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THE PERCEPTION, OF A FORM IN A DARK
FIELD AS INDICATED BY THE :OBSERVER'S
DRAWINGS

Thais for the Beam :6 M. A.
MICHIGAN 5m?! COLLEGE
Thomas Meow NoIson
1953

 

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THE PERCEPTION OF A FORM IN A DARK FIELD
AS INDICATED BY THE OBSERVER'S DRAWINGS

By

Thomas Morgan Nelson

A THESIS

Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

MASTER OF ARTS

Department of Psychology

1953

f'rIEb x *3

t/Il/S’

,2

ACKNOWLEDGEMENT

The author wishes to eXpress his appreciation and
gratitude to Doctor 8. Howard Bartley for his cooperation

and assistance in the preparation of this thesis.

F a
t,

C)
pg.»
Ina
«E
a e\
V

I.
II.
III.

VI.

VII.
VIII.

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . . .
GENERAL STATEMENT OF TRE PROBLEM

EXPERIMENTAL APPARATUS AND SUBJECTS .

PROBLEM l e e e e e e e e e e e e
A. Statement of the Problem .

B. Procedure and Directions to
Subjects 0 O O O O O O O

C. Results . . . . . . . . . .
PROBLEM 2 O O O O O O O O O O O O
A. Statement of the Problem .

B. Procedure and Directions to
SUbjeCts O O 0 O O O O O

C 0 Results 0 O O O O O O O O 0
PROBLEM 3 O O O O O O O O O O O O
A. Statement of the Problem .

B. Procedure and Directions to
Subjects . . . . . . . .

C. Results . . . . . . . . . .
DISCUSSION . . . . . . . . . . .
BIBLIOGRAPHY . . . . . . . . . .
APPENDIXl...........

2 O O O O O O O O O O O
5 O O O O O O O O O O O

4 O O O O O O O O O O O

Page

24
26
33
53

36
38

42

47
47
52
52

55
55
60
69
72
75
79
82
84

87

Table
l.
2.

4.

6.

7.

LIST OF TABLES

Data from Thouless EXperiment .'. . . . .

Real Ratio, Stimulus Ratio and Phenomenal
Ratio Mean Ratios Obtained With and
Without Glasses for a Circle at Four
Inclinations to the Line of Regard . . .

Indices of Phenomenal Regression Computed
on Data Obtained with and Without Glasses
for a Circle at Four Inclinations to the
Line of Regard . . . . . . . . . . . .

Table Comparing Real Shape, Stimulus Shape,
and Mean Phenomenal Shape for "Group A”
and ”Group B“. Standard Deviations for
“Group A” are Included . . . . . . . .

Table Comparing Phenomenal Shape and
Standard Deviations Under Conditions
of Unaided Vision and Two Power Optical
Magnification . . . ... . . . . . . . .

Table Comparing Phenomenal Shape Under
Conditions of Unaided Vision and Seven
Power Optical Magnification . . . . .

Table Showing Corresponding Phenomenal
Shape and Phenomenal Tilt Values for
”Group A”, Unaided Condition . . . . . .

Table Showing CorreSponding Phenomenal
Shape and Phenomenal Tilt Values for
“Group AP, Aided (2x) Condition . . . .

Appendix

1.

2.

Analysis of Variance Values for Phenomenal
Shape Indexes Obtained From All Subjects
of “Group A" . . . . . . . . . .,. . . .

Analysis of Variance Values for Phenomenal
Tilt Indexes Obtained From All Subjects
of ”Group A" Combined . . . . . . . . .

20

20

4O

5O

51

57

78

81

LIST OF TABLES (Continued)

Table (Appendix ) Page

3. Analysis of Variance Values for “Time
to Reaponse' Measures When Condition
was That of Representing Tilt of Target.
Data.from Four Subjects of "Group A" . . . . 83

4. Combined Means and Critical Ratios
Resulting Between Drawing Surfaces
Oriented at 90°, 45° and 0° to the
Observer, When Phenomenal Shapes of
Three Targets are Expressed by Drawing . . 86

5. Combined Means and Critical Ratios
Resulting Between Binocular and
Monocular Conditions of Observation
When Various Shapes are Viewed at Close
Distances . . . . . . . . . . . . . . . 89

LIST OF FIGURES
Figure A Page

1. The Effects of Optical Magnification
on the Perception of a Solid . . . . . . . . l7

2. Cut-Away View of Experimental Rooms . . . . . 29
3. Typical Target Used . . . . . . . . . . . . . 50
4. View from Observer's Position . . . . . . . . 31
5. Stage and Experimenter's Room . . . . . . . . 32

6. Curve Showing Relationship Between
Phenomenal Shape and Stimulus Shape . . . . 41

7. The Effects of Optical Magnification on a
Tilted Plane Figure . . . . . . . . . . r . 44

8. Curve Showing Relationship Between
Phenomenal Shape and Phenomenal Tilt . . . . 59

I. INTRODUCTION

An answer to the question "How do we see things as we
do?" must be given by any system, psychological or otherwise.
purporting to provide a comprehensive account of human behavior.
Despite this, experimental answers to ancient but basic
duestions concerning phenomena apparently central to this
quest are lacking. Generalized statements that treat the
perception of objects without taking recourse to arbitrary
use of artificial devises are largely absent, even though
in recent years psychology has witnessed at least one note-
worthy although partial advance in this direction (6).

Interest in the relationship between a percept and its
correlating environmental object seems to have predated
psychology itself by centuries.* [A similar interest accompa-
nying an increased comprehension.of visual mechanisms gained
throughout the nineteenth century provoked a number of extra
physiological explanations concerning the ”hows” of certain
sorts of experimentally observed phenomena. The phenomenon

referred to came to be known as the “constancies'.

 

*A.historian (4) notes that the 18th century scientist
and philosopher Bouguer evinced curiosity regarding aspects
of the relationship and that an age before Euchid himself
had established a distinction between apparent size and
visual angle.

In.this century. despite formidable technological
progress and the manifold possibilities consequently Opened
for neurological analysis, these phenomenon have so far
eluded explanations from this quarter. This is not to say
however that certain correlations between experience and
neurophysiology, neurophysiology and the illumination
patterns of the retina would not be of direct relevance
to a more complete undertaking than the present. Studies
of the neurophysiological conditions associated with edges
and gradients are presumably propaedeutic to any discussion
of shape. These are considerations however, which have
been treated extensively elsewhere (5) and which are
beyond the scope of this paper.

From the outset constancy enjoyed an ill-defined
existence that apparently has improved little during
the past decades. During the past score years various
writers have questioned its value because a certain
theoretical orientation seems to be implicitly associated
with the word. Nevertheless the quarters in which the
word constancy regularly occurs have increased and are
varied to the extent that its catholicity of use now
approaches that of “perception”. To some observers
this march of affairs perhaps imparts a.flavor cf
homogeneity of method or material, stands for a unity

5

of knowledge within psychology, produces the feeling that
“now we are getting somewhere," etc., while for others
it seems only to add a regretable and avoidable confusion.
One investigator, Sheehan (l4), attempted to discover
whether a high or low constancy will be maintained through,
out a varietyof perceptual Judgements by single subjects.
The universally low intercorrelations which were obtained
lead her to “question any use of the term constancy which
implies the existence of'a unit trait....'I The danger
inherent in abstracting a name for a group of phenomena
that seem off hand to resemble each other is well recognized.
So while the task crucial to this paper of course lies in
a direction that largely precludes an attempt to make this
semantic muddle intelligible, if indeed this be possible.*
nevertheless a certain ordering is demanded if one is to
do otherwise than contribute to the prevalent potpourri.

Within the area of visual perception constancy has
a two-fold meaning. The first might be called the obvious
meaning and the second the current meaning. The first

does not particularly concern us here for the second is

 

*While the present paper must forebear inquiry of
any completeness into the problem, others have discussed
possible meanings that might be given to constancy of
the sort that concerns us. )

encountered most often nowadays. However since both
meanings are employed, and in at least one case even in
the same article (15). it might be well to say a.few words
concerning each.

First, constancy is used to indicate the perceptual
recognition or identification of an object as being a such
and such. This, although it is the obvious usage, implies
an either-or occurrence and for this reason, unless one
chooses to state some further relationship (such as degree
of perceptual certitude, probability of the perceptual
occurrence), is of lesser interest scientifically than
the second.

Currently it is used in a relative sense. It is used
to specify one out of all the possible relationships that
can be obtained between the physically measurable so called
primary or secondary properties of the actual "in space”
concrete entity and its physiological and/or psychological
correlates. Thus in this latter case one always uses or
implies a referent. Using such a referent one can apply
the propositions ”toward”, or I'from" and speak in terms
of derivative nouns such as “regression", “progression“,
”transformation”, “substitution“, etc. It is also possible
tO'scale some property of the perception and, using this,
state the degree to which this property approaches that

5
of the referent. All this would not of course be possible
using the first definition.

Although the properties alluded to Just previously
are apparently infinite in number, color, size, distance,
shape, weight, motion, and lightness of surface are those
which have been commonly studied. Relative constancy of
these properties can be investigated using many methods.
Any manipulation of retinal organization or intensities
could possibly affect the perceptual outcome. Primary
depth cues such as retinal diaparity, accommodation and
convergence may also play a role. In the studies to be
mentioned gross enough manipulations of primary and
collateral cues have been made to alter the consequent
perception measurably.

Systematic investigation of relative object constancy
may perhaps be said to have begun with an extensive series
of experiments reported by Thouless (17). (18). (19) in
1951 and 52. The earliest of these experiments demonstrated
that the perceived shape of obJects* viewed obliquely
under many experimental conditions lay between the concrete

in-space object shape and its retinal correlate.

 

*This is also known as behavioral shape, matching
response, phenomenal shape.

