The Time-error for Size Comparison as a Function of Stimulus Duration and Interpolated Interval

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Karlin, Lawrence, 1917” ' The time-error for size comparison as a function of stimulus duration and interpolated interval. New Y> 1950. [2 ] , 1 2 7 typewritten leaves, diag: tables. 29cm. C58S41 Thesis (Ph.D.) - New York Univer­ sity, Graduate School, 19i>0* "References": p.1211-127*

«Cholf I ict

Xerox University Microfilms, Ann Arbor, Michigan 48106

TH IS DISSERTATION HAS BEEN M IC R O FILM ED EX A C TLY AS RECEIVED.

lIBBARr 09 UNIVSR8IT7 HlflRSITT HEIOHTP

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THE TIME-ERROR FOR SIZE COMPARISON AS A FUNCTION OF STIMULUS DURATION AND INTERPOLATED INTERVAL

by

Lawrence Karlin

A dissertation In the department of psychology submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at New York University, April, 1950*

ACKNOWLEDGMENTS

The writer wishes to express his sincere thanks And to acknowledge a profound debt to Professor Lyle H. Lanier for his guidance, advioe and criticism in carrying out this study. He also wishes to express his appreciation to Professors Thomas N. Jenkins and Presley D. Stout for valuable suggestions.

TABLE 07 CONTENTS I. Iatrodnatloa II. Oaaaral Baokoround........................ ..5 Trtti T h ao r y............................ 5 ErtanalTa Stlaull and TraeaTh a o r y ........ 8 Stimulus Duration...................... 10 Praatiea Sffsata ....................... 11 Csntral Tandanay and BalatadEffacto ..... 14 Tiaa-arror Studlaa of TlaualExtant ...... 19 Tfcaoratlaal Considaratloaa.............. «7 Suaaary

....

III. Outllna of tha Praaaut study

..55 .......... 57

IT. Apparatus aad Oaaaral Proaadura............ SO Prajaatloa 8y a ta a ...................... SO Tlalao S yataa.......................... 40 Stlaalus Matarlala..................... 48 Oparatloa of Xqulpaant

........

T. Naaulta........... Xxparlaaat X Jtxparlaant XX

44 45

............... ....

45 05

Exparlaaat XXX ......................... 78 Exparlaaat X T .......................... 04 Xxparlaaat T ...........

..97

IX.

Dlsauaaloa ................

ThaoratiaalInterpretations

105

.......... 107

TII. Suaaary and Oonelnalona.................. 117 Suaaary.............................. 117 Qoaelualoaa.......................... 1S1 ▼XII* Hafarenas*...............................ltd

I

INTRODUCTION

The constant error resulting from the successive com­ parison of two stimuli is usually described as a "time-error." The sign of the time-error is positive or negative depending on whether the second member of a pair is, respectively, under- or overestimated when compared with the first member. In experiments involving the successive comparison of lifted weights, Pechner (9) found a negative time-error to be the rule; i.e., a persistent tendency was displayed to overestimate the second member of a pair.

Assuming that the

judgments in this situation depended on a comparison of the seoond stimulus with a "memory image" of the first, he attri­ buted the negative time-error to the "fading" of the image during the time interval between two successive presentations. This fading memory-image provided the consistently lower "level" against which the second stimulus was judged, with the consequent overestimation of the second stimulus.

Recog­

nizing further that the time-error situation provided a method for "fraotionating" the course of the memory image in time, he experimented with varying time intervals Interpolated between two successively presented stimuli.

As he predicted, the time-

error became increasingly negative with increasing length of interpolated interval. In subsequent studies of the time-error these results were verified and extended to Include other modalities such

2

as vision and audition.

Although various theoretical in­

terpretations have generally assumed some kind of "’fading" after-effect, the concept of a "memory-image” as an embodi­ ment of this after-effect has long since been discarded. This was done mainly on the basis of introspective evidence (10,26,28) which provided no phenomenal justification for the role assigned to the memory image in the comparison judgment. Most time-error experiments have employed stimuli vary­ ing in intensity (e.g., heaviness of weights, loudness of sounds and brightness of lights), but a few recent studies have investigated the time-error for the successive compari­ son of stimuli varying in extent (e.g., the distances between dots /6,4l7, lengths of lines /25,277, areas of circles and squares

[jj&J).

The results ®f the latter group of studies

have not uniformly suggested the presence of a negative timeerror.

The lack of uniformity of the results for stimuli

varying in size as compared to those obtained with extensive stimuli, may be due to the possibility that each of the two types of stimuli (intensive and extensive) involve comparison judgments governed by different kinds of mechanisms.

Thus,

although most explanations of the time-error assume that the after-effect of intensities fade (diminish) in time, is it equally reasonable to assume that the after-effects of ex­ tensities (or sizes) fade also?

