division of information management engineering user interface laboratory a model for movement time...

Division of Information Management Engineering

User Interface Labora-

tory

A Model for Movement Time on Data-entry Key-boards

Colin G. DruryAnd Errol R. Hoffmann

UI 연구실 백지승



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1. INTRODUCTION

2. A model for optimum layout of keyboards

3. Experiment 1. Test of model with simulated keyboard3.1 Subjects3.2 Experimental conditions3.3 Results

4. Experiment 2. Movement times on a real keyboard4.1 Subjects4.2 Apparatus4.3 Procedure4.4 Results and discussion

5. Experiment 3. Movement times on a calculator keyboard

6. Survey of keyboard devices

7. Conclusions

Contents



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• Very little research has been reported on modelling of key-board motions

• Standard layouts have been developed with little considera-tion ofgeometrical factors affecting performance

• Performance measures of keying time and accuracy had perfect rank-order correlation for the eight different key-boards

• This paper presents a model and experiments which go some way towards rectifying this situation for the simplest case of data-entry keyboards

1. Introduction



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• A model shows the dependence of movement time (MT) on key size spacing

S=centre-to-centre key spacingB= key widthC=distance between key edgesF=finger width (used interchangeably with P=probe width, where ap-

propriate)

• Task: to hit the required key while at the same time missing the surrounding keys

• 2 cases that need to be considered→where the spacing between the key edges is respectively greater and less than the finger width


Fig. 1

The two cases of keyboard lay out considered in the model for perfor-mance• Case 1 : for distance between the keys greater than the finger width• Case 2 : when the finger iswider than the distance between keys * the fingers are 'square-ended‘



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2.1 Case 1. Limited by missing the target key• occurs when C>F or S>B+ F

→ adjacent keys do not interfere with the aiming task• effective target width :W= B+ F• Movement Time for this case,

MT=a+b log2 [2kS/(B+F)} (1) • maximum to minimize the movement time occurs when C=F or S=B+F

MT=a+b log2 [2k] (2)

2.1 Case 2. Limited by hitting adjacent keys• S<B+F and the effective target width is given by W= 28-B-F• If Fitts' Law is applicable, the MT is given by

MT=a+b log2 [2kS/(2S-B-f)] B ↑⇒ the index of difficulty (ID =log2 (2 x amplitude/target toler-

ance)) B should be small → S=B+F ⇒ MT=a+b log2 [2k]




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• The minimum movement time : when C=F• The variation of the movement time comes from a variation of the ID at con-

stant S, due to the changes in effective target width

• The maximum effective width is seen at the in-tersection of the lines describing the two cases; at this point C=F.

• If the keys are space-filling (B=S) ⇒ case 2 is applicable and W=B- F

keys give a minimum effective target width and hence a maximum MT for the given spacing

Fig.2 Demonstration of the effective target width as a function of the key width, and the optimum width predicted by the model




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3.1 Subjects• Ten male subjects, ranging in age from 18 to 27 years• Finger pad size was measured for each subject by inking the index finger and

having the subject lightly press the finger onto paper in the posture used in making the movements.

• Measured finger pad size : 10 ~ 12 mm, mean value : 11 mm

3.2 Experimental conditions• The spacing of the target and constraining adjacent strips : constant at 20

mm the target width was varied to vary the ClF ratio.• The amplitude of movement (A) : 160 mm• Four metal probes widths: 0, 5, 10, 15 mm / target width : 2, 6, 10, 14, 18 mm• F=5 mm: CIF=0.4 to 3.6

F= 10 mm: CIF=0.2 to 1.8F= 15 mm: CIF= 0.13 to 1.2

• Each subject had a different random order of presentation of probes within target size

3. Experiment 1. Test of model with simulated keyboard



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3.3 Results3.3.1 Analysis of Variance

• Analysis of variance ⇒ target width, probe width and target condition • Significant interactions btw. target width and probe width, target width and

target condition and probe width and target condition• for the narrowest probes width: significant differences btw. the target

widthsfor larger probe width : no significant effect of the target width


Table I. Mean movement times (ms) for the various target and probe widths in the single and triple tar-get tasks of experiment 1. Upper value in each case is for single targets, lower value for triple targets.



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• At higher target widths, the differences in MT become significant• This interaction clearly shows the two effects:

target width ↑⇒ the single target movement time continu-ously ↓

the triple target condition first shows ↓ → ↑• Considering only the four metal probes, there was no significant

difference in the movement times of single/triple targets for the pointed probe

• The difference becomes significant : 5 mm → 10mm → 15 mm probe


Fig. 3 Fig. 4



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3.3 Results3.3.2 Regression analysis: single targets

• carried out using a modified form of equation 1, in which the proportion of added probe width (E) to yield maximum was determined

MT=a+b log2 [2A/(B+EP)]• The maximum occurred when E=0.60

MT= -7.7+42.86; =0.962 (3)

• the regression was not greatly sensitive to the value of E

• maximum correlation occurred when a finger pad width of 10 mm was used

MT= 17.76+29.60; = 0·98 (4)


2r

2r

Fig. 52r



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3.3 Results3.3.3 Regression analysis: triple targets

• form of movement time as a function of the ratio of C/F=clearance between keys/probe width.