6
Thouless speaks of this as ”regression to the real object“
(Hg).* This concept and those of the ”real“ object,
”stimulus" object, and "phenomenal” object enjoy wide-
spread usage by shape constancy experimenters and will
be used by this writer. By the term “real” object (R)**
is meant the physical character of an inpspace object.
The “real“ shape of an object is independent of any
context. The retinal correlate is stylefithe ”stimulus"
shape (S)*** and the experiential result the "phenomenal”

 

*Thouless suggested ”phenomenal regression to the
real object” because it seemed to be an apt description
of the process and because it seemed devoid of the
implications of'all or none” that constancy has.
Although it doubtless has been an improvement, as far
as concerns clarity, still it seems to carry the
implication that the target rather than the subject
is the organizing force.

*wThis is also referred to as the distant object,
distant stimulus, distant shape, real stimulus, real
shape, objective shape, objective stimulus, objective
object, test-object, target.

Bartley (2) employs the last term when he refers
to what is looked at. Target seems to be a preferable
term to use in all instances that we shall be dealing
with, because, as he points out, it does not Specify
what is being looked at but only indicates that
-differentiation exists within the visual field. Hence
it does not tend to render the concrete correlate of
the perception the organizing force as other of these
terms seem prone to do.

During the first section the present author will
not generally attempt to maintain a strict terminology
although the term target will be used exclusively in
the latter part.

_ ***Also called proximal shape, proximal stimulus,

proximal object, stimulus object, projected shape,
projected stimulus, and projected object by different
authors.

shape (P). The three shapes are most often expressed
operationally for circles and ellipses by the minor-major
axis ratios. The operations defining a phenomenal shape
are frequently performed on figures matched or drawn by
the subjects.*

The data entered in Table l perhaps are representative
of the results that are obtained when no attempt is made
to control physiological or collateral cues.

Thouless found it desirable to have a numerical measure
to express the degree to which the so-called regression
takes place. The index arrived at he called the "Law of
Phenomenal Regression”. The law can be expressed in its
simplest form as P-S/R-S.** It will be at once observed
that this formula is designed to yield coefficients between

0 and 1.0. Expressing the results given above by means

 

*Hastorf (8) has added the fourth member, the
"assumed size”. .This addition was made on the basis
of an experiment in which he found that a suggestion
as to the identity of the real object influenced the
perceived distance of a rectangular object.

E. Brunswik’s (5) ”Psychology of Objective
Relations" recognizes a similar relationship. He
emphasizes that perception is greatly influenced by
the implicit "hypotheses" the organism entertains
concerning the real object.

*fiThouless included the formula (log Phlog S)/
(log R-log S) and advised its use since it precluded
anomalies of measurement that arose when the simpler
form P-S/R-S was employed in brightness and size
regressions. The formula included in the text proper
however is just as satisfactory for purposes of stating
shape regressions.

8
of this law yields a Rg of .57 for circle A, a Rg of .46
for circle B, and a Rg. of .44 for circle C. It is a
potentially very useful measure, for by means of this
formula it is possible to compare the extent to which
phenomenal regression occurs for different shapes in
identical surrounds as well as the "cue value” of the

various surrounds themselves.*

 

*A criticism similar to that made in a previous
footnote concerning Rg can be extended to the indexes
of Hg, i.e. (P-S/R-S and log P-log S/log R-log S).
The implicit assumption inherent in this formulation
renders the target the organizing force rather than
the organism. This leads to serious difficulties of
several kinds.

A priori there seems to be no reason why the
perceptual shape of a circle tipped at an angle 45
degrees to the line of regard should lie between 1.0
and .707 (minor axis/major axis values for the real
object and stimulus object reapectively). If, to cite
one possibility, P occurs as less than the value for S,
the result is a negative value about which it is difficult
to say anything meaningful using the concept regression.
This would actually occur if we would attempt to express
size relationships of S, P, and R existent in the Kbster-
phenomenon. The opposite is possible a-priori also and
indeed has occurred in color and shape experiments.
Considering the latter case, Koffka remarks (12, pp. 227)
"This seems at first not to impair the values of the.
measures, the constancy would simply assume values
greater than 100 in Brunswick's formula and greater
than 1 in the log-arithmetic measure. ----And yet it
comes as something of a shock to find values which are
greater than complete constancy. The main point however
is this: These measures were so useful because, by
referring each result to a well-defined range, they
yielded comparable figures for very diverse constellations,
each having its own range defined in the same way. But
the fact of more than complete constancy destroys this
advantage. The range itself becomes a function of the
constellation----.'

TABLE 1
DATA.FROM THOULESS' EXPERIMENT

Mean of drawings for circle gt A (pg.5 cm, from obgerygrz
b s b ect S.

 

 

 

Reproduced ratio Stimulu§_rati_ Real ratig
.78 .56 1.00

Mean of drawings for gircle at B (l09 pp. from obggrver)
by sgbject S.

 

Reproduced ratio Spimulus ratio Reg; ratig
.58 .56 1.00

Mean of drawings for circle at C (l65.5 cm. from obggrver)
by sgbject S.

Reproduced ratig Stimulgs ratio Real ratio
.47 .255 1.00

 

10

Using his index Thouless eXperimentally related
shape Rg to several factors and found that: l) Rg
diminishes to zero with a circular figure inclined at
both 90 degrees and 0 degrees to the line of vision in
uncontrolled situations. The largest indexes were
obtained at a 10 degree inclination, 2) Hg is correlated
with target size, shape, and distance,* 5) Rg decreases
as cues acting to indicate the real object are controlled,
4) Rg can be eliminated in certain well-controlled
situations, 5) Rg does not seem to increase if the
subject has knowledge of the objects being presented,
6) Rg tends toward the real figure and not necessarily
toward assuming a "best shape”, 7) Rg does not occur
with after images.

Eissler (12) computed Brunswik ratios**.for shape
perceptions gotten under a number of different conditions
in which various depth cues were reduced. The ratios

obtained under these reduced conditions*** show the

 

*No data given.

**This ratio is identical to the simpler ratio of
Thouless except that the initials are selected according
to a different terminology.

“*SThe reduced conditions were: 1) moving head from
side to side while viewing the object, 2) fixating a
point between the standard and comparison object which
put both in poor focus, 5) monocular vision, 4) monocular
vision and poor focus, 5) monocular vision through
tinted glasses, 6) viewing the object through half
opened eyes.

ll
reduction of constancy from "normal” to be approximately
equal under all conditions. This led Eissler to conclude
that the different cues can be substituted for one another
without this affecting the perceptual outcome importantly.

Color perception and perception of illumination,
perceived size and distance have been experimentally
related. However the usual phenomenal shape responses
have not been supplemented by phenomenal responses
orientation although this has been generally recognized
as desirable. Koffka (12) stated his eXpectations in
this regard most strongly, holding that the two aspects
of the percept will be coupled together in a way that
makes the relationship an ”invariant“ (pp. 229). That
is, when one aspect of the percept, orientation or shape,
changes the other must change also. Relating this to
constancy theory he declares, "The amount by which the
figure appears turned from the normal decreases as the
'constancy of shape' decreases” (pp. 255). An attempt
by Stavorianos (16) to test a hypothesis that shape
depends upon explicit perception of orientation met
with only indifferent success. From Koffka's statement
that “the amount by which the figure appears turned from
the normal decreases as the 'constancy of shape' decreases”

(pp. 255) she derived the Operationally testable statement”

12
that “when the tilt of an object is correctly perceived,
the apparent shape of the object should correSpond most
closely to the real (objective) shape" (pp. 6). The test
made however does not seem to have been a fair one. A
number of possibly vitiating factors may have conditioned
the outcome. Besides those related to the apparatus and
methodology employed, no account seems to have been taken
of what Bartley has called "geometrical equivalence".
These three factors will be considered in a later section.

Stavrianos tested the hypothesis in three major
experiments using rectangles and ellipses as targets.
The experimental set-up and analysis of data lead her
to conclude that: l) shape judgements of tilted figures
were accurate and showed little variation as a function
of presented angle or different conditions, 2) tilt
judgement values varied and fluctuated greatly as a
function of presented angle and different experimental
conditions, 5) correlations of paired shape and tilt
judgements revealed no constant relation to that of the
real object, 4) accuracy of tilt judgement decreased
as a result of one reduction (via reduction tube and/or
monocular vision). This was not accompanied by a decrease
in accuracy of shape judgement and there was no uniform

decrease in constancy. It was noted however, that an

l5
approximate relationship between apparent shape and
judged inclination occurred for some observers under
the conditions in which depth cues were at least abundance.
Also when the possibilities of reaponse were reduced, an
approximate relationship held.

The not too completely reported work of several other
experimenters also has yielded results that are not in
accord with the expectations of befka. Eissler's and
Klimpfinger's experiments, discussed in several places
(11). (12), generally are imputed to demonstrate a lack
of relationship between shape perception and phenomenal
orientation of simple plane form. They report instances
in which-a target perceived as non-frontal parallel-plane
oriented showed almost no constancy and more frequent
instances in which nonafrontal parallel-plane targets
were seen normally positioned and exhibiting constancy.
Koffka diaputed these findings and pointed out that the
effect might be due to the serial character of presentation .
or that the orientation differed in some third aspect.

In the well known book Thg Perception 9; Eye Viggal,
MiG) Gibson asserts that shapes manifesting constancy
are not disembodied geometrical contours but rather are
shapes existing in phenomenal three dimensional space.

For the above author, however, depth perception

. l4
fundamentally is not mediated by the traditional primary
and secondary signs. He hypotheses ”the possibility that
there is literally no such thing as perception of Space
without the perception of a continuous background surface“
(pp. 7). Accepting this as true it follows that the
problem of shape constancy or shape at a depth can then
be largely reduced to the determinants of surface perception.
Gibson suggests that the determination is retinal, namely,
due to the occurrence of unidirectional compression of the
texture gradient and foreshortening of the contour in the
retinal correlate when a surface is non-normally oriented
(pp. 172-175). Traditional cues are supposed generally
effective only as they interact with these that are more
primitive. If however, surface texture and foreshortening
become ambiguous or are noneexistent, and if retinal
disparity and motion are controlled, he predicts that the
form will phenomenally assume the frontal parallel plane
position (pp. 174). It would also be expected from what
he has said, that the correlating phenomenal shape would
show zero constancy, that is, the phenomenal shape should
be a “copy" of the proximal stimulus shape.