In brief, how does the concept

of a fading after-effect apply to size comparisons; is "fading",

in the case of extensive stimuli equivalent to "shrinkage?" Limited information is provided by the studies using visual extents in that they did not investigate the timeerror for varying interpolated intervals but determined it only for a single interval (eight seconds).

It is not known,

therefore, whether the time-error for this kind of stimulus varies systematically with changing interpolated interval* The only conclusion that might be drawn at present is that, for this kind of stimulus, there may not be a consistently negative time-error at 8-seoond interpolated interval. The "time-error function", as described in the experi­ mental literature, usually refers to the real or assumed relationship between the time-error and Interpolated inter­ val.

Further study of the experimental literature dealing

with the successive comparison of visual stimuli in a broader context, suggested that stimulus duration might be another important, if neglected, parameter of this kind of situation. The possibility was suggested by the results of these studies (£2,45) that the time-error might be a function of stimulus duration as well as of Interpolated interval.

Also of in­

terest in this connection is the finding by Vada (44) that time-errors for auditory intensities vary systematically with 1 stimulus duration. The results of this experiment suggest that additional comparison could be made between extensive l7 this article has not been translated from the original Japanese. Information was obtained from an English abstract and from inspection of the tables in the Japanese text.

4

and intensive stimuli in.terms of stimulus duration as well as interpolated interval. The present study is concerned with the question raised by these considerations; namely, do time-error functions ex­ ist for extensive magnitudes similar to those previously found for intensive magnitudes?

To answer this question, the

present study was designed to investigate the successive com­ parison of the size of circles as a function of stimulus dura­ tion and interpolated interval. Further examination of the techniques and procedures used in the studies of the time-error for visual size indicates that the lack of consistency in the results may be partly due to a failure to deal adequately with such factors as aontrol of illumination, adaptation effects, practice effects and modes of presenting stimuli (e.g., projection vs. direct, background size, etc.).

For this reason special considera­

tion was given in the present study to the design of equip­ ment and procedures in order to accomplish a greater measure of control over these factors than has been achieved in earlier studies.

9

II

GJBHBBAL BACKGROUND

Trace Theory The more recent speculations and researches on the timeerror were largely initiated by Kohler’s experiments (23)* He interpreted his results in a manner which revealed the historical continuity of his explanation with Fechner’s, sub­ stituting for the "fading memory image" a "fading" physiol­ ogical trace*

Briefly, he postulated a physiological after­

effect or trace of initial stimulation consisting of a cortieally localized ionic concentration*

It was the autonomous

diffusion of these ions in a return to equilibrium that was responsible for the fading trace*

The comparison itself was

•antained in neither stimulus but corresponded isomorphieally to the "leap" of current created by the potential difference between the excitation process of a present stimulus and the trace of a previous one* Kohler based his theory upon the results of his exper­ iments with auditory Intensities (telephone clicks)*

From

these results he plotted the hypothetical course of the trace as shown below*

F5E

T ime in S e c o n d s

The figure is based on results obtained by the method of constant stimuli in which the second stimulus was judged lover for short intervals (0-3 see.) and Increasingly greater for longer intervals (6*12 sec.)*

The positive time-error

obtained with short Interpolated intervals, he attributed to an initial recruitment that took place for a short period immediately following stimulation. Lauenstein (24) modified Kohler's hypothesis, pointing out that Kohler, in emphasizing the dynamic transition between two cortical states in the same region, was neglecting the possibility of the effect of the ground and of adjacent traces on the course of the trace of the first stimulus.

He main­

tained that the course of the trace could be described not only in such terms as autonomous diffusion or fading but also as active assimilation of potential to groundal levels or to other traces.

To test this hypothesis he Introduced two sound

backgrounds such that one was louder and one softer than the standard*

With the louder ground, he obtained positive time-

errors, with the softer ground negative time-errors.

He ex­

plained these results on the basis of assimilation of the trace "upward” to the louder ground and "downward” to the softer ground.

The former condition yielded positive time-errors

and the latter, negative time-errors.

His theory, like that

of Kohler's, was eouehed in eleetroehemleal terminology ex­ cept that he emphasized "active” assimilation as a determinant of the course of the trace.

Pratt (39) performed an experiment with sounds related to this hypothesis.

In this ease, however, the Interpolated

interval was not filled with “groundal” stimulation but with a sound of brief duration midway between the two stimulus presentations.

His results confirmed Lauenstein's, but he

noted that the time-error was lowered more by a "soft” stim­ ulus than by a "zero” stimulus, i.e* by a blank interval. Pratt concluded that Lauenstein had ”overgeneralized” ; "a phenomenally empty background does not stand in close enough connection with the impressions upon which judgment is being passed to permit of assimilation of these impressions.”

Under

these conditions then, Pratt believes that a negative timeerror will generally be obtained due to some "subsiding after­ effect."

In short, providing that there is nothing in the

background to which it can assimilate, the trace merely "sinks. The present state of our knowledge and technique does not permit us to test the physiological assumptions made in Kohler'8 or Lauenstein's theory.

