fingertip force, surface geometry, and the perception of

SUSAN J. LEDERMAN* and M. M. TAYLORtDefence and Civil Institute of Environmental Medicine

Downsview, Ontario, Canada

Fingertip force, surface geometry, andthe perception of roughness by active touch

Ss made magnitude estimates of the perceived roughness of grooved metalplates under conditions of active touch with controlled finger force. The widerthe grooves in the plate. the narrower the lands between the grooves, or thegreater the fmger force, the greater was the perceived roughness. Increase infinger force also slightly increased the slope of the magnitude estimationfunction, suggesting not only that the roughness of a uniform surface but alsothe contrasts in the roughness of differing parts of a patterned surface would bealtered by changes in the manner of feeling the surface. An analogous effect hasbeen reported in vision, in that increases in illumination increase the apparentcontrast of a surface.

The world we live in is primarily avisual one. We use our eyes to tell usabout the shape of an object, its size,its color, and its orientation. Theinformation is obtained rapidly andusually proves amazingly accurate. Thevisual modality plays such a dominantand dominating (e.g., Rock & Harris,1967) role in our world, however, thatit is often easy to overlook theimportance of tactile exploration. Thetouching process tells us a good dealabout the more intimate qualities ofthings, such as temperature andsurface texture-roughness, hardness,oiliness, stickiness, slipperiness, etc. Atailor examines the quality of a pieceof cloth by passing it between hisfingers; a housewife assesses theripeness of a piece of fruit on the basisof its firmness or hardness, ani oneusually decides how to proceed acrossa slippery looking part of the sidewalkby stepping along it carefully at firstand "feeling it out," to determine thedegree of friction between shoe andice.

In recent years, there has been anincreasing interest in haptic (activetouch) perception as opposed toperception by passive touch (e.g.,Gibson, 1962, 1966). However, mostresearch has dealt with the ability ofpersons to determine the spatialcharacteristics of objects. Vision is themodality most suited to such tasks,and, in general, the findings indicatethat, although the visual and tactualpercepts tend to yield basically thesame results, touch is usually the lessaccurate of the two for spatialperception.

*This paper is based on a thesis by thesenior author to be submitted to theUniversity of Toronto in partial fulfillmentof the requirements for the PhD degree.

tThis is DCIEM Research Paper No. 824.For reprint requests. write to Defence andCivil Institute of Environmental Medicine.P.O. Box 2000. Downsvtew, Ontario.Canada.

Less work has been done on aspectsof perception unique to the touchingsystem. Stevens and his associates(e.g., Stevens & Harris, 1962; Stevens,J. C., & Stevens, S. S., 1960) forexample, have used magnitude scalingtechniques on various tactiledimensions, including roughness. Theusual linear relation between (log)physical stimulus and (log) perceptualresponse found in magnitude scalingstudies has been found in thesedimensions. However, the studies havegenerally been concerned with themagnitude estimation process ratherthan with the tactile percept itself.

In our view, "active" and "passive"touch do not constitute a dichotomy,as suggested by Gibson (1962).Rather, the touching process may beconsidered more or less "active,"depending upon the degree of controlthat the S has over the variouscomponents of the touching process.To study the effect upon perceivedroughness of one such component,fingertip force, we reduced the S'scontrol over the force with which hepressed down on the surface he wasexamining. In the two experimentsreported here, the effect of thegeometrical characteristics of thesurfaces upon the perception ofroughness was also of primary interest.

This paper represents a first attemptto define stimulus characteristicsrelating to the percept of "roughness."

EXPERIMENT 1Method

Apparatus and stimuli.! Theapparatus used to control finger forcewas designed along the lines of theclassical balance scale (Fig. 1). As longas the balance is steady, the momentsof the two arms must be equal, and,hence, the fingers must exert awell-defined force to balance theweight on the other arm of the

balance. The constancy of the force ofthe fingers on the stimulus arm isdisturbed only by small accelerationforces as the arm moves up and down.This variation is a small proportion ofthe total force exerted by the fingers.In simulation tests, we substituted aforce gauge for the S's fingers andfound that th~ "finger" force usuallyremained within about 20% of itsnominal value.