It is possible that the experiment of Miller (15)
and certain of Thouless' were conditioned to an extent

by these then.unrecognized factors. 0n the other hand,

15
experiments in which Thouless had his subjects view the
targets monocularly, texture gradients and foreshortening
did not seem to have had a demonstrable effect. Stavrianos'
test of the shape-orientation hypothesis may have been
complicated by the same factors.

In the previously reviewed experiments, changes in
object identity were effected chiefly by means of manipu-
lation of orientation and/or manipulation of primary and
secondary cues. Another variable, little studied until
of late, which can alter the identity of certain properties
is that of Optical magnification. These changes arise
because of the way in which the magnifying instrument
itself behaves and because of the way in which the observer
organizes the stimulus materials awarded it.

Dee of an optical instrument, such as binoculars,
changes the two dimensional retinal representation of a
focused object. These instruments enlarge the retinal
image but the characteristics of the image resulting are
different in some reapects than they would be if the
magnification was accomplished by bringing the object
closer. This can perhaps best be understood through
study of the several illustrations in Figure l. The
target represented in Figure l is a solid object viewed
under three conditions, 1) at distance A, 2) at distance

l6

l/2 A, and 5) at distance A with two power Optical magni-
fication. FOr the sake of simplicity only a half of the
solids are represented. Comparing condition 1 with 2,
it can be seen that with physical movement of the target,
the retinal image has been made twice as large and that
the visual angles formed by light refracted from the
corners o, a, b, and converging at nodal point N have
increased diaprOportionately. Thus correSponding points
01, a1, bl, of the retinal image bear a different relation-
ship to one another than they did at distance A. In short,
assymetry has increased.* This does not occur with optical
magnification, rather all the visual angles as well as
the size are increased proportionately. That is, size
is doubled when two-power binoculars are used and the
distributions about the fovea is left unchanged. Assymetry
is not altered. Condition 5, Figure 1 demonstrates this.
The question now arises, however, as to just how the
organism will utilize this unique set of circumstances.

An all-inclusive answer to this question cannot be
given beforehand deSpite the fact that a lawful relation-
ship exists between the object and its retinal representation.

 

*Assymetry is present when the fovea is not in the
center of the image. It is always present to some extent
when a non-Spherical solid object is seen as three
dimenSional, or when a two dimensional object is perceived
as not lying in the frontal parallel plane.

l7

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18
However in most circumstances in which Optical magnifi-
cation is employed the object observed appears to maintain
a constant size. It is perceived as being nearer rather
than larger. When as a result of 2 power binocular magni-
fication, for example, the target is seen as being twice
as near rather than as twice as large, certain departures
from normal "twice as near” appearance must be expected.
This is because, as we have already observed, the internal
components of this double sized image are dissimilar from
those resulting when the target is actually moved nearer
by one half the distance. Uninvolzwed. objects such as
cubes usually seem to be foreshortened because the distance
from all points is perceived as having been prOportionally
decreased.*

A study in some respects similar to the shape constancy
eXperiments of Thouless previously discussed was performed
by Miller (15). He concerned himself only incidentally
'with phenomenal regression however and seems to have

principally directed himself toward determining just

 

*More complex objects such as buildings exhibit
what is known as "chinese perspective”. In this case
alterations in apparent shape differ according to the
various surfaces of the object and the end result is
”peculiar”, although presumably precisely determined.
This :0 lo has been given extensive treatment elsewhere

1 , 2 .

19
what experimental effects can occur when a simple two-
dimensional real object placed in a relatively cueless
environmental field is viewed with the two-power binocular
and with the naked eye. His subjects observed the targets
through reduction screens at close range and were asked
to draw the shape they saw. The targets themselves were
black circles and ellipses drawn on white cardboard and
presented at various angles of inclination to the observer.
Target shape was Operationally defined as the ratio of
minor to major axis. It was expected that the phenomenal
ratio would indicate the way in which the optically altered
distributions on the retina are utilized when visual field
conditions are less than "compelling”. The outcome illus-
trated in Table 2 is typical. As one can readily see the
phenomenal shapes show the same characteristics as those
of Thouless. Namely, they generally occupy a position
somewhere between the real object and phenomenal object
although the values are somewhat smaller on the average.
The degree of relative object constancy under both con-
ditions was eXpressed in terms of Thouless' simpler index
of regression. Table 5 contains the Rg's corresponding

to the Table 2 shapes.

20

TABLE 2

"REAL” RATION, “STIMULUS” RATIO.AND 'PHENOMENAL'
MEAN.RATIOS OBTAINED WITH AND WITHOUT GLASSES FOR
A CIRCLE AT FOUR INCLINATIONS TO THE LINE OF REGARD

 

 

at 90° at.67.55 at 4.5: at 22E

 

“Real” ratio 1.00 1.00 1.00 1.00

”Phenomenal" unaided ratio 1.02 .99 .85 .71

FPhenomenal" aided ratio .99 .96 .69 .62

“Stimulus” ratio 1.00 .92 .71 .58
TABLE 5

INDICES OF PHENOMENAL REGRESSION COMPUTED ON DATA
OBTAINED WITH AND WITHOUT GLASSES FOR A CIRCLE AT
IFOUR INCLINATIONS TO THEMLINE OF REGARD

 

at 90° at 67.5° at 45° at 22,?

Uhaided .02 .83 .49 .54
Aided -.01 .50 -.17 .39

 

21
Miller's major finding however had to do with
Optical magnification rather than constancy. That is,
the tables show that there is a lesser amount of Rg with
instrumental observation than without. This outcome
prompted several conclusions; namely that: 1) two
dimensional objects occupying three dimensions in space
in reference to the observer can undergo changes similar
to three dimensional objects, when they are viewed through
binoculars, 2) the operation of a different set of retinal
cues, brought about through binocular magnification, can
lead to a two dimensional object being seen approximately
twice as near rather than twice as large even in a
restricted visual field, 5) retinal image assymmetry
for some properties under certain circumstances in
interaction with other cues, can assume a determining
role as regards magnitude of relative object constancy.
The full considerations which dictated the foregoing
interpretation must forebear discussion here. However,
it should be recognized that in his interpretation of
the data, Miller has been oriented primarily toward
gaining an understanding of the effects that instrumental
magnification has on shape when conditions of encounter

are Specified. This need not have been the case.

22

In an attempt to provide a more comprehensive set
of principles to account for all perceptual behavior,
Bartley has discussed the broader implications of Miller's
results. In a short monograph (1) he suggests that it is
possible to account for perceptual performance with three
broad generalizations. The generalizations, based on
experimental evidence, are the principles of ”geometric
equivalence”, "constancy", and "internal consistency”.
While his treatment of constancy parallels that of this
paper closely enough to make further discussion redundant,
it is necessary, before proceeding further, to afford.
formal recognition to the first and last because of their
relevance for all later sections.

”Geometrical equivalence” is simply a.formal
recognition of the fact that any given visual angle or
set of angles can be subtended by an infinite number of
shapes and an infinite number of orientations.

The principle of “internal consistency" points up
the fact that while all-factors, that is the’total retinal
patterning, are taken into account certain factors always
have greater prepotence than others. Bartley Speaks of
the process as being analogous to reasOning, wherein
certain facts serve as the premises on which the organism

bases a conclusion. In.Nflller's experiment, for example,

23
the fact that increased retinal asymmetry did not follow
increased retinal size seemed to serve as a leading factor
or premise for the organism. Internal consistency rejects
the idea that a simple isomarphism can exist between the
retinal components and the perception. This principle
insists that the functional significance of differential
light intensities impinging on the retina rests upon
more central considerations. This principle, and that
of constancy, are at the bottom of descriptions of the
two general ways by which the organism confronts geometrical

equivalence in its environment.

II. GENERAL STATEMENT OF THE PROBLEM

In the introduction, the varying perceptual behavior,
displayed by the human organism with reference to similar
stimulus shapes, was described. The foregoing introduction
indicated the subtility of the problem of ascertaining the
factors that determine the apparent shape of objects.
Variations in apparent shape were correlated with many
coordinate extra-shape retinal existencies, binocular
factors, and reSponse conditions. The experimental
evidences concerning the role of the correlates treated
are impressive, but nevertheless, a great number of questions
still remain to be answered. The studies indicated that
there is still much to be done to reduce the matter to
systematic understanding. The present study aims at
making a step in this direction.

The present study is one in which the targets consist
in forms in an undifferentiated field, where obviously
there are no visual-field influences. The sole influences
outside the targets themselves are those of experimental
design, and the characteristics of the observers themselves.
Accordingly the present work is an eXperimental attempt
to study the perceptual behavior of the organism in rather

unique circumstances. The circumstances are unique in

25
that while the retinal patternings responded to can be
definitely determined, they are not of the sort that seem
e-priori to allow for only a single phenomenal outcome.
It is heped that this approach will demonstrate the relation
of certain stimulus and response variables under more
extreme conditions than others have hitherto been able
to realize. For these reasons, it will not be possible
to state a fixed hypothesis regarding any specific
phenomenal outcome.

The chief problems of interest are three in number.
Briefly they concern: (1) the relative shape constancy
obtained with circular and elliptical outline targets in
an impoverished situation, (2) the effect of instrumental
magnification as regards perception of shape when cue
conditions of observation are at a minimum, and (3) the

relation of shape to Judged inclination.*

 

*In addition, while the eXperiments were not
designed to test the role of general variables of the
perceptual task, a statement of the matter is to be
given. These incidental findings will be found in the
Appendixes l, 2, and 3. Also included in the Appendixes
(4 and 5) are two short studies related to the main
problems.quite directly.

..—

III. EXPERIMENTAL APPARATUS AND SUBJECTS

b ec ‘

Fourteen subjects, divided equally as regards sex
were used in this experiment for "Group A”. For "Group B"
ten different subjects, mostly female, were used. All
subjects were in their twenties. All had, at minimum,
sixteen years of education and possessed or were corrected
to, normal vision. As far as could be determined, all
observers were unaware of the nature of the experimental

variables and naive as to the method of their manipulation.