• assumed that the full finger width is added to make up the effective target width

• each probe width shows the same patterns of movement time; firstly a decrease with increase of C/F

and then an increase with C/F values greater than unity


Fig.6Fig.7

• The simple explanation of this behavior lies in the way in which the effective index of diffi-culty changes with effective target width for the various experimental conditions MT=110+24.65 (ID); =0.62 (5)• Assumption of a finger pad width of 10 mm shows a minimum movement time at the cor-rect location of C/F = 1, however the variation of MT was small• The maximum variation was 11 ms, with the metal probe case of P= 10 mm

2r

Fig.8

• The other strange feature of this data is that at the most extreme values of C/F, the data show a decrease in movement time, although not to the extent of the minimum MT

The model needs to be tested on real keyboards in order to determine its validity under more realistic con-

ditions



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4.1 SubjectTen subjects(six male) ranging in age from 16 to 45 years

4.2 Apparatus• Five boards were built on a standard 19mm matrix board.• Each of these keyboards had a set of five keys, set in a "cross' pattern, at

one end, the centre one of which was the target key• Key caps were machined to have square tops of sizes 2, 6, 10, 14, and 18

mm• Starting keys were set at spacings of 2, 4, 6, and 8 keys from the target key • The experiment was similar to experiment 1 except :

(i) the finger was used

(ii) different amplitudes of movement were used(iii) square target keys were used

• The aim of the experiment ⇒ not only to test the model for real keyboards, but also to determine the effect of different levels of index of difficulty

4.3 Procedure

4. Experiment 2. Movement times on a real key-board



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4.4 Results and discussion4.4.1 Measurement of effective target width


Fig. 9

• the optimum key widths for each subject have been determined from plots similar to figure 9

• Note that for subject 9, who had a very wide finger, the optimum key width is less than 2 mm

• The mean values of MT in table 1 indicate that the effective target width is a maxi-mum at a key width of 10 mm; the mean opti-mum key width is however about 7 mm (table 2).

Table 2



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4.4 Results and discussion4.4.1 Measurement of effective target width

• The model prediction for the optimum key size, for a given key spacing

B=S-0.5( - ) (6)• Regression of effective target width as a function of key width and

finger pad width gave (17 cases) =-4.46+0.64B+1.73F; =0.32 (7)

• the data for case 2 effective target widths were well represented by the model predictions, yielding (33 cases)

=40.8-0.97B-1.33F; -0.914 (8)• The optimum key width for this group of subjects

=28.2-1.90F (9)


1F

2F

opt

eW

eW



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4.4 Results and discussion4.4.2 Movement times


• The mean data showed a very weak, and non-significant, minimum in the movement time at a key size of 6 mm

• Movement times on real keyboards (experiment 2), showing the effect of key size and amplitude of movement.

• Indexes of difficulty have been calculated for each experimental condition using the mean values of effective target width in table 2. • A plot of movement times as a function of this 10 is shown in figure 11. The relationship is MT=3.8+40.57 (ID); =0.93 (10)

2r

Fig.10Fig.11Table 3

• Key size (mm) at which mini-mum movement time occurred as a function of amplitude and direc-tion of movement, for each of the ten subjects in experiment 2

• The overall mean minimum movement time occurs at a key width of about 8 mmFig. 12

• Error rate was controlled in the experiment so that no more than one error occurred in a give condition

• The total percent of errors, averaged over the ten subjects along with the mean movement time

• The figure shows that a minimum error rate occurs at B=6 mm, which is in agreement with the location of the minimum in movement time



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• A small experiment was carried out using an HP35 calculator• Measuring the number of movements made between various keys on the

board over a period of 10 s. • Ten subjects between the ages of 14 ~ 55• It is seen that the classic form of Fitts' Law

is obtained, with levelling-off of MT at low values of 10• Fitts' Law cannot be simply applied to

the calculation of keyboard movement times as, at low 10 values, the MT will be underestimated

• Above an index of difficulty of about three, the MTs show a linear increase with 10

5. Experiment 3. Movement times on a calculator key-board

Fig.13



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6. Survey of keyboard devices

• In order to compare current practice with the results of these experiments, a survey of electronic devices containing keyboards was undertaken• Many of these devices had spacing and key size which differed in the vertical and horizontal directions, thus results of the survey are presented separately for the two directions• The upper line on each of these figures is for B=S, that is, for space-filling keys• The lower line is for B=S-10 mm, which would be about the optimum key width with keys of small deflection



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• A model for keyboard movement times shows that, for a given key spacing, there is an optimum key size for minimum movement times

• Experiments to determine the effective finger width indicate that, when there is a single target, the effective target size is close to the sum of the target width and the finger width

• Experiments on real keyboards with subjects using their fingers showed a minimum in both movement time and error rate at a key width of about 6 to 8 mm, when the key spacing was 19 mm.

• The width of the subject's finger was important in determining the optimum key size, but despite this variability, an optimum could be demonstrated

7. Conclusions

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