However, a great deal of

the subsequent experimentation has been occupied with the formulation of "crucial” and exploratory experiments which would reflect the validity and scope of these generalizations. These experiments have been concerned with the time-error and such factors as:

varying magnitudes of the standard stimulus

(19,30,48), absolute and relative judgments (11,40,47), pract­ ice (31,49), intra-serial effects (20,29,48), reflex activity (12,33,34,35), etc.

Although some experimenters (19,20) have

8 questioned whether the time-error varied systematically with interpolated interval, the bulk of the experiments have pro­ vided evidence to indicate the generality of its negative sign, under a variety of circumstances, as well as a tendency for it to vary systematically with Interpolated time interval in the manner indicated. Intensive Stimuli and trace Theory In most of these experiments, stimuli varying in intensity (e.g. loudness, brightness, heaviness) were employed.

The

present study, it has been noted, is concerned with the invest­ igation of the time-error for stimuli which vary mainly in ex­ tensity, specifically, visual areas.

Although many studies

in the past have been concerned with the MmemorialM changes in visual form with time (1,14,36,46,50,51), only a few recent ones (25,87,41,42) have used the successive comparison paradigm for such investigation.

The hypotheses under test in these

studies were predicated mainly on time-error theory.

On this

basis all of them have used an 8-second interpolated time in­ terval, expecting to find, if Kohler's time-error function applied, a negative time-error at this interval.

However, a

comparison of the data reveals a lack of consistency in the results.

With studies using the same kind of judgment (e.g.

lengths of lines), positive and negative time-errors have been obtained and only rarely are these errors significant. In evaluating these results it is of first importance to understand the relationship of the type of stimulus employed

9

to time-error theory.

Kohler’s theory, as a specific appli­

cation of isomorphism, implies that the dimension of stimulus variation has a correlative dimension of variation in the trace. In this context the "fading trace" means a diminishing inten­ sity level.

On the other hand, the correlative dimension of

trace variation for stimuli varying in size (area of circles, length of lines, etc.) might be the changing distribution of excitation in the trace.

On this basis, Kohler’s theory would

be tested by the use of extensive stimuli only if it contained or implied the additional statement that traces also "shrink." The failure to make this point explicit, or even to recognize it, has made for some unclear thinking in discuss­ ions based on time-error experiments with extensive stimuli. These experiments have confined themselves to an eight-second interval largely on the assumption that an interval of this length had been sufficient to yield a negative time-error pre­ viously.

However, the considerations stated above suggest

that even if a time-error function exists for extensive stim­ uli, it need not vary with time in the "traditional" manner. Generalizations about extensive stimuli based on trace theory are premature if they depend, as do the studies above, on a single time interval whose value is determined on what may be an irrelevant basis.

The need is therefore indicated for a

study which will explore the time-error for extensive stimuli at varying time intervals to determine whether or not a timeerror function exists for extensive stimuli.

10

Stimulus Duration Studies of the time-error In general have not considered the theoretical importance of exposure time or stimulus dura­ tion as a parameter of the situation in which stimuli are successively compared.

While this variable has been held con­

stant in the various experiments, in those studies which part­ icularly concern this investigation they have been held con­ stant at different values.

Thus Andrews (2) used one-half

second, Tresselt (41,42) and Crannell (6) one second, and McClelland (27) two seconds.

To be sure the differences cited

above are not very great but the effect of exposure time in this situation is not known; therefore, to what extent it would limit the comparability of experiments using different exposure times is likewise unknown.

Furthermore, other experimenters

working with forms have used different exposure times.

Thus

Irwin and Seidenfeld (18) and Irwin and Rovner (17), who were interested in "bridging the gap* between studies of memory changes in figures and time-error experiments, used a 5-second exposure time.

They worked with more complicated figures than

those described above but used the "conventional" time-error paradigm of successive comparison.

Allport (1), Wallen (46)

and others have used exposures of 10 seconds..

Although these

experiments differ from time-error experiments (they used the method of reproduction), they were concerned nevertheless with the size changes in visual figures. In addition, it may be that stimulus duration as a

11

parameter of the situation has theoretical significance. This possibility can he illustrated by reference to Kohler’s hypothetical trace curve (see p*5).

He postulated an initial

rise in trace level to account for the positive time-error obtained with short interpolated time intervals.

However,

he suggests, as do others (23,49), that a fatigue effect might be operative.

This effect would act to reduce response

to the second stimulus.

The net result of such a process

would be a positive time-error which would be attributed not to a trace change but to a change in the receptor surface re­ sulting from exposure to prior stimulation.

It is reasonable

to believe that the results of pre-exposure, which might condition the response to the second stimulus, would be rela­ ted to both stimulus duration and interpolated interval.

If

this were true, we could expect systematic changes in the timeerror function for different stimulus durations. Practice Effects Kohler (23) found that as the experimental series was repeated on successive days, the time-error became progress­ ively more positive or less negative.