Assassin

All exPeriments were performed in the same two
adjoining light proof rooms (see Fig. 2). An aperture
14 x 28 inches was cut into the wall between the two
rooms and located at eye-level to the subjects who were
seated at a table thirteen feet six inches from.this
aperture. Attached to the center wall and immediately
around the aperture was a large plywood box.referred to
as the stage,and which measured 46 inches long, 30 inches
wide, and 35 inches high, and contained an Opening 7 inches
square into which the targets were placed for presentation
(see Fig. 5). Thus the distance from target to observer

became 17 feet 4 inches. Located above the front aperture

27
and inside the stage was the light source, a General
Electric CH~4 ultraviolet lamp and its accessory parts,
which included its screw base socket, transformer and
Special filter which eliminated the fractional percentage
of white light emitted by the source. The lamp was of
spotlight construction and was beamed directly on the
target area. All surfaces except those of the target
preper (see Fig. S-A) were painted flat black to absorb
not only the fractional amounts of white light which
might still have been present in the emission from the
source but also to absorb the traces of white light
reflection caused by any foreign matter present in
commercial fluorescent paint used to coat the targets
themselves. Between presentations, all target changing
activity was hidden from the observer by means of a pair
of monks cloth curtains suspended from a traverse rod.
The traverse rod was Operated.from.the rear of the stage
by the experimenter. The curtains provided complete
occlusion of the stage interior during target changing.

There were 12 targets fabricated from 12 gauge
wire. The targets are described in terms of the size
of their minor-major axis ratios and angles at Which
they were mounted. Thus three different sized targets

were used: a) 5 x 3.2 (a major axis of five inches

28
and a minor axis of 3.2 inches), b) 5 x 4, and c) 5 x 5.
Four each size targets were constructed and one each of
the four mounted at a different angle than that of the
others. The angles of presentation were approximately
90° (upright), 57.50 (22.50 away from the subject), 45°
and 22.50. These twelve figures were mounted on 7 inch
squares, constructed to afford a light-tight fit when
placed in the Opening at the rear of the stage for
presentation (see Fig. 3 and.Fig. 5-B). Although many
of the targets were mounted at a tilt the use of the
fine gauge wire assured that the difference in perceived
size between the nearest and farthest segments was never
sufficiently great to have cue value for distance.

A reduction screen with an aperture 2-1/4 inches
high and 3-l/4 inches wide was placed 30 inches from the
subject to restrict the field of vision (see Fig. 4-B).
The aperture in the reduction screen was movable to
compensate for variations in sitting height of the
subjects. The relationship of the various apparatuses
to one another can be seen in Fig. 4. In this Figure,
apparatus A held the glasses and was removed when the

condition was that of unaided vision.

29

 

 

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STAGE AND EXPERIMENTER'S ROOM

IV. PROBLEM I.

A. §tgtement of Egoblem;

' This problem concerns the measurements of shape,
for the circular and elliptical targets described, when
visual-field influences are totally lacking. It is known
from the results of previous experimentation that the
experienced shape varies as a function of collateral
retinal stimulation. Usually a decrease in relative
constancy accompanies the elimination of collateral cues.
In Thouless' experiments for example as the traditional
depth cues were reduced, the index of Hg approached zero.
Nevertheless despite existence of this continuum, reduction
of a regression index to zero has been difficult to
accomplish. Thouless, Eissler, and Miller show no values
of zero for binocular observation or monocular observations
in an.unrestricted field. In explaining this, one is, of
course, tempted to conjecture that these greater than
zero indexes occurred because all relevant stimuli
collateral to the retinal image itself had not been
successfully controlled. This argument appears to be
rendered all the more likely when one recalls that texture
gradients were not conceived of as being salient features
until the advent of Gibson's book and could have been

complicating factors in all cases where target surfaces

34
were involved. Compelling as the above alternative may
sound however there are two other possibilities that
cannot be ruled out summarily.

Certain shape targets observed in very impoverished
circumstances might yield phenomenal shapes showing an
index other than zero. For example, under our experimental
conditions the targets are structurally simple outline
shapes tipped from the line of regard and viewed in
complete darkness at distances too great for binocular
disparity to be operative. The observer is responding
to a simple retinal organization and for several reasons
regression or progression seem a-priori as possible in
this situation for some of the targets as does an index
of zero.

Eissler's results for example indicated that no
single condition of those he considered was an absolute
necessity for depth perception. All members were found
to a large extent replaceable by others. The function
of one cue does not seem to be independent of the presence
of other cues. If the extent of the relative constancy
expressed is, as it seems, a function of the prepotent
cues that serve as ”premises“, or as the ”frame of
reference” for the others, a dearth of ”common” premises

might lead the organism to center the perception on

35
conditions previously given little weight, or to center
the perception on cues discriminant over only a small
part of the entire range Of possible reSpOnses. For
example, to state a possible case, tipped targets are
always foreshortened. In regard to ellipses and circles
this is known as the ”flattening effect". Flattening
probably has steadily less cue value as the target
approaches the line of regard. Hence an ellipse vertical
to the line of regard might show a differing extent of
constancy than a circle at 65 degrees. This might occur
because Of a foreshortening cue even though the Operational
stimulus shapes were identical. Here we could Speak of
foreshortening as a discriminant Or differentiating
determinate. Conversely however, when the targets lie
close to the line of regard identical stimulus shapes
might produce identical phenomenal shapes even though
the real targets were an ellipse, a circle and an .
elongated ellipse (ellipse hinged on its minor axis).
This is because differences in.foreshortening would be
too slight to be usable by the organism. Foreshortening
would not be a discriminant in this part of the range
and, if used as a premise, might result in progression,
regression or zero constancy depending upon the real

target used as the referent.

36

Other factors such as Koffka describes as "external“
and "internal forces” produced by the retinal configuration
might be Operative. Neuro~physiological factors relatively
independent of the proximal stimulation might also play
a role under such circumstances. Other agents not having
to do directly with the retinal stimulation such as ”assumed
shape" might prove impossible to preclude in this setting.
Accordingly, even though any comprehensive attempt to
determine the nature of any ”new” premise possibly Operating
is beyond the scope of this paper, no assumption concerning

the exact indexes to be expected can be entertained.

B. Procedure and Directiong to the Subject

During this part of the experiment the binocular
mount and the variac with tilt board coaxial with it were
removed from the Table (see Figure 4). The experiment
then proceeded in the following manner. The subjects
were asked to seat themselves at the end Of the table
supplied with paper and pencils. After the subject had
seated himself, normal illumination was removed and
-replaced by illumination afforded by a red bulb of 25
watts. The subject was partially dark adapted in this
environment for three minutes, during Which time he was
given the instructions and allowed to Operate the buzzer

system which informed the eXperimenter in the other room

37
Of the completion of a reaponse to one target and readiness
for the next.

The following directions were given, ”Draw what you
see as accurately as you can. Take all the time you care
to. Size is unimportant, but what is desired is that the
internal‘relationships, that is, the relation Of the major
to the minor axis, the prOportions, be in as close accord
with those of the target as you can make them.” After
this the experimenter indicated to the subject‘that the
eXperiment was about to begin. Then placing in position
the first of the twelve targets Of the series (the order
of appearance of which had been determined by reference
to tables of random order), the experimenter drew Open
the curtains, exposing the target. When the subject had
satisfied himself as to the adequacy of his response, he
pressed the buzzer to indicate completion Of the task.

The experimenter then closed the curtains and replaced

the target with the next. This cycle was repeated through
the series of twelve targets. The complete series was
repeated ten times without pause under these conditions.
After the complete set Of reaponses were made, the
drawings were tranSposed into shape indexes and the

means for all trials per target were derived. Standard
deviations were then computed and an analysis of variance

applied to the compiled data Of “Group A”.

58

Comm

The data for this experiment are presented in
Table 4. It may be observed that the means of the
phenomenal shape responses are both larger and smaller
than those of the respective stimulus shapes. Twice as
many of the means are less than the stimulus shape ratio
as are greater than the same ratio. Also the average
deviation is somewhat larger in the less than stimulus
ratio direction. The range Of reaponses varies from a
greater than of .09 to a less than Of .12. There is a
general tendency for phenomenal ratios greater than those
of the stimulus ratio to occur at the ends Of the distri-
bution of shapes while those values occurring in the
middle ranges are uniformly smaller than their reapective
stimulus ratios. This is depicted graphically in.Figure l
in which the mean phenomenal ratios are plotted against
the stimulus ratios. A simple isomorphism would demand
that all points fall on the diagonal line. The Figure 6
shows the plot of points to roughly conform to the contour
Of a positive accelerated curve. The pattern Of changes
varies consistently as a function of the magnitude Of
minor major axis ratio. Table 4, column 5 contains the
standard deviations for each mean of the phenomenal

reSponses Of Group A.reported in the table. The

39
variability does not appear to be closely dependent upon
either angle Of presentation or on the real shape presented.
Because of the very small size Of these standard deviations
some Of the differences between phenomenal and stimulus

shape values would doubtlessly be found to be significant
statistically.

40
TABLE 4
TABLE COMPARING REAL SHAPE, STIMULUS SHAPE,

AND MEAN PHENOMENAL SHAPE FOR “GROUP A” AND “GROUP B”.
STANDARD DEVIATIONS FOR ”GROUP A? ARE INCLUDED.*

 

-_

Real Stim. Phengmenal S. D.
A roupgA Group B Grogp A

(1.00 1.00 1.01 .97 .08
90° ( .80 . .78 .88 .88 .07
( .88 .88 .56 .58 .07
(1.00 .95 .95 .92 .08
87.5°( .80 .78 .87 .88 .07
( .88 .59 .55 .57 .08
(1.00 .70 .80 .85 .08
45° ( .80 .85 .51 .54 .08
( 068 ‘ 058 O45 047 006
(1.00 .51 .28 .29 .05
22.5°( .80 .28 .50 .52 .07

( .68 .24 .28 , .51 .06

 

*Each combined mean.f0r "Group A" represents 140 unaided
condition reaponses. Each combined mean for ”Group B"
represents 100 unaided reaponses. Total number Of unaided
reSponses for "Group A" is 1680. Total number of unaided
reaponses for ”Group B" is 1200.