The stimulus object was a smoothedaluminum alloy plate, 5lh x 4lh x3/16 in., scored with a set of parallelgrooves, parallel to the line of thebalance arm, and extending across thewidth of the central third of the plate.The plate fitted into a tray that couldbe fIXed at any position along one armof the balance, permitting E to adjustfor differences in the arm length of Ss.A free-swinging pan hanging under thetray held removable weights that wereused to alter the finger force requiredwithin any trial.

The stimuli were cut by a machine(shaper), which forms accurate lineargrooves. The grooves were cut so as toleave 0.010 in. (.25 mm)2 ofundisturbed surface (a "land")between each pair of grooves (Fig. 2).The groove depth was always 0.005 in.(.125 mm), and different plates werecut with different groove widths,varying from 0.005 in. (.125 mm) to0.040 in. (1 mm) in nominalincrements of 0.005 in. (.125 mm).The shaper could cut a groove or landto within 0.002 in. (.05 mm) of thenominal value. The plates of the firstset cut were numbered from 1 to 8,where plate number k had a nominalgroove width of 0.005 (.125) x kin.(mm). The "pitch" (land + groove) ofthe first set of plates thus varied from0.015 in. (.375 mm) (Plate 1) to0.050 in. (1.25 mm) (Plate 8). Thegroove and land widths were measuredusing a traveling microscope, and these"true" values are used in the figures tofollow. After grooving, all plates wereshaved on the reverse side to equatetheir weights. For obvious reasons, wewould have preferred to usesinusoidally cut tiles but could find notechnologically feasible way toproduce them. Even the tiles we diduse were difficult and expensive toproduce. Stimulus control is a majorbarrier to the effective investigation oftouch.

Experimental procedure. The S saton a stool beside the apparatus, hisright elbow resting comfortably in ashaped padded armrest mounted on aswivel over the fulcrum of the balancearm. The stimulus side of the balancewas occluded from the S's view by acurtain. The stimulus tray was fixed insuch a position that the tips of the S'sbent fingers would rest on the middleof the stimulus plate when the balance

Perception & Psychophysics, 1972, Vol. 12 (5) Copyright 1972, Psychonomic Society, Inc., Austin, Texas 401

Fig. 1. (a) A side view of the apparatus. The E is seated at the front end of theapparatus. The S, on the E's right, has placed her three middle fingers on thegrooved portion of the tile to indicate when the balance arm is in a level andsteady position. The E may adjust the force by adding to or removing weightsfrom the pan suspended under the stimulus tray. (b) A front view of the sameapparatus.

arm was level. With all the weights inplace in the pan under the tray, thecounterweights at the other end of thebalance arm were then adjusted toprovide a net upward force of 1 oz(""28 g) at the middle of the plate.This was the total force the 8's fingershad to apply in order to keep thebalance arm steady and level. Weightscould be removed from the pan toincrease the finger force required tokeep the balance even. The fingerforces used were 1 (""28 g), 5(",,140 g), and 25 (""700 g) oz. Thebalance apparatus was explained to the8, who was told that he must exertenough force to keep the balance armsteady and level at all times while hewas feeling the roughness of thegrooved surfaces. After he hadthoroughly washed his hands and driedthem in an airjet, he began theexperiment.

The experiment was one ofmagnitude estimation. The 8 was toldthat he must give a numbercorresponding to the roughness ofeach of the stimuli and that he shouldignore the changes in force whenmaking his judgments of roughness.Neither standard nor prespecifiedmodulus was used for the magnitudeestimation. Instead, before the runstarted, two practice stimuli weregiven to generally define the range ofroughness that the 8 should expectand to permit him to establish forhimself a range of response numbersthat could include any positive(nonzero) value. Examples of possiblerange values, such as 1 to 10, or 10 to100, were suggested to each 8. Inpractice, the highest range used was60-950 and the lowest was 0.24-5.0. Itwas pointed out to the S that therewas an infinite set of possible numbersthat he might use between 0 and 1.The two practice stimuli were Plate 1with low finger force (described as"one of the roughest ..."). Ss weretold that they might well be presentedwith tiles that felt rougher orsmoother than the two practice plates.They should feel free, therefore, to usenumbers above or beyond the range ofresponses chosen, when such an eventas this occurred.