Even with intervals of

two or three days Intervening between sessions he found that this effect was still noticeable.

To explain this curious

phenomenon, he postulated a sedimentation process.

By this

he meant that the traces of previous stimulation accumulated during the sessions so that the course of the trace of a stimulus in any given comparison would be changed by its

1£

oontaot with the residual traces of previous stimuli.

This

effect was noted during a single experimental series as well. In this case, it could not be attributed to fatigue (at least in the ordinary sense) since, as stated, the effects were still noticeable even when rather long periods (three days) intervened between the experimental sessions.

According to

Kohler, this change was not due to repeated comparison but rather to the repeated exposure to individual stimuli which effectively built up the trace level.

Thus, Kohler pointed

out that in his experiment when the experimenters themselves tried to make judgments, they generally made less negative (or more positive) errors than those of the subjects. Another kind of practice or "repetition effect" is the development of an "absolute impression" first observed by Uartln and Muller (£6).

This phenomenon was noted in those

judgments where the subject reported judging a second stimulus (or a first one) apart from the other member of a comparison pair.

Thus, a given stimulus was judged to be "absolutely"

louder or softer, heavier or lighter without any apparent re­ ference to the other member of the comparison pair.

Kohler

believed that the development of an absolute impression could be understood in terms of the practice effect de.soribed above. Thus, with repeated trials, the successive "layering" (sedi­ mentation) of traces provided an Increasingly Important basis for a given judgment.

"Phenomenologically .... /particularly

when the interval between first and second stimuli is long,

13

one has the Impression of 'ascent* or 'descent*, not from the first stimulus but from what has formerly been present," amounting to a sort of "general backward reference" (23), Both of these effects have been noted in other expert** ments (11,15,48,49)*

Needham (11) reports results (in graphic

form only) for the effects of repeated experimentation similar to those obtained by Kohler.

Investigations of the time-error

employing the method of single stimuli (40) also suggest the presence of an "absolute impression." These two practice effects indicate the need for consid­ erable caution in attempting to increase the reliability of experimental determinations both by increasing the number of observations and by using more practiced subjects.

Failure

to observe these precautions may yield changing values for the time-error.

Thus the attempt to improve the reliability

of determinations by using either practiced subjects or in­ creasing the number of observations may not just yield more reliable results, it may produce different results.

Further­

more, it may not be sufficient to equate practice effects within an experiment since different total amounts of practice may introduce differences from one experiment to another.

In

addition, absolute impression introduces a kind of comparison which may not be strictly comparable to the "usual" kind of comparison judgment.

Obviously, a judgment made on this basis

might not reveal the same dependency on time interval that

14

would obteln between the two stimuli involved when they are compared directly. Central Tendency and Related Effects The central tendency of judgment is a well known phenom­ enon first brought into prominence by Leuba and Eollingworth (50).

Briefly, this phrase describes the general tendency of

judgments to be based on an "indifference point" that "gravitates toward the series mean" as the number of judgments increases. The indifference point is that value in a series of magnitudes which does not result in a constant error.

The

central tendency phenomenon refers not only to the tendency for the Indifference point to be determined by the objective series mean but also to the tendency for magnitudes below the Indifference point to be overestimated and for those above the Indifference point to be underestimated.

It may be ex*

pected, acoordlng to the above principle, that magnitudes above this point, will yield a negative time-error and those below this point will yield a positive time-error. These concepts have been utilized in formulating judg­ mental theories of the time-error, sueh as those of Voodrow (48) and Eelson (15), which avoid the use of physiological assumptions.

Kohler has also taken eognlzanee of the oentral

tendency effect and explains it in terms of an averaging effeot of the traee residual so that in the course of time, lower traee values rise and higher traee values drop.

15

It is obvious that the central tendency phenomenon is another kind of repetition or practice effect and may be directly related to the formation of the absolute impress­ ion*

Thus, the absolute impression of a stimulus may be

related to the position of the subject's indifference point. The use of these concepts in explaining how the Indifference point is formed before and during the course of the experi­ mental series may be important in understanding the nature of 2 Individual differences in this area* Hollingworth's experiments (16) on the central tendency include one of special interest to this study because it in­ volved Judgment* of sizes of squares, and also because the treatment of the data is a good illustration of the ambiguity that may result from overlooking repetition or practice effeots* In this study, squares of light gray cardboard were pre­ sented one at a time by an "exposure apparatus" for five sec­ onds each.

The subject, after eaoh five second exposure waited

for five seconds, the eyes resting meanwhile on a dark screen. He then turned to the standard series (30 squares ranging in size consecutively from 2.5 cm. to 50 cm. on a side) and was allowed five seconds in which to select a card corresponding in size to the one previously exposed and to write its number on the record.

The experiment began with the smallest series

of five cards with three trials for each magnitude in chance order.

