Acta Psychologica 38,331-336. 0 North-Holland Publishing Company 1974

ADDING AND AVERAGING ANGLES:

COMPARISON OF HAPTIC-VISUAL AND VISUAL-VISUAL

INFORMATION INTEGRATION

Gordon STANLEY 1 Department of Psychology, University of Melbourne, Australia

One group of Ss added and another group of Ss averaged pairs of angles presented simulta-

neously according to a factorial design. One set of angles was presented haptically and then

visually, the other set being presented visually on both occasions. Although analysis of variance

indicated no main effect due to sensory mode of presentation, some interactions due to sensory

mode were significant. The adding functions were parallel, but the averaging functions con-

verged with a significant interaction, suggesting a differentially weighted integration model.

1. Introduction

In recent years much research effort has been directed towards the problem of intersensory equivalence. Experiments by Abravanel (197 la), Caviness (1964), Cashdan (1968), and Rude1 and Teuber (1964) suggest that intramodal visual equivalence matches for shape properties are superior to either intrasensory haptic or intersensory visual-haptic matches. In contrast, Abravanel (197 1 b), Kelvin and Mulik ( 1958), and Teghtsoonian and Teghtsoonian ( 1965) reported that visual and haptic judgments for length are essentially similar.

The study to be reported here was concerned with the integration of visual and haptic information about angles. This is a useful task to study since judgments of angularity do not appear to be well practiced, as evidenced by the dispute about the direction of deviation of angle judgments from normative values (Maclean and Stacey 1971). The recent development of information integration theory and the tech-

1 This experiment was completed while the author was a visitor at the Center for Human

Information Processing at the University of California, San Diego, and was supported by NIMH

grant MH-15828 to the Center, and by NSF grant GB-21028. The author is grateful to the late Holly Halvorson for assistance in data collection, and to N.H. Anderson for helpful advice.

nique of functional measurement has permitted the determination of the combinatorial rules whereby sensory information is integrated (Anderson 1970; 1972). It is of interest to determine whether judgment tasks involving cross-modal information obey simple or complex inte- gration rules. For this reason both adding and averaging tasks were studied in a factorial design.

2. Method

2.1. Subjects

The Ss were 32 male and 8 female undergraduate volunteers from the University of Califor-

nia, San Diego.

2.2. Apparatus

Haptic stimuli were presented by means of two sticks of wood 220 mm long, 20 mm wide

and 10 mm thick, hinged together such that they could be separated at angles of 20,40, or 60

degrees by the insertion of appropriate metal supports. These sticks were housed in a black box

300 X 350 mm which was covered with black cloth on S’s side and open on E’s side. On top of

the box was a support on which white cards 200 X 125 mrh could be placed for visual

presentation. Angles of 10, 20, 30, 40, 50, 60, and 70 degrees were made with two sections of

black tape 1.5 mm wide and 51 mm in length. The angles were located centrally on the cards.

The response card consisted of a 200 X 125 mm white card with a circle of 51 mm radius. A

horizontal black line of 1.5 mm width was placed on the card from the centre to the circumfer-

ence of the circle. The circumference of the circle was marked at five degree intervals and each

mark was labelled with a letter of the alphabet. To provide sufficient letter labels, repeated

letters had a bar over the top and letters in the upper half of the circle were in blue ink, those in the bottom half in red ink. The letters were ordered randomly and the Ss were informed of this fact.

2.3. Procedure

The S was seated at the table and 6 showed S the apparatus and instructed him to feel the

angle with his left hand by rubbing his thumb and index finger up and down the angle side five times. He was then told: “Your task is to mentally add (average) the two angles and then

afterwards indicate the sum (average) of the two angles on this response card. You respond by

indicating the letter on the circumference of this circle which would make an angle with this

line corresponding to the sum (average) of the two angles”. The visual and haptic presentations

wcrc simultaneous and the response card was presented after removal of the visual angle and

cessation of the rubbing of the wooden angle. In the visual-visual condition both angles were presented simultaneously, followed by the response card.

G. Stanley, Adding and averaging angles 333

2.4. Experimental design

The Ss were randomly divided into four groups of ten. Two groups added and two groups

averaged. One group in each pair of groups made haptic-visual judgments on one occasion and

visual-visual on the second occasion of testing. The second group in each pair of groups did the

tasks in reverse order. On each occasion, one sensory condition was used, and the angle-pairs

were presented in a 3 X 4 factorial design, with one of the 20, 40, or 60 degree angles being

paired with one of the 10, 30, 50, or 70 degree angles in each judgment. The 20, 40, or 60

degree angles were presented haptically or visually depending on condition. Presentations were

in random order and eight replications were obtained in each session. The first three replica-

tions were considered practice trials and were not included in the analysis. Separate analyses of

variance were made for the results of the adding and averaging groups.

3. Results

The results will be considered, fistly in terms of the haptic-visual effects, and secondly in

terms of the fit between the adding and averaging task data and algebraic adding and averaging

models.