When feeling the stimuli, the 8 wasinstructed to use only the tips of histhree middle fingers, not the pads ornails. No motions along the grooves inthe plate were allowed. The 8 couldmove his f'mgers back and forth (in thehorizontal plane) across the stimulusgrooves at any rate he wished, but hewas not permitted to hold the stimulusdown with one or two stationaryfingers while exploring it with theother(s). If he were to do so, he mightfeel the grooves at a force greatlydifferent from that intended, thestationary fingers taking the weight offthe active one.

402 Perception & Psychophysics, 1972, Vol. 12 (5)

Fig. 2. A grooved aluminum plate. The outer thirds of the plate He smooth;the inner section has parallel linear grooves cut along the width of the plate.

ResultsAn analysis of variance was

performed on the data, using acompletely crossed five-factor design,the factors being Ss, days, runs, groovewidths, and forces. The most strikingresult is that fingertip force and groovewidth affect the perceived roughnessof the grooved surfaces (p < .001).Figure 3 shows the relation ofroughness to groove width andfingertip force. As all the data werelogarithmically transformed beforeanalysis, only the log (magnitudeestimates) are reported here. Log(magnitude estimate) of roughness isplotted as a function of log ("true"groove width) for each of the threeforces. The plotted groove widthvalues are the measured rather thanthe nominal sizes. Each data pointrepresents the average of 32 responses(8 Ss, 2 days, 2 runs/day). As can beseen in Fig. 3, the greater the force,the rougher the tiles feel. The exactform of the relation between groovewidth and apparent roughness,however, is unclear. A straight line,which would represent theconventional (e.g., Stevens, 1957)power law, is an adequaterepresentation of most of the data foreach force.

The analysis of variance showed a

SMOOTH

1-6

/1-4

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------lOZ 0/SOl '/---25OZ

I I1-2 I 0 I

II /0/ ~/

1- 1° .//0 l, ,fir; ~o ,.

~~0-8 /0 /

, 0 ,

/ ./0-6 ' "/ ~/

"""0-4 ..,.'

S 10 20 50

TRUE GROOVE WIDTHI thousandths ofan inchl

Fig. 3. Experiment 1: Magnitude estimate (roughness) as a function of "true"groove width and fingertip force.

institute. Their ages ranged from 19 to50 years. None knew the purpose ofthe experiment when initially tested,although most had previously served asSs in other psychophysicalexperiments.

DIRECTION OF FINGER MOVEMENT.... ~

'GROOVED" SURFACE

SMOOTH

Whenever he wished, the S made hisestimate and released the balance. Ethen changed the stimulus plate, addedor subtracted weights on the pan, andthe next trial began. All runs consistedof 24 trials. Each of the eight plateswas used at each of the threefinger-force settings (1 (~28 g), 5(~140 g), and 25 (~700 g) oz]. The Swas permitted a short rest at any timeif he felt that his fingers werebecoming less sensitive or undulysweaty.

After the first run, there was a10-min break, during which the Sagain washed and dried his hands andafter which the second run was begun.Between runs, the S was permitted tochange the range of response numbersthat he wished to use. He was notallowed to change the range withinruns. One complete session of tworuns lasted approximately 40 min.After each session, the tiles werecleaned with trichloroethylene solvent,using a typewriter brush to removeany embedded particles.

Experimental design. Theexperiment was treated as a factorialdesign, the factors being the 8 Ss, 8plates, 3 finger forces, 2 runs withineach experimental session, and 2separate sessions (i.e., days) for each S.The presentation order of the 24conditions (Plates by Forces) duringeach run was determined by E, whofilled in the 8 by 3 stimulus matrix(Tiles by Forces) haphazardly, withthe single stipulation that Plates 1 and8 never immediately follow eachother.