JH

Following this, the smallest card was dropped and the

An interesting illustration is provided by Tresselt and Volkmann (43), who report differences in constant errors for lifted weights which bear a relationship to the subject's occupation.

16

next higher was added to make up a new series of five cards* The experiment progressed in this way, each series always consisting of five cards. It was expected that the indifference point would pro­ gressively increase as the objective series mean progressively increased.

The constant error for a given stimulus magnitude

would thereby shift in a positive direction as the size of the stimulus, in relation to the series mean, changed from largest to smallest value.

With this in mind we may consider

Hollingworth*s analysis of some of his data reproduced in Table A. Hollingworth notes first "that the phenomenon of the I.P. is concealed .... by a strong positive constant error which comes from a general tendency to overestimation in the judg­ ments of square magnitude."

In order to make more explicit

the central tendency effect he derives another table from the one above.

This is based on the assumption that the obscuring

positive error will be eliminated if the size of the constant errors for each stimulus magnitude are expressed as deviations from the constant error for a given stimulus magnitude when it is the central value in a given series.

This derived table,

Table III in Hollingworth’s report, is reproduced as Table B. In this table Hollingworth notes complete substantiation of the central tendency hypothesis.

In the earlier series the various

magnitudes above are larger than their respective series means and hence the constant error should be negative when compared to the "neutral" point.

Below this neutral point the error is

positive since the same magnitudes are now smaller than their

co

o

te­

o w o> ^

rn

to

• •

02 G OO

o> o» in

in cm. of each card in experiment 10 Observers, 1500 trials (After Hollingworth)

A

o co

in to in in

in 02

H r* r-l «5

• • • •

C2H 02 02

to ^ 02 o CO C- ^

O

O

• • • • •

02

02

r lr lH O l

o )______

1

Interval (sec.) 4

8

Mean

1

-2.8

-0.4

-3.5

-2.2

3

4.6

3.5

3.1

3.7

5

4.4

6.7

-1.5

3.2

Moon

2.1

3.3

—0.6

Tbe time-error for each condition is the mean of nine time-errors.

Table IY Analysis of Variance of Means* by Stimulus Duration and Interpolated Interval

Souree of Variation

D.F.

Sum of Squares

Durations

2

65.67

Intervals

2

Residual Total

F Ratio

F.05

F.01

32.84

7.22

6.94

18.00

23.87

11.94

2.62

4

18.21

4.55

8

107.75

13.47

Mean Square

*These means are the means of the roes and columns inTfeble

III.

53

8 6

4 8

-£

4 -6 Interval in Seconds Vlg. 3.

liean Time-error as a Function of Interpolated Interval For 8aeh Stimulus Duration

laoh point Is the mean of nine observations

54

8i

-4-6 Duration in Seconds Fig. 4* Mean Time-error (E%) as a Function of Stimulus Duration For Each Interpolated Interval Each point is the mean of nine observations.

55

for the 1- and 8- second Intervals are similar in showing a maximum at three seconds duration*

All three curves indicate

a change in time-error from negative to positive when stim­ ulus duration changes from one to three seconds* Practice effects are indicated in figure # which shows the average time-error for the nine sessions of each experi­ mental day*

These values show considerable fluctuations, but

on the average there is a tendency for the time-error to become more positive as the number of sessions increases*

Some of the

irregularities that obscure this trend may be due to the fact that after the fifth experimental day, sessions were no longer held on consecutive days, but were separated by intervening holidays, as noted in figure 5*

The rise in the time-error is

rather marked and regular over the first five days.

This dis­

tinct rise of the curve on the second experimental day may be due to an atypically positive time-error made by one subject* The broken line in figure 5 shows how this portion of the curve is changed when this subject’s value is eliminated from the average*

The possible influence of practice may be further

indicated by a survey of the time-errors in Table II which re­ veals that most time-errors in this study were positive and that the average overall time-error for all but one subject was positive.

It is noted that initially, as in Hollingworth's

study (16), the time-errors were generally more negative.

It

may be also that the preponderance of positive time-errors in the present study is due partly to the influence of the longer

*% 0

-8

-

-6

-8 Day Fig. 5.

Mean Tima-error aa a Function of Practlaa.

laeh point la tha naan of nlna observations. Inter­ vening holidays are lndloated on the abclsaa by an •x*. The broken line shove the function with one atypical value removed.

57

stimulus durations. All of the graphs hint at systematic variation in the time-error.

However, the magnitude of individual differ­

ences apparent from inspection of Table II, compared to the changes introduced by the three variables considered (interpolated interval, stimulus duration and practice), suggests the need for considerable caution in making any interpretation. In Table IV, a variance analysis of the average effects of stimulus duration and interpolated intervals is made. Significance is indicated for variation in the time-error as a function of a stimulus duration but not for variation as a function of interpolated interval. Standard deviations of the judgments for each session were determined by use of Spearman’s summation formula (50). To facilitate the computation of means, the squares of the standard deviations were used as measures of variability. a

clear tendency for mean variability to decrease with in­

creasing practice is noted in Table V and Figure 6.