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V. PROBLEM 2

A. ‘§t§tement of the Problem

The second question concerns the effect of low power
optical magnification on phenomenal shape under conditions
in which the target is viewed in an undifferentiated field.
It was noted in a previous section that two power binoculars
double all visual angles and hence exactly double the
retinal image size. This increase is effected however
without changing the relative distribution of the image
about the fovea. Asymmetry is not altered. The size of
the retinal image can also be doubled in another way.
That is by halving the original observation distance.
However when the increase is brought about by moving the
target closer, an alteration in the distribution Of the
images about the foveas does occur and asymmetry increases.
If these conditions of retinal asymmetry are the only
variants and are supraliminally different then we may
expect, as Koffka (12, p. 250) points out, not entirely
equal perceptual effects. The direction of the change
is predictable under ordinary conditions because certain
objective and subjective factors are known.

Under ordinary conditions when glasses are used to

view simple two dimensional target shapes maintenance

43

of size seems to be more basic than maintenance of the
invarient of distance.*

That is, with two power magnification the target is
seen as being of a fairly constant size but almost twice
as near rather than as being at a fairly constant distance
with approximately twice as large a size. Because of this
and our knowledge of the geometry of optical magnification,
several givens or premises are available from which the
direction of change, that is the approximate shape and
orientation to be expected under ordinary conditions can
be predicted.

As an example, in Figure 7, retinal distance a b
and the associated visual angles a N b and A N B are
Objective facts under the illustrated conditions. Now
suppose that a two power magnifying instrument is interposed
between the retina and the two dimensional target at the
nodal point. Under this latter condition the doubled
visual angle and the doubled retinal distance designated
x y are now the objective facts. Putting these Objective
factors together with those of size and distance determines
target X Y. This is because the relative constancy of size,

if expressed in terms of Hg, would approach 1.0 while that

 

*The invarient relationship has been demonstrated
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45
of distance would approach 0. Distances N A and N B
would be perceived as approximately halved. Drawing a
line through points T and S, which are halves of this
distance, and extending it to the visual angle determined
by the Optical instrument should approximate the phenomenal
outcome. The line X Y suggests that the phenomenal result
should be a perception with approximately the shape and
orientation qualities of X Y.

Miller's experiment generally bears this out as far
as shape is concerned. He obtained, on the whole, smaller
indexes of Hg for drawings of tilted circles and ellipses
with conditions of optical magnification than with conditions
of unaided observation.

Reduction of retinal stimulation collateral to the
stimulus shape to a point below threshold value does not
make possible prediction of the shape indexes to be ob-
tained. This is because, although the Objective facts,

1. e. retinal patternings, are just as determinable here
in ordinary conditions of perception, there is no way to
know prior to examining the data how the organism will
structure the subjective factors of size and distance.
Appriori all three shape reSponses are possible. Namely,
the shape indexes can be larger, the same, or smaller than

those got under the unaided condition of observation.

46
Considering these facts several things may perhaps be
said.

If the Obtained indexes are larger or the same as
those of the unaided condition than the results will not
be in accord with those obtained in eXperiments in which
less severely reduced fields were used. From equal or
larger indexes one would surmise that retinal asymmetry
is not functioning as a premise and/or that size has
varied, with distance showing a greater relative constancy.
If smaller indexes should occur with instrumental magni-
fication the differences would be in agreement with those
Obtained in less reduced situations by other experimenters.
Given this the case, one would perhaps suppose that retinal
asymmetry was functioning as a premise and that with Optical
magnification distance and not size had been altered.

A comparison of the absolute positions of the shape
responses on the range of possible reaponses should suggest
the factors on which the responses are founded. However
the possibilities in this connection are so manifold that
any attempt to delve into all logically possible relation-
ships prior to treatment of the data would be wasteful Of

the reader's time.

47
B. Procedure and Directions to the Sgbjegt

During this part Of the experiment two and seven

 

power binoculars and the binocular mount were used.
The variac with tilt board coaxial to it were removed
from the table (see Figure 4).

The eXperiment consisted of the same task performed
under the same conditions as those previously described,
except for the introduction of instrumental magnification
into the situation. The subjects were divided into two
groups as regards the aided situation, twelve using two
power (2X) Opera glasses (Group A), and nine using seven
power (7X) military glasses (Group B). In both the aided
and unaided situations, techniques of presentation by
experimenter and representation by the subject were the
same.

After the complete set of responses were made, all
drawings were transposed into shape indexes and the means
for the all trials per target, were derived. Standard
deviations were then computed and an analysis of variance

applied to the compiled data of “Group A“.

C. Besglts

The mean phenomenal ratios for "Group AN, unaided
and two power optical magnification, and “Group B”,

unaided and seven power binocular magnification are

48
entered in Tables 5 and 6 respectively. Noting first
the data in Table 5, we can Observe that the subjects
tended to draw slightly larger shapes where the targets
were viewed through two power binoculars. Although these
larger ratios were obtained for eleven of the twelve
computed means, an analysis of variance shows the difference
to be insignificant (F - .0088). Turning to Table 6 one
can observe in the case of "Group B” data a trend in an
Opposite direction from that of the data of "Group A”.
It may be noted here that only in two of the twelve cases
are the phenomenal ratios larger than the stimulus ratios
in instances where the targets were viewed through seven
power binoculars. This difference was not tested for
significance because it is of smaller magnitude than that
found to be insignificant for ”Group A". These relationships
may be seen more clearly in Figure 7. In this figure the
phenomenal ratios for both groups, under both conditions,
are plotted against the stimulus ratio. All of the four
plotted distributions roughly correspond to the contour
of a positively accelerated curve. It will be noted that
consistent within all of the experimental conditions is
the occurrence of phenomenal shape values which were
greater than the stimulus shape values at the ends of

the distributions of the shapes, and less than stimulus

49

shape values in the middle ranges. The pattern of change
suggests that the shape indexes of the reaponses vary
absolutely as a function of the minor-major axis ratios.
That is, the contour and position of the curve does not
seem to be significantly influenced by optical magnifi-
cation Or differences in optical magnification in our
situation. The standard deviations are contained in

Table 5, columns 4 and 6. They show only small differences
in variability of observation under unaided, and two power
binocular aided condition. When these small differences
are found, they are generally in favor of the unaided

condition.

50
TABLE 5
TABLE COMPARING PHENOMENAL SHAPE

AND STANDARD DEVIATIONS UNDER CONDITIONS OF
UNAIDED VISION AND TWO POWER OPTICAL MAGNIFICATION*

Real etim. ‘Ffiénonenai ome

 

 

Unaided s. p. 2 Pr. ggg. s.p,

(1.00 1.00 1.01 ‘.08 1.00 .05

900 ( .80 .78 .88 .07 .70 .06
( .68 .68 .56 .07 .58 .06

(1.00 .95 .95 .08 .97 .07

67.5° ( .80 .78 .67 .07 .88 .08
( .68 .59 .55 .06 .56 .06

o (1.00 .70 .80 .08 .64 .08
45 ( .80 .85 .51 .06 .54 .06
( .88 .58 .45 .08 .45 .07

o (1.00 .51 .28 .05 .50 .05
22.5 ( .80 .28 .50 .07 .52 .06
( .68 .24 .28 .06 .50 .05

 

*Each combined mean represents 140 reaponses. Total
number of responses per condition is 1680.

51
TABLE 6

TABLE COMPARING PHENOMENAL SHAPE UNDER CONDITIONS
OF UNAIDED VISION AND SEVEN POWER OPTICAL MAGNIFICATION“

 

 

Real Stim. :Phenomenal
Unaided 7 Pr. Mgg,

o (1.00 1.00 .97 ’.98
90 ( .80 .78 .68 .64
( .68 .88 .58 .56
o (1.00 .95 .92 .89
87.5 ( .80 .76 .68 .85
( .68 .59 .57 .55
o (1.00 .70 .65 .61
45 ( .80 .65 .54 .51
( .68 .58 .47 .47
o (1.00 .51 .29 .29
22.5 ( .80 .28 .52 .55

( .68 .24 .51 .33

 

*Each combined mean represents 100 reaponses. Total
number of responses per condition is 1200.

VI. PROBLEM 5

A. Statement 0;; the Problem

v This part of the paper concerns the relation of
perceived shape to judged orientation of the target.
Although Stavrianos was unable to show a consistent
relation, the problem is of significance. The determi-
nation is felt to be of importance because inherent in

the work of most experimenters in the area Of shape
constancy is an implicit assumption that these abstractions
are related in some orderly, if not necessarily direct,
fashion.

As previously indicated, the present writer suspects
that Stavrianos' failure to confirm the shape-orientation
hypothesis may have been conditioned to some extent by
the method Of experimentation employed. Accordingly the
present experiment will employ apparatus and methodology
entirely different than those of Stavrianos. Besides
these there is a difference in the orientation of the
present experimenter from.that of Stavrianos. These
factors will lead to a difference in the organization
of the data.

Firstly, as regards apparatus, the test will be made
using outline target shapes as standards instead of surface
target shapes. It is felt that a combination of lighting

effects and the use of surface targets for both standard

55
and comparison targets could have produced material
.dissimilarities in texture gradients in Stavrianos
experiment. Secondly, the standard target and tilt
comparison target will be at different distances and
be of different shapes to assure that an abstraction
rather than a gross matching is being made. Thirdly,
shape will be expressed via drawing. In Stavrianos'
experiment shape was shown by the adjusting of a light
patch lying on a milk glass screen until it appeared to
be of the same proportions as the standard. The drawing
method would seem to better assure that an abstraction
and not a match is being made. This is particularly
true because with Stavrianos' setup any representation
with less than the greatest expressable minor axis would
be bound to be foreshortened, with the foreshortening
increasing as the minor axis was decreased.