3.1. Haptic-visual effects

The mean angle judgments are depicted in figure 1. The functions for haptic-visual and

ADDING AVERAGING

16C

z BC

4 I

6C

HAPTIC-VISUAL

, VISUAL-VISUAL l HAPTIC-VISUAL

.: ?@J VISUAL-VI SUAI

T

SIZE OF ANGLE PRESENTED VISUALLY

Fig. 1. Plots of group mean response to pairs of angles. Solid lines indicate responses, broken lines indicate normative values.

334 G. Stanley, Adding and averagitrg a&es

SOUICt!

A (Subjects)

B (Haptic-visual)

AU

(‘ (Three angles)

AC

UC

AK I> (I’our angles)

AD

BD

AUD

(‘I)

AC’D

** ,’ < 0.01

Table I Analysis of variance table for adding task.

S.S. di, M.S. I. l’cst

83973.53 19 4419.66 515.26 I 575.26 0.30 A 1%

36537.45 19 1923.02 643609.14 2 321804.57 488.08’“:” AC

25054.18 38 659.32 803.39 2 401.69 0.80 ABC

lYOOO.77 38 500.02 1014289.44 3 338096.48 349.12.“” .AD

55199.51 57 968.4 1 9984.86 3 3328.2X 8.01 +:* ABD

23694.92 51 415.70 1965.27 6 327.54 0.74 A(‘D

50186.39 114 440.23

visual-visual appear very similar and analysis of wriancc yielded no mam effects due to the

haptic-visual factor in either adding or averaging task& (1” < I in both cases). The left-hand point

on the top curve for the adding tasks is discrepant between the haptic-visual and the visual-

visual conditions. This trend was visible in individual data and the reliability of this discrepancy

is evidenced by a significant interactlon (BD) between the haptic-visual factor and the angles

represented by the column factor. For the averaging task the vertical spread of the functions

differs somexvhat between the two sets of data, as the anple represented by the rows increases in

magnitude. Thi‘; trend i\ reflected in a significant interaction (UC) bctwccn the haptic-visual

factor and the angles reprcscntcd by the row fact[)r.

Source

A (Subjects)

B (llaptic-visual)

AB

c (Three angles)

AC’ IK

ABC D (I:our angles)

AD

BD ABD

CD

ACD

** p < 0.01; * p < 0.05

Table 2

4nalysih of variance table for averqing task.

S.S. L1.S. 1.’ Test

49466.5 2 19 2603.50 141.13 1 141.13 9.40 Al3

6597.31 19 347.22 118312.66 2 59156.33 335.82”* AC‘

6693.73 38 176.15 320.63 2 160.31 3.31** AK

1838.76 38 48.38 169301.88 3 56433.96 370.58”* AD

8680.13 57 152.28 287.47 3 95.82 1.81

3013.87 51 52.87 1910.89 6 318.48 5.78** ACD 6271.63 114 55.01

.~~ ___ _~

G. Stanky, Adding and averaging angles 335

3.2. Adding model

An adding model makes a simple geometric prediction about the data in the left panel ot figure 1. If the S$ are indeed adding the subjective values of the stimuli. then thcsc curves

should exhibit parallelism (Anderson 1970). That is approximately the case as can be seen. The

statistical test of deviation from parallelism is the row X column interaction (CD), and that was not significant. In both sensory modeu the data obey the adding model.

3.3. A veragilzg model

The Gmple averaging model also predicts parallelism (Anderson 1970), but this prediction is

disconfirmed in the panel on the right in figure 1. hch set of three curves converges toward the

right, and this convergence was significant as shown by the row X column interaction ((‘II). This convergence could be accounted for by either a multiplicative model or a differentially

weighted averaging model (Anderson 1970). Since Ss were rcquircd to avcraq, the former

possibility is unlikely. Moreover, differential weighting does not affect parallelism m an additive

task (Anderson 1971: 180), so that differential weighting in the averaging task need not

indicate any fundamental change in perceptual processing of the stimuli in the averaging and

adding tasks.

4. Discussion

The results of the present study imply that, in general, haptic and visual information about angles is fairly equivalent. However, the pres- ent results show that haptic information is influenced by known anchor points in a different manner from visual information. The influence of the 90 degree and 45 degree positions on the response scale can be seen in the top curves for the adding task and in the centre for the averaging task. The other significant effect related to the haptic-visual factor. the vertical spread in the averaging functions, is small in absolute magni- tude.

Weiss and Anderson (1972) used both line-mark and magnitude esti- mation in an angle averaging task. Their results for both response modes supported a simple averaging model, whereas the present results suggest a differentially weighted integration model. The present study differed from theirs in response mode, range of angles used, and degree of practice on the part of the subjects. Potentially any of these factors could be responsible for the different result, but practice is a likely candidate. Weiss and Anderson ( 1972) used more practiced subjects. and practice may reduce differential weighting, if such were due to attitudinal factors (Anderson 1972).

336 (;. StarrleJ’. Adding and al,eragitg angles

The present results reinforce the need for further study of algebraic models for tasks involving the integration of perceptual information. Clearly no single experiment provides compelling evidence for a particu- lar model. as is evidenced by the difference between the present result and that of Weiss and Anderson ( 1971). Moreover the successful fit of a given model does not carry any strong implication about the psycho- logical processes involved as liodges ( 1973) and Anderson ( 1973) have recently stressed.

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