However,

in Figures 7 and 8 it is difficult to find any consistent trend for changes in variability as a function of stimulus duration or interpolated interval.

Slight evidence for a

trend appears in the increase in variability when 1- and 8second interpolated intervals are compared. for the three curves shown in Figure 7.

This is true

58

Table V Mean Variability of Judgment by Number of Experimental Days

Experimental Day 1 Variability

2.11

2

5

4

2.02

1.48

5

1.71

6 1.60

7 1.66

8 1*26

9 1.27

1.45

Each value in the table is the average of nine squared S.D.*s. The superscripts next to a day number indicate the number of days intervening between that experimental day and the next exper­ imental day.

Table VI Mean Variability of Judgment by Condition

Condition*

Variability

1-1

1-4

1-8

3-1

3-4

3-8

5-1

5-4

5-8

1.47

1.47

1.79

1.44

1.68

1.52

1.46

1.81

1.74

*The first digit in the number for each condition is the stimulus duration in seconds and the second digit is the inter­ polated interval in seconds.

59

2.1-

1.9-

2

1 .61.51.4r

1.2 Day Fig. 6.

Variability (S.D. squared) as a Function of Practise

Each point is the mean of nine observations. Interven­ ing holidays are indicated on the abclssa by an "x".

60

1.80

1.70-

(S.D. )2 1.60

1.50-

1.40 Interval in Seconds Fig. 7.

Variability(S.D. squared) as a Function of Interpolated Interval

Bach point is the mean of nine observations.

1.801.70 (S.D.)2 1.60 1.50 1.40 Duration in Seconds Fig. 8.

Variability(S.D. squared) as a Function of Stimulus Duration

£ach point is the mean of nine observations.

61

Discussion The results suggest that time-error fluctuations are most clearly related to stimulus duration.

Time-errors in

this experiment tend to become more positive with increas­ ing stimulus duration, although the curves of Figure 3 sug­ gest that this may not be a simple monotonlo relationship. It may be that the regular increase (algebraic) in timeerror breaks up after three seoonds because a new factor enters the picture.

The inflections in these ourves would

accordingly represent the operation of two factors which are differentially Important at different durations.

Another

possibility is that the change in time-error depends mainly on one faotor whose influence reaches a maximum after about three seconds.

These data, however, are not regular enough

to allow any detailed discussion of curve shape; this point is discussed further in .Experiment IY in which additional data have been presented. The effect of varying interpolated interval is apparent­ ly not as great as that of stimulus duration for the range of values employed in this study.

Since none of these changes

is significant, the issue is still in doubt.

The data sug*

gest a tendenoy for time-errors to become increasingly nega­ tive, or less positive, iftien interpolated interval increases from four to eight seoonds.

However, these changes are not

sufficiently regular or large enough to support, without further evidenoe, any hypothesis which would predict systematic

62

variation in the time-error with increasing time interval. The possibility remains that the changes are small over the range of intervals studied and that extending the range to include larger intervals will yield more reliable results. Practice effects, although not large, are of interest since they are similar to effects found in studies using in­ tensive stimuli.

There may also be a similarity between

these results and those obtained by Holllngworth (see p.16). The results obtained for precision give evidence of a trend only for the overall decreasing variability with prac­ tice.

Inspection of figure 6 indicates a tendency for pre­

cision to decrease with increasing interpolated interval. Varying the stimulus duration produces no systematic effects. There is little evidence in these data to suggest that the variation of precision provides any foundation for the dis­ tinction in theoretical import previously made between con­ stant error and precision.

It is possible that these results

are unreliable because only 12 judgments per stimulus mag­ nitude were secured.

However, an increase in the number of

judgments per magnitude would have prolonged the sessions and, through praotice and other effects, might have inter­ fered with the reliable determination of the time-error. An increase in the number of judgments is not necessary for adequate determination of the time-error since its value is oomputed from the total number of judgments.

63

Summary and Conclusions The effects of Interpolated interval, stimulus dura** tion and practice on the time-error and variability of judgment were studied in this experiment* The results indicate that stimulus duration has a sig­ nificant effect on the time-error but has no consistent ef­ fect on variability.

In general, time-errors on the average

become less negative (or more positive) when the stimulus duration increases from one to three seconds. There is a tendency for the time-error to decrease vith increasing interval, but this is complicated by a re­ versal in trend from one to four seconds.

It is suggested

that the lack of significance indicated here may be due to the restricted range of intervals used. Practice effects vere observed in the slight tendenoy for time-errors to become less negative and more positive with increasing practice as well as in the fairly steady de­ crease in variability with increasing practice. No systematic trends of any importance could be ident­ ified for variability as a function of stimulus duration and interpolated interval. Experiment II The effeot of interpolated interval on the time-error for outline circles when stimulus duration is constant and only one stimulus magnitude is used.