Methodologically it is felt advisable to deal with
the abstractions independent of one another. This is
done to preclude interaction of the very things tested.
Stavrianos subjects were required to make successive
determinations, first of tilt and then of shape. However
it is recognized that in her case interaction may not
have been an important factor because she reports using
observers who were all skilled in making the type of

judgement necessary for the experiment.

54

Stavrianos attempted to demonstrate the invariance
by relating phenomenal tilt and phenomenal shape to those
of the real object. The assumption was made that if the
tilt was perceived correctly, that is, if it was in
accordance with that of the standard target, the shape
should correspond most closely to the shape of the real
object. She supposed that an eXperimenter with knowledge
of the stimulus shape and knowledge of the perceived
inclination should be able to predict phenomenal shape.
Although in her eXperiment phenomenal tilt does seem to
agree fairly with real target tilt, it appears to be
needless to confound the test of invariance by positing
a vertical aspect to perception, particularly under the
conditions of her experiment. To the present writer it
would seem to be preferable to simply treat the phenomenal
responses independently of the objective measurements.
By doing this a test might be effected without making
the assumption of a simple isomorphism between the two.

In the present experiment, phenomenal tilt responses
will be plotted against phenomenal shape reaponses. If
the Operational phenomenal shape reSponses are demon-
strated to be identical under our conditions to the
operational stimulus shape, than phenomenal tilt, if it is

an invariant, will show a similar relation. That is

55

it will be a straight line function just as shape. An
invariant relation will be represented by a straight line

function in any direction.

B. Procedgre
The shape indexes already reported for “Group A”

were compared to tilt judgements made to the same targets
by the same subjects.* The tilt responses were made after

all shape data had been collected.

C. Results

The corresponding phenomenal shape and phenomenal
tilt values are presented in Tables 7 and 8. Table 7
contains the phenomenal values for "Group AP, unaided
condition, and Table 8 the phenomenal values for “Group A”
observations, when vision was aided by two power binoculars.
From these tables it can be seen that the judged inclination
of the targets observed increases as the phenOmenal shape
values decrease. Comparing Tables 7 and 8 it can be seen
that the values for phenomenal tilt are in all cases larger
than those of the unaided condition. Figure 8 illustrates,
graphically, the functional relationship obtained between
phenomenal tilt and phenomenal shape for all "Group A"
conditions. Phenomenal tilt has been plotted against.
phenomenal shape in this Figure. The data appears to fall

 

*Regarding the data for the tilt experiment see
Haan (7).

56
in a fairly straight line along the dotted function repre-
senting the objective relationship between tilt and shape,
that is, the relationship of real tilt to stimulus shape.
It is thus apparent from the location of the points that
the relationship between these phenomenal abstractions is
very similar in position and direction to that of the
Objective abstractions. It is further Obvious that if a
line were drawn to depict the phenomenal relationships
for I'Group A” data, under the aided and unaided conditions,
that the aided function would occupy the higher position
on the graph. This is because while the phenomenal shape
indexes did not differ significantly between the aided
and unaided conditions, as the previous section showed,
the inter-condition phenomenal tilts do differ signifi-

cantly. This outcome was not entirely unexpected.

57
TABLE 7
TABLE SHOWING CORRESPONDING PHENOMENAL SHAPE

AND PHENOMENAL TILT VALUES FOR "GROUP A",
UNAIDED CONDITION*'

 

 

 

 

Approximate
Real Real Stimulus Phenomenal Phenomenal
shape Tilt snaga_ g. Shgpg Tilt
1.00 90° 1.00 1.01 85.5
1.00 67.50 .95 .95 85.5
1.00 45° .70 .60 50.5
1.00 22.5° .51 .28 25.5
.80 90° .78 .68 58.0
.80 87.5° .76 .67 58.0
.80 45° .65 .51 44.0
.80 22.5° .28 .50 29.0
.60 90° .88 .56 46.0
.60 67.5° .59 .55 44.0
.60 45° .58 .45 56.0
.60 22.5° .24 .28 25.0
*Each combined mean represents 140 reaponses. Total

number of reaponses per condition is 1680.

58
TABLE 8
TABLE SHOWING CORRESPONDING PHENOMENAL SHAPE

AND PHENOMENAL TILT VALUES FOR “GROUP A“,
AIDED (2X BINOCULARS) CONDITION 2

 

 

 

Approximate

Real Real Stimulus Phenomenal Phenomenal

Shana:; ..Tilt Shams Aéhane Tits...

1.00 90° 1.00 1.00 85.5

1.00 87.5° .95 .97 58.0

1. 00 45° . 70 . 64 85. 0

1.00 22.5° .51 .50 27.0
.80 90° .78 .70 77.5
.80 67.5° .76 .68 58.0
.80 45° .65 .54 48.0
.80 22.5° .28 .52 51.0
.60 90° .68 .58 65.0
.60 67.5° .59 .56 59.0
.60 45° .58 .45 46.0
.60 22.5° .24 .50 25.0

*Each combined mean represents 140 reSponses. Total
number of reaponses per condition is 1680.

59

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VII. DISCUSSION

The phenomenal shape responses resulting when the
circular and elliptical outline targets were viewed in
the described circumstances, are, in certain respects,
consistent with those of previous investigators. The
present experiment has again demonstrated that perceptual
shape reaponses are determined in large measure by the
presence or absence of retinal factors collateral to the
image itself. It has been shown that when these collateral
factors are completely eliminated the shape perceptions,
as indicated by the Observer's drawings, show a decrease
in the minor-major axis ratiOs over those obtained under
other conditions. Tables 1, 2, and 4 illustrate this by
making possible comparison of the outcomes of two previous
phenomenal shape experiments with that of the present.

However, in an important reapect, the shape indexes
reported in the preceding section (Table 4) are at variance
with expectations one might entertain on the basis of the
prior publications. In this regard we may state that,
in many cases, the phenomenal shape values are less than
those of the reSpective stimulus shape. That is, the
data in Table 4 clearly shows that all mean phenomenal
shape values do not fall within the range tacitly assumed
by the equations of the types developed by Thouless and

61
Brunswik. There is not a simple copy of the peripheral
stimulus shape even when collateral retinal stimulation
is at bottom. Relative object constancy-like reSponses
tend to occur toward the ends of the distribution, while
the combined means of the middle ranges fall significantly
outside the assumed range of reaponses. Thus, if the
results are accepted, and if one is to use the objective
or real shape as the referent, then it is manifest from
the data that it will be necessary to Speak of "progression
from the real object," as well as, "regression toward the
real Object." The eXpression, 'progression.from the real
object,” or its equivalent however, while perhaps satisfy-
ing enough as a descriptive devise, certainly would seem
to pose special problems for 8 “Psychology of Objective
Relation,” and the “Law of Phenomenal Regression.’I Neither
previous knowledge of a real character nor present perceptual
indicants of a real character seem to be able to account
for the results. Responses suggestive of those labeled
“relative object constancy“ do occur in the absence of
collateral cues. The dependence of Hg on the presence
of the usual perceptual indicants over the whole range of
possible reaponses has not been demonstrated. It is perhaps
also worthy of recognition that, under identical environ-

mental conditions, drawings representing both regression

62
and progression were obtained to stimulus shapes on
different parts of the continuum.

The data shown in Table 4 and the contour of the
correlated graph in Figure 6 might be considered attributable
to several possible factors. Gibson has suggested, for
example, that foreshortening of an outline, when it is
inclined to the observer, can determine constancy. However,
the outcome of this eXperiment fails to substantiate this
tenet. Two facts suggest that this determination is un-
likely. One, the largest phenomenal indexes, relative to
the stimulus shape used, occur at the ends of this distri-
bution. This occurs although one would expect a general
decrease in constancy or an increase in progression as the
targets approached the frontal plane, if foreshortening
were functionally effective. Two, given similar stimulus
shape ratios, similar ”regression" or "progression” can
result irreSpective of the extent of fOreshortening involved.
In fact, a glance at Table 4 shows that, with those targets
of greatest inclination, the smallest indexes of regression
are shown by the real circle rather than by the real
ellipses. This, too, is contrary to the foreshortening
hypothesis.

Discarding foreshortening, one might suspect that

the results are a function of the method of representing

65
the experience. Thouless, for example, abandoned the
method of drawing in favor of a matching reaponse, since
with drawings he discovered that slightly less than stimulus
shape reproductions were consistently made. Nevertheless,
several facts lead us to doubt that the method of repre-
sentation can account for the outcome. Firstly, the under-
estimations, Thouless reports, are too small to account
for the progression. Secondly, the data of an unreported
study, done under the supervision of the author, demon-
strated that the Operational perception shape did not

\‘change in terms of the surface on which it is projected.*

Thirdly, because phenomenal shape and phenomenal tilt
have been demonstrated to act as invariants, we know that
the reported shape perceptions probably did not occur as
artifacts of the method of expression.

The data indicate that all targets were treated as
though lying on the frontal plane regardless of the amount
of foreshortening present. Analysis of verbal reports by
the subjects supports this possibility. On a descriptive

 

*Three of the targets were drawn twelve times apiece
on surfaces at different orientations to the observer.
The differences in the combined means of several subjects
for reproductions of single targets made on a surface
upright to the observer, at 45° to the Observer and 0°
to the Observer showed no critical ratios of above .075.
More complete data are contained in Appendix 4.

64
level, the results are in.keeping with Koffka's hypothesis
concerning perception of non-normal orientatiOn. He
maintains that shape constancy is a result of a stimulus
shape being organized into a field of stress. That is,
he predicts that as collateral retinal cues are eliminated,
the perceptual reaponse will indicate an approach in the
direction of frontal plane orientation.* Gibson's similar
hypothesis, that perception of space is not possible
independent of continuous background surface, also receives

confirmation.