Subjects. There were four male andfour female Ss, all right-handed and allemployed in various capacities at this

Perception & Psychophysics, 1972, Vol. 12 (5) 403

-_...._-- 10ZFNGERTIP FORCE

version of the set used inExperiment 1, consisting of theoriginal Plates 1-5 from Experiment 1plus three new plates cut to duplicatethe groove widths of Plates 6-8, butwith a new groove depth of 0.010 in.(0.25 mm). The modification wasmade because we thought that theapparent depression of the roughnessof Tiles 6, 7, and 8 might be due tothe finger touching the bottom of thewider grooves. We name the groove-settiles of this experiment G1 to G8. Forthe land set, the groove depth andwidth were held constant at 0.005 in.(0.125 mm) and 0.010 in. (0.25 mm),respectively; the lands varied from0.005 in. (0.125 mm) to 0.040 in.(1.0 rom), in 0.005-in. (0.125-mm)nominal increments, giving a pitchseries the same as that for the grooveset. These tiles are known as L1 to L8.Tile L2 was actually the same tile asG2. G1 was paired with L1, G3 withL3, G4 with L4, and so forth. Themembers of each pair had the samepitch.

If pitch were the most importantvariable affecting apparent roughnessof the tile surface, then the roughnessshould be similar for the two membersof each pair; if groove width were theprimary variable, then the roughnessof all the tiles in the land set should beroughly the same, whereas that for thetiles of the groove set should vary, aswas shown by Experiment 1. Finally,if land width were another effectivevariable, then differences among theland set should be evident, but thepairs need not match. Note that thepitch determines the frequency of thevibrations set up in the skin by thetile.

MethodSubjects. There were five male and

four female Ss, all right-handed and allemployed in various capacities at thisinstitute. Their ages ranged from 20 to34 years. One of the Ss hadparticipated in the first experiment.The others did not know the purposeof the experiment, although most ofthem had had previous experience inpsychophysical experiments.

Procedure. We used the sameprocedure as that of Experiment 1 butwith minor modifications. (1) Ss nowdried their hands in the warm airprovided by a commercial portablehair drier. (2) At the beginning of eachtrial, E steadied the balance arm andplaced the S's fingers on the smoothportion of the left side of the tile. Ereleased the balance arm, the Sbalanced it himself, and, when ready,began to feel the grooved stimulussurface. In Experiment 1, the Shadplaced his fingers on the grooved partof the surface and then pushed downon it to balance the arm properly

50

i',20

EXPERIMENT 2In the first experiment, it was

impossible to separate out the effectsof groove width on perceivedroughness from those due to pitch.Within this set of tiles, an increase ingroove width implies an equal increasein pitch, since all the lands are equal.To eliminate this ambiguity, a secondexperiment was run in which two setsof tiles (eight in each set) were used:pitch remained constant betweencorresponding pairs of tiles; groovewidth increased (lands constant) inone set ("groove set") and land widthvaried similarly (grooves constant) inthe other ("land set"). Each tile wasthus a member of a pair having thesame pitch.

The groove set was a modified

precision in the data. The resultsindicated that, as one might expect,there were differences in the precisionwith which various Ss responded.These differences were not correlatedwith sex, nor did groove width, force,or the interaction of the two havesignificant differential effects upon theprecision with which the Ss judged theroughness of the plates.·1t wasunfortunately impossible to assessaccurately the correlation betweenprecision and the range of numericalresponses chosen, since Ss couldchange their scales both within andacross days.

°--°_0~o-.o

10

TRI.E GROOJE WIDTHIthousandths of aninchI

----25OZ---- 50l

o

+0-1

-0-1

+0-2

Fig. 4. Experiment 1: Difference in magnitude estimate (roughness) between(1) mean roughness of groove widths averaged over fingertip force conditions,and (2) mean roughness of corresponding groove widths presented at each forcelevel as a function of "true" groove width and fingertip force.

Groove Width by Finger Forceinteraction term that was highlysignificant (p < .001). The interactionproved due to a slight divergence ofthe curves for roughness VB groovewidth, which may be better seen inFig. 4. The difference between (1) themean scores for each groove widthaveraged over all forces and (2) theindividual score for that same groovewidth at each force level is plotted as afunction of groove width. It isapparent that, as groove widthincreases, there is an increasingcontrast in the roughness of a groovedplate when using the three differentforces. The S by Groove Widthinteraction, which is of scanttheoretical interest, also provedsignificant (p < .001), though small.Of course, main effects, other thanthose already plotted for groove widthand pitch, are of no interestwhatsoever, because the Ss changedtheir response ranges from session tosession.

Beyond the simple determination ofperceived roughness, we wereinterested in determining whether theprecision of the Ss' responses wasinfluenced by the particular groovewidth and/or finger force.