64

Introduction In Experiment I the results obtained for interpolated intervals vere inconclusive*

It was possible that the prac-

tice and interaction effects provided by nine days of exper­ imental sessions tended to obscure any systematic trend. For this reason, the present experiment was designed to check one of the functions obtained in Experiment I under eomparable, but simplified conditions*

The conditions vere simpli­

fied by (1) holding stimulus duration constant at one second in all sessions; (2) obtaining the necessary data in three sessions; (3) shortening the sessions by requiring a total fo 30 judgments per session; and (4) using only one stimulus magnitude. Since this experiment vas not concerned vith a determin­ ation of preoision, it vas felt that the use of only one stimr* ulus magnitude, rather than five, vould be of interest.

The

use of one magnitude tends to increase the number of judgments effective in determining the time-error, because magnitudes vhieh differ from the standard by an amount too much greater than the time-error vould naturally yield judgments that vould not measure it*

This consideration vould particularly apply

to individuals vhose time-errors and variabilities are small relative to the differences betveen the magnitudes used. The range of stimulus magnitudes may affect time-error determinations in another related fashion.

Thus, if a given

time-error is large relative to the range of magnitudes used,

65

it may introduce a kind of "one sided" cut-tail error or skewed psychometric function.

The larger the time-error

relative to the range of magnitudes, the more skewed will the psychometric function be.

In general, if the range of

magnitudes is not large enougih, positive skewness will be produced by negative time-errors and negative skewness will be produced by positive time-errors.

If the objective mag­

nitudes of the variable stimuli are symmetrical with respect to the standard, the net effect will be to reduce the measured value of the time-error. Ji'inally, using one stimulus magnitude insures that the image will be projected in the same position on the screen since the need for changing slides is eliminated. Statement of the Problem The purpose of this experiment was to subject to further study, using one stimulus magnitude, the time-error for out­ line circles at 1-, 4-, and 8-second intervals at a constant duration of one second. Procedure 1.

One stimulus magnitude, 92 mm. in diameter, was used

for all presentations. used in Experiment I.

This magnitude was the standard value Operation of the equipment was now

fully automatic, since no slides had to be changed.

In all

other respects operation was the same as in experiment l. 2.

Nine subjects, students in an elementary psychology

course, were used.

None of them had ever been a subject in

a psychological experiment before and all were ignorant of

the purpose of the experiment. 5.

Each subject was tested ones each day, and for

three consecutive sessions.

The stimuli were presented

with interpolated intervals of 1, 4 and 8 seconds.

The

stimulus duration for both first and second members of a pair was constant at one second and the rest period was constant at 15 seconds.

All conditions of presentation

were constant within any single session; 30 judgments were made in each session which lasted approximately 15 minutes. 4.

The order of the sessions was arranged so that each

interpolated interval was given an equal number of times each day. Results and Discussion Table VII presents time-errors arranged by interpolated interval and experimental session while Table VIII presents the same data rearranged by subject and interpolated interval, figure 9 shows the average time-error as a function of inter­ polated interval. The salient feature of these data is indicated in Figure 9.

The time-error function shown here is similar in all re­

spects to the comparable function in Experiment I.

Both curves

have a "maximum" at four seconds and the mean time-error for each condition is negative.

It would be of interest to de­

termine the shape of the time-error function for each indiv­ idual, but this is not possible since practice is confounded with conditions in the individual cases and is only equal­ ized in the totals.

67

Table VII Time-error (E?&) by Interpolated Interval and Experimental Session

Day

Interval (sec •) 4 8

1 13.3

—23.3

-20.0

6.7

•3.3

•6.7

■•6.7

•6.7

•23.3

•6.7

10.0

•6.7

•30*0

10.0

•20.0

0.0

13.3

3.3

•10.0

3.3

6.7

•16.7

•16.7

0.0

16.7

•3.3

0.0

Mean

-3.7

•1.9

•7.4

SD

13*9

11.7

10.6

SE

4*9

4.2

3.7

t*

•8

•5

2.0

1

2

3

*t.05 * 2.31

Mean

SD

-7.8

12.0

•3.0

13.8

-2.2

10.3

68

Table VIII Time-error (E%) by Interpolated Interval and Subject

Interval (sec*) Subject

1

4

8

Mean

SD

Bu

-6.7

-6.7

6*7

•2.2

6.2

De

-10.0

10.0

-20.0

•6.7

12.5

G1

-16.7

-23.3

•6.7

-15.6

6.7

Hi

•6.7

3.3

•6.7

-3.3

4.7

Iv

6.7

-16.7

-20.0

-10.0

11.9

Li

16.7

10.0

3.3

10*0

5.4

Hu

0.0

-3.3

0.0

•1.1

1.9

Se

-30.0

-3.3

•23.3

-18.9

11.3

Sh

13.3

13.3

0.0

8.9

6.4

69

H

Interval in Saeonda Tig* 9.

