for randomly indicated targets with a pencil from a home posi-tion along to clicks of a metronome.

• Their results showed that Fitts’ Law did not hold in the fusion

Beggs, Graham, Monk, Shaw & Howarth (1972)

• home-to-target paradigm but they tested their participants with both sequential tasks (visual stimulus) and concurrent tasks (before knowing where the target is).

• Their results showed that Fitts’ Law was successful only sequential condition

Hoffmann and Lim (1997)

• modeling performance in text entry using soft keyboards.• Incompatibility of the two laws in their model.

Soukoreff and MacKenzie (1995)

Two laws share much in common

a. Both laws were analogies based on Shannon and Weaver’s Information Theory soon after its introduction.

b. Both laws employed temporal dependent measures and accuracy to address per-formance rates and limits of a human system.

c. Both have received substantial support in research that demonstrated their gen-erality and in process models that explained possible underlying mechanisms.

☞ When one considers HCI research and applications of the laws, however, the Hick-Hyman Law falls short.


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7. The Hick-Hyman Law and HCI

Reason why H-H Law lacked the momentum in HCI Laming (1966, 1968)

Discrepancies between Shannon’s theory and Hick’s analogy.• “[t]he attempt to explain choice-reaction times in terms of Communication

Theory must now be abandoned … it has been shown that this analogy [of humans as communication system] cannot be maintained”

Newell and Card (1985)

It is also reasonable to speculate that the H-H law fell victim to what Newell and Card (1985) referred to as the eviction of the soft sciences by the hard sciences.• First evidence against this argument: H-H law and Fitts’ law have compa-

rable quantitative components but the latter did not suffer the same fate.• Second, HCI has shifted its focus to include what some may refer to as soft

sciences, such as sociology. (individual psychology → cooperative paradigm)


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7.1. Difficult in Application

Few HCI research projects have hardly been past this stage is because there was no need to engage in the complexity of the information theoretic measures.

7.2. Complexity of Stimuli Psychology and psychometrics: simple unidimensional stimuli HCI: a variety of multidimensional stimuli (buttons, menus, text, animation, etc.)

7.3. Levels and Types of Performance Fitts’ law: automated, kinesthetic, and related to dexterity. H-H law: performance can gradually improve over time, such as with optimal

SRC and practice


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Codify equivalent events involved into al-

ternatives

The probabilities of these alternatives must

be determinedCalculate their entropy

The validity, theoretic roots, and quantitative caliber of the law seem unlikely to be significant factors that prevented the Hick-Hyman Law from gaining momen-tum in HCI.

What is plausible is a combination of several factors.

First, the inherent difficulty in applying the law is obvious. This is likely due to the relatively more complex stimuli in HCI.

Additionally, an inability to account for performance in a highly familiar, automated, or trained task may have also limited the law’s applicability to HCI problems.

Nevertheless, within limits, the relationship between information load and choice-reaction time captured by the Hick-Hyman Law is robust and demonstra-ble at the basic level.

The challenge lies in codifying complex multidimensional stimuli and extend-ing the law beyond novel performance.


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8. Conclusion

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