A computer program was written3

to perform what we have calledANOVAVA, or analysis of variance ofvariance (described in the Appendix).ANOVAV A analyzes the patterns of


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Fig. 5. (a) Experiment 2: Magnitude estimate (roughness) as a function of "true" groove width and fingertip force.(b) Experiment 2: Magnitude estimate (roughness) as a function of "true" land width and fingertip force.

before beginning to move his fingersacross the tile. But in Experiment 2,the S obtained information as to theroughness of the grooved portion onlywhile his fingers were moving. (3) Theintroductory tiles that were used toindicate the range for the land ret weredifficult to choose because it wasobvious from preliminary observationsthat the relation between apparentroughness and land width was not anincreasing monotonic function, as it isfor groove width. Not knowing whichstimuli of the land set would proveroughest or smoothest, we chose topresent both L1 and L8 at both 1 ozand 25 oz. They were described as"four examples of the tiles you willfeel."

Experimental design. Ss were run atotal of 4 days (not necessarilyconsecutively). Either the land set orthe groove set was presented duringthe first 2 days, followed by the otherset on the final 2 days. The two sets ofstimuli were not mixed together fortwo reasons. First, even if we wantedto mix the sets, it would have beenimpossible to run 96 trials on the sameday, because of finger "fatigue."Second, we felt that to perform aproper replication of the firstexperiment for variable groove widths,we had to avoid the possible biasingeffects that the small roughness

differences between the tiles of theland set might have had on the rangeof numbers that would otherwise beapplied to the more widely varyingtiles of the groove set. The effects ofsuch biasing in task related tomagnitude estimation has beendiscussed by Stevens (1957) anddemonstrated for loudness by Pollack(1964).

A completely crossed factorialdesign was used, and the data for thegroove set and land set were analyzedseparately, each as in Experiment 1.The factors analyzed were: Ss (9),groove width (or land width) (8), days(2), runs (2), and force (3).

ResultsIn Figs. 5a and 5b, log (magnitude

estimate of roughness) is plotted as afunction of log ("true" groove width)and log ("true" land width),respectively, for each of the threeforce conditions. The three ascendingcurves in Fig. 5a represent the resultsof varying groove width for the threeforces: the descending curves inFig. 5b represent the effect of landwidth and force on perceivedroughness.

An analysis of variance performedon the groove-set data indicates that,as in Experiment 1, apparentroughness was strongly affected by

fingertip force (p < .001) (Fig. 5a).The three force functions were againnot parallel, as indicated by the highlysignificant Groove Width by Forceinteraction (p < .001). The analysis ofvariance (not shown in this report)performed on the data from the landset indicated strong effects due to landwidth and force (p < .001) (Fig. 5b).The significant noriparallelism of theforce functions for the groove-set andland-set data is shown in Figs. 6a and6b, respectively.

No direct comparison may be madebetween the "land" and "groove"functions regarding differencesbetween absolute roughness scoresbecause Ss were allowed to changetheir number systems across days andruns, but the slopes may be compared.

Inspection of the two sets of curvesin Figs. 5a and 5b indicates that pitchis not an important factor in thedetermination of the roughnesspercept for these tiles. If it had been,the two sets should have the sameslopes. However, perceived roughnessactually decreased with increasing landwidths, the size of decrease beingdependent upon the force used(p < .001). The positive slopes aremuch steeper for the groove set thanare the negative slopes for the land set,suggesting that although both variablesinfluence apparent roughness, groove


I I

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TRUE GROOVE WIJTH(thousandths ci an inch'

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Fig. 6. (a) Experiment 2: Difference in magnitude estimate (roughness) between (1) mean roughness of groove widthsaveraged over fingertip force conditions, and (2) mean roughness of corresponding groove widths presented at each forcelevel as a function of "true" groove width and fingertip force. (b) Experiment 2: Difference in magnitude estimate(roughness) between (1) mean roughness of land widths averaged over fingertip force conditions, and (2) mean roughnessof corresponding land widths presented at each force level as a function of "true" land width and fingertip force.

width is the more influential of thetwo. On the other hand, it may beseen (Figs. 3, 4, 5a, and 5b) that theroughness contrast of pairs of tiles atdifferent forces does seem to increasesomewhat with increasing pitch, i.e.,the relative differences in magnitudeestimates of roughness are larger forthe wider lands or grooves than for thenarrower ones. Irregularities in thecurves, particularly for the land set,are possibly due to idiosyncracies inmachining of the individual tiles.