 

*Koffka conceives of space as being anistrOpic in
the main directions and as being dynamically balanced
within itself only in the frontal parallel plane. He
holds that Special forces are required to turn the figure
into a non-normal orientated plane and that these in turn
are Opposed by field forces which direct the figure toward
the normal orientation. Because Of this, any stimulus
pattern of a figure that is nonefrontal parallel plane
oriented leads to an organization in a field of stress,
which in turn leads to a different perception that can
occur in a stress free field. In addition to the field
forces, SO-called ”external forces“ and "internal forces”
produced by the retinal pattern itself are said to be
Operative. Hence, within this framework, any perception
is seen as being the resultant final equilibrium between
all participating forces. The relation is not, however,
one of the simple proportionality but rather the pro-
portionality is determined by total field conditions.
Because of this we find degrees of relative constancy.

Koffka's theoretical position is largely founded
upon deductions which have in turn arisen from broad
principles abstracted from simple perceptual demon-
strations. Often his tenets are devoid of experimental
support.

Successful experimental predictions of shape, however,
have previously been made by several workers who used an
approach dictated by a similar theoretical scheme. These
have been reviewed by Bartley (5).

65
Turning to the results obtained when Optical magni-

fication was used, we can see by comparison of the results
of Table 5 to those of Miller in Table 2 that the effect
of optical magnification differed in the two situations.
There were not the significant differences between aided
and unaided vision that Miller reports. "Regression” and
'prOgression" were not altered in our case. Evidently
when collateral retinal conditions are sufficiently
improverished, the same functional set of perceptual
circumstances will operate in both instances. The
statistical indexes in Table 2 of the Appendix confirm
this fact. The pertinent F score suggests that the
disparate retinal cues provided by Optical magnification
and/or the size of the retinal image per se were not
important variables. The question as to whether these
results indicate that the targets were seen as nearer
or as larger with Optical magnification, can probably
not be answered conclusively. The differences in the
sizes of the reproductions, from condition to condition,
hint that size rather than distance is the chief variant.
However‘the fact that assymetry was not sufficient in
isolation or with foreshortening to produce the experience'

of.or shape correlate of an object in three dimensional

66
Space*makes test of this, with the shape indexes reported,
difficult-

It is apparent from the graphed function, Figure 8,
that a relationship of invariance holds between phenomenal
shape and phenomenal tilt over the entire range considered
as well as under conditions of aided and unaided vision.

The fact that the phenomenal shape values decrease, as

the judged inclination increases, hints that the observers
treated the targets approximately as though they were all
circles at various inclinations to the observer. Perceptual
veridicality, the assumption believed to have confounded
Stavrianos test, occurred only accidentally. In light of
Hastorf's work it might seem possible, on the basis of

these results, to infer than an assumed Shape; i.e., a
circle, at various inclinations, played the decisive role
in determining the internal consistency of these reaponses.
This inference is believed to be untenable, however, because
of several considerations. For example, the subjects'

statements, concerning what they were ”really looking at,”

 

“a

*In another unreported study, done under the super-
vision Of this author, outline targets were viewed by
several subjects at a very close distance under binocular
and monocular conditions. The targets, circles and ellipses,
were four in number and mounted at four inclinations. The
data showed no significant differences in the combined
phenomenal shape indexes under these two conditions. “a
Assymetry evidently did not act as an important determinant
in isolation. For more complete data see Appendix 5.

67
fail to confirm the existence of such an Object. Only
one-half of the subjects judged the targets to be circles
at various inclinations while, deSpite the urging of the
eXperimenter, the remainder ranged from 'no idea“ to ”all
different from one another." This strongly suggests that
the perceptual responses were of the nature of 'givens.‘

It is also important to note, in this regard, that knowledge
of the real conditions evidently did not influence the
responses of the subjects. The test of invariance was
successful even though, in the first instance, (drawing
task) the subjects were given no reason to and did not
assume that the targets were other than frontal-plane
oriented targets, while in the second they were necessarily
told that some of the targets were inclined to the observer.
In addition, the less than stimulus shape ratios found for
the phenomenal shape indexes ”progression" was obviously
counterbalanced by "regression” in the tilt reaponses and,
conversely, the shape ”regression” by tilt ”progression."
Again, this occurred even though the responses were rendered
in qualitatively differing conditions. Koffka's hypothesis,
that the two abstractions are coupled together in an
invariant relationship, seems to be confirmed in this

instance.

68

Finally the present experiment has again demonstrated
the fundamental contribution that the organism makes to
the internal consistency of perception. The retinal
patterning is frequently dealt with as though it determines
the occurrence of one shape out of almost an infinity of
possible perceptions. Internal consistency is treated as
though it can be accounted for as being a direct result of
the stimulus patterns existing on the retina. It appears
to this author as likely that any explanation of these
results, on the basis of proximal or distal stimulus
conditions, will prove difficult.

Further correlations to and manipulations of these
reported functions might well be considered as inviting
problems for further eXperimentation. New shapes and
surface targets might be embedded in the experientially
undifferentiated visual-field.

VIII. SUMMARY

The purposes of this experiment were three-fold.

They concerned: (1) the measurement of phenomenal shape
for circular and elliptical outline targets embedded in

an undifferentiated visual-field, (2) the effect of optical
magnification on perceived shape for the same targets under
the same visual-field conditions, (5) the relation of
phenomenal shape to judged inclination.

Twenty-four observers were used in this experiment.
Fourteen served in "Group A” and the remaining ten in
"Group B.” All presumably were experimentally naive.

A The apparatus was such that all visual-field influences
collateral to the stimulus shape itself was absent.

The targets were twelve in number and all "outline
shapes.” Physically, four were circles with 5 inch
diameters, four were ellipses with a 4 x 5 inch measure-
ment, and four were ellipses with a 5.2 x 5 inch measure-
ment. One each of the three target types described above
were mounted at approximately 22.5° to the observer, one
each at 45°, one each at 67.5°, and one each at 90°
(upright).

I Theobservers were told to draw what they saw, particu-
larly, to reproduce the internal relationships as accurately

as possible.

70

One hundred-twenty drawing reaponses were recorded
with unaided vision for both I'Group AP and "Group B.”

An additional one hundred-twenty drawing responses were
recorded for "Group AF using two power binoculars and
another one hundred-twenty responses for "Group B“ using
seven power binoculars. This made a grand total of two
hundred-forty responses for each observer.

The ratios of the reproductions were measured and
grand means computed. Standard deviations for all "Group
A” data were found and an analysis of variance run On the
data.

The major findings are six in number and are entered
below:

(1) The elimination of retinal conditions collateral
to the stimulus shape reduced the minor-major axis ratios
in the direction expected on the basis of previous experi-
mentation.

(2) The reductions were both greater and smaller than
one would expect on the basis of proximal stimulation alone.
The perceptions showed both ”regression" to and ”progression‘
from the real Object.

(5) The data indicated that foreshortening of the
outlines, through tipping, did not play a role in determining

the "regression" or ”progression" Obtained.

71
(4) Simple targets seen in an undifferentiated field
appeared to assume the frontal-parallel position.
(5) Optical magnification did not alter perceived
shape significantly.
(6) Phenomenal tilt and phenomenal shape enjoy an

invariant relationship.

(I

\_J
'1

l.

5.

4.

6.

72
IX. BIBLIOGRAPHY

Bartley, S. H. A Study of the Flattening Effect
Produced by Optical Magnification. Minneapolis,
Minn.: Monograph 119, 1951, American Journal
of Optometry Publishing Association.

Bartley, S. H. Beginning Experimental Psychology.

New York: 1950, McGraw-Hill.

Bartley, S. H. VisionL A Study of Its Basis.
New York: 1941, Van Nostrand.

Boring, E. G. Sensation and Perception in the Historx
of ExperimentaliPSycholggy, New York: 1942,

D. Appleton-Century Co., Inc. '

BrunSwik, E. Psychology of objective Relations.
in Marx, Melvin H. Ed., Psychological Theory,
New York: 1951, The Macmillan Co.

Gibson, J. J. The Perception of the Visgal World.
Cambridge, Mass.: 1950, The Riverside Press.

Haan, E. L. The perception of a form in an.un-
differentiated field as indicated by the observer's
use of a tiltboard. Unpublished master's thesis,
1955, Michigan State College.

Hastorf, Albert H. The influence of suggestion on
the relationship between stimulus size and perceived

distance. J. of Psychol., 1950, 29, 195-217.

10.

11.

12.

15.

14.

15.

16.

75

Hermans, J. G. Visual size constancy as a function
of convergence. J. Exper. Psychol., 1957, 21,
145-161.

Knox, George W. and Williams, Robert D. Studies in
contemporary psychological theory: What is
behavioral constancy? J. of Psychology, 1940,
10, 269-274. '

Koffka, K. Gestalt interpretation of perception.
in Marx, Melvin H. Ed., Psychological Theoyy,
New York: 1951, The Macmillan Co.

Koffka, K. Principles of Gestalt Psychology.

New York: 1955, Harcourt, Brace.

Miller, J. W. A study of the effect of Optical
magnification on the perception of ellipses.
Unpublished master's thesis, 1950, Michigan
State College. I

Sheehan, M. R. A study of individual consistency
in phenomenal constancy. Arch. Psychol., 1958,
222.

Stagner, R. Homeostasis as a unifying concept in
personality theory. Psychol. Rev., 1951, 58,
5-18.

Stavrianos, B. K. The relation of shape perception
to explicit judgments of inclination. Arch.
Psychol., 296.

74

, 17. Thouless, Robert H. Phenomenal regression to the
real object. I. Brit. J. Psychol., 1951, 21,
559-559.

18. Thouless, Robert H. Phenomenal regression to the
real object. II. Brit. J. Psychol., 1951, 22,
1-50.

19. Thouless, Robert H. Individual differences in
phenomenal regression. Brit. J. Psychol.,

1952, 22, 216-241.