It would seem reasonable, on theface of it, to combine the absolutelevels of the results for the land setwith those for the groove set, throughthe common tile known as L2 or G2.This cannot be done, however, becauseof the "stimulus range effect"(Poulton, 1968), which expands thedifferences in magnitude estimateswhen the stimulus range is small. Thiseffect can be seen in the effect offinger force on the roughness for L2,which is greater than the same effectfor G2. It was in anticipation of thiseffect that we did not conduct theland experiment mixed with thegroove experiment. The excessivenumber of smooth tiles we would haveintroduced would have been expectedto enhance the slope of roughness vsgroove width (e.g., Stevens, 1957;Pollack, 1964).

DISCUSSIONThe two experiments reported here

demonstrate that there is an effect offingertip force upon the perceivedroughness of a grooved surface. As theforce increases, so too does apparentroughness. At first sight, this findingmight seem to be directly related tofinding that the perceived magnitudeof a vibration increases as the force ofthe contactor on the skin increases(Craig & Sherrick, 1969). However,Craig and Sherrick used a fairly largecontactor area (4 mm in diam), andother studies (e.g., Verrillo, 1963,1971) have shown other integrativeeffects of vibratory amplitude todisappear with small contactor areas(e.g., lh mm up for the frequencies ofinterest to us). The effects ofroughness in this study must dependon discriminations within very smallareas which are always less thanVerrillo's minimum integrating areas.Hence, any application of Craig andSherrick's result to the effect of forceon the roughness of our tiles is ratherdubious.

We have chosen extreme forcevalues to determine the limits of theforce effect. A person using threefingers can apply no more thanapproximately 25 oz of force whilestill being able to move smoothlyacross the tiles used in theseexperiments. With light forces, ourapparatus cannot effectively set theimgertip force at less than 1 oz, sincethis nominal value is altered by theacceleration forces of the balance arm

as it moves up and down.Furthermore, with the presenttechnique, it was physically possiblefor a person to support the force ofthe balance arm against the outer twofingers while using the middle fingertipto explore the surface texture with lessforce than E intended. Such tacticswere prevented to some extent byinstructions and by the vigilance of E.

In addition to force, severalcharacteristics of the surface groovesin the aluminum tiles affected theperception of roughness; the width ofthe groove and the land influencedperceived roughness, but to differentdegrees and in different directions.Increasing groove width resulted inincreasing roughness, whereasincreasing land width resulted indecreasing roughness, although thedifferences were a great deal less thanthose brought about by varying groovewidth. The inverse effects permitted usto rule out pitch as the single mostinfluential factor on the perceivedroughness of the grooved plates. Theinverse relation between the effects ofgroove width and of land widthsuggests the possibility that groove topitch ratio might be a key variableaffecting perceived roughness.However, when roughness is plotted asa function of this ratio (not shownhere), it proves to be a rather poorpredictor.

Pitch seems to have a different butinteresting effect of its own. As pitch


*One 3D limits listed. In each case the difference between the slope for I 02 and thatfor 25 02 is significant beyond the 5% level.

Table 1Slope of Log (Magnitude Estimate) as a Function of Log (Groove

Width) or Log (Land Width)

(Received for publication January 6, 1972;revision received June 30, 1972.)

NOTES1. We are most grateful to Mr. J. Royce

and the members of his workshop for thetime and energy spent in producing theapparatus and aluminum plates.

2. Since our machine shop works in theEnglish system of measurement, alldimensions were produced in units of.005 in. nominal. Metric equivalents arereported in parentheses.

3. We thank Dr. D. M. Sweeney forprogramming the ANOVAVA procedure.

Lands

-.55 ± .10-.33 ± .10-.26 ± .06

Experiment 2

Grooves

.92 ± .111.05 ± .081.12 ± .06

these estimates. Hence, the name "analysisof variance of variance."