APPENDIX 1

75

A statement has yet to be made concerning the rate
of certain of the “grosser' variables in perpetual per-
formance. An inquiry of this sort might serve to suggest
possible co-ordinate areas of research for further experi-
mentation just as it has provided statistical indexes
useful for discussing problems more particular to this
paper. To achieve this eight variables were analyzed out
and the contribution each makes to the total experimental
variance calculated. Designation of the variables is as
follows: “sex", "binocular magnification", "targets",
"degrees", "figure“, ”figure X degrees", ”trials” and .
“subjects". The classification ”sex" needs no explanation.
The variable ”binocular magnification” separates unaided
reaponses from those of vision aided by two power optical
magnification. "Targets" includes the contribution made to
variance by the twelve separate targets. The variable
”degrees" indicates the extent to which the tipping of the
targets from the vertical influenced the subjects per-
formance. ”Figure“ refers to the three real shapes used,
i.e. the 5.2 x 5, the 4 x 5, and the 5 x 5 targets.

“Degrees X.figure” is an “interaction index" and measures

the effect of the two previous variables in combination.

By use of this latter index, it was hoped that one could

76
determine whether, if given the three groups Of real
shapes and four groups of angles of inclination, certain
combinations would result in significantly more variance
than others. “Trials" indicates how consistently the
same target was reproduced from trial to trial by the
same subjects. ”Subjects“ recognizes the importance of
individual determination.

‘ An analysis of variance was undertaken on all of the
data.for"Group A"relating to the shape drawing task. The
mathematical values are entered in Table 1.

As can be seen from this table, ”binocular magni-
fication" shows an F of .0088 indicating that binocular
magnification did not influence the index of shape we
used significantly as compared to unaided vision. The
variables, ”Targets“, ”Degrees“, and I'Figure", show
”F's“ of significant magnitudes. ”Figure X Degree“ is
not significant, indicating that trend lines are similar
for any degree through the different figures or any
figure through the different degrees. This suggests
that while these two abstractions are significant as
regards the shape indexes, that they may not in isolation

account for the perceived shapes. There were significant

77
differences between "Trials” and "Subjects”. "Sex" has

an insignificant F.

TABLE 1.

APPENDIX

78

ANALYSIS OF VARIANCE VALUES FOR PHENOMENAL SHAPE INDEXES
OBTAINED FROM ALL SUBJECTS OF “GROUP A'*

 

 

 

variables Contribgtion 52 1g *ieve;
1. Aided (2 power mag) .0088 5.84 6.64
vs. Unaided
2. Targets 4.7488 1.76 2.24 1%
8) Degrees 5.9075 2.60 5.78 1%
b) Figure 17.0499 2.99 4.60 1%
c) Figure and Degree 1.0656 2.09 2.80
5. Trials 141.2516 1.17 1.25 1%
4. Subjects 280.6840 1.79 2.24 1%
5. Sex .0559 5.84 6.64
6. Sittings

 

* N 8 5560

APPENDIX 2

79

For similar reasons, an analysis of variance was
undertaken on all of the data for “Group A”, relating
to the perception of tilt task. The contribution of the
same eight variables were analyzed out. The mathematical
values are entered in Table 2.

The "F" scores of this Table show, as before, that
there were Significant differences between “Target”,
"Degree", and ”Figure”. However in this analysis, the
interaction term, "Degree X Figure”, was found to be
significant beyond the 1% level of confidence. This is
taken to indicate lack of consistent trend lines for
any degree through the different figures or any figure
through the different degrees.*

A “Significant F' was also obtained with the

variable I'binocular magnification”.**

 

*InSpection of the combined means Show that,
in this case, phenomenal tilt, correlation with the
"Targets“, tipped at a real 22.50, appeared to violate
the trend occurring at the other degrees.

**However this outcome was probably conditioned
by a single subject who registered her responses
during the aided condition in a different quadrant
than any of the other responses obtained. A translation
of these reaponses to the apprOpriate quadrant SuggestS'
no difference as regards this variable.

80
A highly significant difference between the two

sexes is shown:*

 

*This, but to a lesser extent, might also be a
function of the one subjects responses.

81
TABLE 2. APPENDIX

ANALYSIS OF VARIANCE VALUES FOR PHENOMENAL TILT INDEXES
OBTAINED FROM ALL SUBJECTS OF 'GROUPAP COMBINED”

 

 

 

 

Variapggs Conggpgtiop: 1g fags;

1. Aided (2 power mag) 554.75 6.64 _1%
2. Targets 940.89 2.24 1%

a) Degree 1916.40 5.78 1%

b) Figure 1516.54 4.80 1%

c) Figure and Degree 527.98 2.80 1%
5. ' Trials _ 4.54 2.41 1%
4. Subjects 878.98 2.52 1%
5. Sex 2285.01 8.84 1%
6. Sittings 1.04 6.64

 

* N = 2800

APPENDIX 5

82

”Time to response" records were taken for four
subjects when the task was representing tilt. For
reasons similar to those of Appendix 1 and 2, an
analysis of variance was undertaken on the data. The
breakdown of the variables is identical to those of the
previous appendixes. The mathematical values are entered
in Table 5.

It will be noted from the Table that all the
variables are significant at the 1% level with the
exception of ”Degree” and the interaction term “Degree
X Figure”. The latter is significant at the 5% level
and the former is insignificant.*

 

*The large difference between aided and unaided
was doubtlessly produced in large part by conditions
related more closely to the apparatus than optical
magnification per se.

85

TABLE 5. APPENDIX ‘
ANALYSIS OF VARIANCE VALUES OF uTIME TO RESPONSE" MEASURES
WHEN CONDITION WAS THAT OF REPRESENTING TILT 0F TARGET.
DATA.FROM.FOUR SUBJECTS OF "GROUP A**

 

Varigbles

 

 

flContribgtion 52 12 Lgvgl
1. Aided (2 power mag) 116.60 5.86 6.70 1%
vs. Unaided
2. Targets 2.57 1.81 2.29 1%
a) Degree .26 2.62 5.85
b) Figure 6.72 5.02 4.86 1%
c) Figure and Degree 2.54 2.12 2.85 5%
5. “ TrialS' . 22.47 1.96 2.55 1%
4. Subjects 199.61 2.62 5.85 1%
5. Sex 555.24 5.86 6.70 1%

 

* N 3 960

APPENDIX 4

1.2222124.
The problem is to determine whether the perceptual

Shape reSponses (drawings) are in any way a function of

the inclination 0f the surface on which they are expressed.

2. Procedure

The experiment was carried out under circumstances
identical to those of Problem 1 of the main experiment,
excepting for the orientations of the drawing surface
and the number of targets used.

As regards the former, the surface was, at various
randomized times, flat to the subject (00 inclination),
inclinated at 45° to the subject, and vertical to the,
subject (90° inclination). As regards the latter only
three targets were used.- The targets were, a 4 x 5
ellipse, tilted at approximately 67.50 to the observer,
a 4 x 5 ellipse, tilted at 45°, and a 4 x 5 ellipse
tilted at 22.5°.

'Two naive subjects were used. These subjects made
nine reSponses to each of the three targets when the
drawing surface was at each orientation. This made a

grand total of eighty-one reaponses per subject.

85

5. Result; gag Igterprgtatiog

Table 4 shows the critical ratios, student t's,
resulting from comparison of the combined means for
each target. The table shows that differences resulting
from the expression of the perceptions, projected on the
various surfaces, are uniformly insignificant. Hence,
the perception does not seem to be a function of the
surface on which it is expressed and some validity is
lent to the drawing method as it has been used in measuring

phenomenal shape.

86
TABLE 4. .APPENDIX

COMBINED MEANS AND CRITICAL RATIOS RESULTING BETWEEN
DRAWING SURFACES ORIENTED AT 90°, 45°, AND oo TO THE OBSERVER

WHEN PHENOMENAL SHAPES OF THREE TARGETS ARE EXPRESSED BY DRAWING

 

4 x 5 Target at 4 5 5 Target at 4 x 5 Target at
67.5° Inclination 45 Inclination 22.5o Inglinatign
5030* D080* D060* D030“ DOSO* D080“ D080* D080* D080.“
_93 .450 .900 .0° ggso -90° -0° .g§° 90°

 

Combined 0.80 0.76 0.75 0.65 0.65 0.59 0.55 0.57 0.54
means

Critical
ratios**

 

*Drawing Surface

*fiThe largest difference showed a critical ratio of only
0.075. Because of this small sized ratio, no further
statistical checks were made.

APPENDIX 5

87
1. Pyoblem
The problem is to determine whether retinal disparity

alone will serve to mediate depth perception.

2. Pyocedgre

The experiment was carried out under circumstances
identical to those of Problem 1 of the main experiment,
excepting for distance, method of observation, and the
use of a chin rest.

As regards the first change, the distance of ob-
servation was reduced to five feet, so as to make retinal
disparity pronounced. As regards the second change, in
order to control for size, the targets were viewed both
binocularly and monocularly at this distance.

Four targets were used. The targets were a circle
with a 5 inch major axis, presented at approximately 90°
to the observer (upright), a 4 x 5 ellipse at 67.5°, a 4 x
5 ellipse at 45°, and a 4 x 5 ellipse at 22.5°.

Two naive subjects were used. The subjects drew
each figure four times under both the monocular and the

binocular conditions. Target presentation was randomized.

5. Rgsglts ang Igterpretationg
Table 5 shows the critical ratios, student t's,

resulting from comparison of the combined means for

88

each target. The differences resulting from perception,
monocularly and binocularly, are insignificant for each
target. Retinal diSparity, alone, was not sufficient

to mediate depth perception.

89
TABLE 5. APPENDIX
COMBINED MEANS AND CRITICAL RATIOS RESULTING BETWEEN

BINOCULAR AND MONOCULAR CONDITIONS OF OBSERVATION
WHEN VARIOUS SHAPES ARE VIEWED AT CLOSE DISTANCES.

 

5 x 5 circle 4 x 5 ellipse 4 x 5 ellipse 4 x 5 ellipse
at 90° at 67.5° atgso gt 22.5°
monoc binoc. monoc. binoc. gonoc. binoc. monoc. binoc.

—-T _

Combined
means 1.05 0.94 0.60 0.65 0.44 0.42 0.26 0.25

Critical
ratios 0.11 0.05 0.02 0.01