ANOVAVA has two separate uses.Firstly, it permits a test of the manner inwhich the data for an ANOVA depart fromhomoscedasticity and may suggest ways toseparate the original data into separate,more sensitive, and justified analyses.Secondly. and more importantly, it permitsone to assess what effect the experimentalvariables have on the precision of thedependent variable, which may be atheoretically important question. Werecommend that ANOVAVA be carried outas a matter of course in coniunction withany ANOVA that contains a variable thatpromises to allow a sensible assessment of"within-cell" variance for the individualcells at some level of the ANOVA pattern.

The conceptual foundation ofANOVA V A is very simple, although thereare some technical problems in itsimplementation. Briefly, the procedure isthat one chooses an appropriate ANOVA V Adesign, say a factorial such as the S byGroove Width (G) by Finger Force (F)design basic to the present study. One thenadds a variable or variables intended to serveas replications; in the present studv, we haveDays (D) bY Runs (R). These latter permitthe assessment of the variation in thedependent variable (perceived roughness)under each unique combination ofconditions of the experimental variables.There are problems in determining theseindividual variances, which we shall considerlater. Once they have been determined, theyare logarithmically transformed to maketheir distributions more nearly normal, andthese log variances form the data for anordinary ANOVA in the experimentalvariables (S by G by F). ANOVAVA, then,consists of finding a factorial pattern of logvariances and subjecting it to analvsts as ifthe log variances had been raw data.

Two problems arise in implementingANOVA V A. Both have to do with actuallyfinding the most appropriate value for thelog variance in a single cell. The first is aconceptual problem, relating to the fact thatthe variables intended to serve merely asreplications may themselves affect thedependent variable. There may. forexample, be learning and fatigue effects. Ifthe simple repeated scores were used toestimate the variance within a cell, theseextraneous effects would be incorporated inthe variance estimate, which would beinflated. Consistent effects such as theseshould be removed so far as possible fromthe variance estimates that go into the finalstage of the ANOVAVA. One simple way toremove some extraneous effects is to ensurethat the "replications" variables have morethan one degree of freedom within each celland that identifiable extraneous effects can

Grooves

1.01 ± .08*1.20 ± .041.21 ± .07

Experiment 1

10z50z

250z

GIBSON, J. J. The senses considered asperceptual systems. Boston: HoughtonMifflin Company, 1966.

JAMESON, D., & HURVICH, L. M.Complexities of perceived brightness.Science, 1961, 133, 174-179.

POLLACK, I. Neutralization of stimulusbias in auditory rating scales. Journal ofthe Acoustical Society of America, 1964,36, 1272-1276.

POULTON, E. C. The new psychophysics:Six models for magnitude estimation.Psychological Bulletin, 1968, 69, 1-19.

ROCK, I., & HARRIS, C. S. Vision andtouch. Scientific American, 1967, 216,96-104.

STEVENS, J. C., & STEVENS, S. S.Warmth and cold: Dynamics of sensoryintensity. Journal of ExperimentalPsychology, 1960,60,183-192.

STEVENS, S. S. On the psychophysical law.Psychological Review, 1957, 64,153-181.

STEVENS, S. S., & HARRIS, J. R. Thescaling of roughness and smoothness.Journal of Experimental Psychology,1962,64,489-494.

VERRILLO, R. T. Effect of contactor areaon the vibrotactile threshold. Journal ofthe Acoustical Society of America, 1963,35, 1962-1966.

VERRILLO, R. T. Vibrotactile thresholdsmeasured at the finger. Perception &Psychophysics, 1971, 9, 329-330.

APPENDIXANOVAVA:

The Analysis of PrecisionAn analysis of variance (ANOVA) permits

one to assess the influence that each ofseveral independent variables singly andconjointly have on the value of somedependent variable. The analysis of varianceof variance (ANOVA V A) similarly allowsone to assess the effects that theindependent variables have on the precisionwith which the dependent variable can bedetermined. Just as the ANOVA takes as itsdata the raw measurements of thedependent variable. so the ANOVAVA usesfor data the patterns of variation in themeasurements. To perform an ANOVAVA,one attempts to assess the variance inherentin a measurement under a particularexperimental condition and then performsan analysis of variance on the logarithms of

increases (Figs. 3, 5a, and 5b), so toodoes the difference between theapparent roughnesses of a surface attwo forces. This is apparent in all threesets of curves, with land or groovewidth increasing.

Stated another way, perceivedroughness as a function of groovewidth increases faster with high fingerforce than it does with low force. Thischange in slope is real, as is shown bythe numerical values given in Table l.This implies that the roughnesscontrast of a patterned surface shouldincrease with increasing finger force.There may be an analogous effect invision. Light surfaces increase inbrightness faster with increasedillumination than do dark surfaces(Jameson & Hurvich, 1961; Flock &Noguchi, 1970), so that the apparentcontrast of a scene increases withillumination.

Finally, one must consider that themaximum forces used in theseexperiments are unrealistic. It is mostunlikely that a person would freely use25 oz (~700 g) of force to examinethe roughness of an object. A logicalextension to the experiment would beto permit the S total control over thefingertip force and also, therefore,over the entire touching process. Wewould like to know what force the Sdoes use, whether he alters it duringhis tactual explorations, and whethersuch alterations in force affect theroughness percept.

In respect to the initial aim of thestudy, which was to shed some lighton the stimulus characteristics leadingto the perception of "roughness," wecan say with some certainty that"roughness" is dependent on the forceapplied between the fingertip and thesurface and that it is not closelyrelated to the frequency of vibratoryimpulses applied to the fingertip.Roughness seems to depend more onthe distribution of regions over whichthe skin is and is not supported by theunderlying surface than on thedistribution of transitions betweensuch regions. This is shown by thegreat difference in roughness betweentiles with groove width and land widthinterchanged. A wide groove leads to alarge roughness, a wide land to a smallroughness. Beyond this, the results ofthe experiments reported here do notpermit us to go.

REFERENCESCRAIG, J. C., & SHERRICK, C. E. The role

of skin coupling in the determination ofvibrotactile spatial summation.Perception & Psychophysics, 1969, 6,97-101.

FLOCK, H. R., & NOGUCHI, K. Anexperimental test of Jameson andHurvich's theory of brightness contrast.Perception & Psychophysics, 1970, 8,129-136.

GIBSON, J. J. Observations on active touch.Psychological Review, 1962, 69, 477-491.


be separated from the measurement errorwe are trying to determine. This can bedone by having more than two replicatesand removing a linear trend, or, as in thepresent case, bv arranging the replicates sothat they themselves form a factorial design(0 by R) from which the interaction meansquare may be extracted as an estimate ofmeasurement error variance. Of course, theD by R interaction within any cell mayitself contain real effects, but these can beeliminated only by comparisons amongcells, a technique that introduces thepossibility of spurious mutual effects withinthe final analysis.

The second major problem in determiningthe log variances for the final analysisderives from the quantized nature of thedata. All data are quantized. In the presentexperiment, the quantization arises from thetendency of the S to say "20," whether heexperiences 19.8774... or 20.3126 ....

Any single response must be considered tobe an index to a distribution of underlyingperceived magnitude. Under thesecircumstances, it is quite conceivable thatthe measured 0 by R interaction in somecell will be exactly zero, although theinteraction due to the "true" perceivedmagnitudes would have been finite. Sincethe log of zero is minus infinity, zeroscannot be admitted as variance estimates.However, since a zero indicates only thatthe "true" interaction term is smaller thansome ill-specified limit dependent on thesomewhat variable quantization step size, itmakes sense to replace the zero with someless biased estimate of that "true"interaction. We have chosen to use one-halfthe smallest nonzero variance estimate toreplace all zeros before transforminglogarithmically.

The full ANOVAV A procedure is then asfollows: (1) construct an experimental

design having experimental and replicationvariables, where preferably the replicationvariables form a factorial pattern withineach unique combination of theexperimental variables (Le,; within eachcell). (2) Make the best possible estimate ofthe measurement variance within each cell,preferably using the interaction term of aminiature ANOVA on the data pointswithin the cell. (3) Logarithmicallytransform the variances thus determined,replacing all zeros with one-half the smallestnonzero variance before transformation.(4) Perform a regular ANOVA over thespace of the experimental variables, usingthe logarithmically transfonned variances asdata.

An ANOVAVA program has been writtenin FORTRAN for the POP-9, and may bemade available on request.


fingertip force, surface geometry, and the perception of

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