Haan Tima-arror as a Function of Intarpolatad Intaryal Kach point is tha maan of nlna obaarvationa.

0 -• *

I* -♦ -• •0

Fig. 10. Haan Tina-arror(lfc) as a Function of ?raetiaa Kach point Is tha maan of nlna observations.

Non* of the time-errors in this study is significant* ly different from zero, but the comparison made in Table IX between the data obtained in this study and the comparable data obtained in Experiment I is instructive*

In all

cases the time-error is more negative and the standard devi­ ation for each condition is smaller in this study. be noted that both sets of V s terpolated interval.

It will

vary in the same way with in­

In addition, each .t in this study is

considerably larger than the corresponding one in the prev­ ious study* The general increase in these jt values is due both to a decrease in each of the standard deviation obtained for each interval and to an increase in the negativity of all corresponding time-errors*

Both of these facts, and more

particularly the increasingly negative time-errors, would have been predicted on the basis of the discussion made in the introduction to this experiment. Figure 10 confirms the trend for practice effects show­ ing that time-errors become decreasingly negative with in­ creasing practice* These results suggest that the combined effect of the changes made toward simplifying the situation in this exper­ iment had the desired effect, as is indicated by the over-all increase in reliability.

71

Table IX Comparison of Results Obtained in Experiments I and II

______ Experiment I _____________ Eg SB

"T

Interval (sec.)___________________ 8 ----S D---- T -- SD " " t

M

W

I

«»2.8

17.8

.44

-0.4

15.5

.07

-3.5

13.2

.75

II

-3.7

13.9

.75

-1.0

11.7

.45

-7.4

10.6 1.98

72

Summary and Conclusions 1*

The time-error function for 1-, 4- and 8-second

interpolated intervals at the 1-second stimulus duration was determined in this experiment*

While none of the values

was significantly different from zero, the function obtain­ ed had the same shape as the corresponding function in Ex­ periment I. 2*

An increase in reliability for each point was noted

when comparison was made with Experiment I*

It is suggested

that this increase in reliability was due to the net effect of the changes made in the procedure as described above. 3.

In the light of these results, it may be concluded

that the mean time-error is a function of interpolated interval, the shape of the function being approximated by irigure 9. 4.

It is also concluded that subjects, on the average,

tend to make negative time-errors for these three Intervals when stimulus duration is constant at one seoond. 5*

Practice effects support the trend obtained in Ex­

periment I* Experiment III The time-error function for outline circles at 1-second stimulus duration, for four interpolated intervals and with three ettegories of judgment. Introduction The trend noted in Experiments I and II suggested the possibility that an interpolated interval beyond eight seconds

73

would yield a significantly negative time-error*

In

addition, a fourth point was needed in order to provide more information on the shape of the function. In Experiments I and II it was noted that none of the time-errors was significantly different from zero, although the results in Experiment II indicated a trend toward in­ creasing reliability*

This increase was achieved, it was

felt, by the indicated changes in experimental procedure. The consistency in the results for both experiments and the trend toward increasing reliability suggested that further changes might be made in experimental technique in order to improve its sensitivity in the determination of time-errors* In Experiments I and II the use was

not

of an "equal" category

permitted* The decision not to use an equal category

at the outset had been made partly on the basis of the fact that all of the time-error studies of visual extents had used an equal category*

The possibility was considered that in

these studies the use of an "equal" category had obscured the small but persistent errors that ordinarily give rise to the time-error*

It was felt that the subject’s "doubtful" judg­

ments might represent real discriminations which would ordin­ arily be lost in the "equal" categoiy*

It was partly on this

basis that Experiments I and II used only two judgment categ­ ories* In Experiments I and II however,

the impression was form­

ed from various spontaneous comments made by the subjects that

this foroed guessing procedure ought to be reevaluated. This was particularly clear in Experiment II, when the sub­ jects were presented with the same stimulus magnitude re­ peatedly.

They all reported seeing definite differences

part of the time; the fact that they could not say equal when so often they looked equal seemed to be disconcerting to some, and may have been conducive to making inattentive, "routine" responses. Another possible disadvantage of forced guessing was suggested by recent experimental evidence.

This evidence was

contained in a study by Doughty (7) which was concerned with an investigation of the relative accuracy of the methods of successive comparison and average error in the determination of constant errors.

It was maintained that the method of

successive comparison introduced an artifact into the deter­ mination of constant errors.

Mis basic point was that an ob­

jectively symmetrical arrangement of variable stimulus mag­ nitudes around the magnitude of the standard stimulus did not imply effective or "psychological" symmetry for the subject unless the subject's PSE was equal to the standard magnitude. Psychological asymmetry would be reflected in this method by a preponderance of one kind of judgment, depending on the direction of asymmetry.

The preponderance of one kind of

judgment resulting from the subject's constant error would be counterbalanced by the subject's tendency to equalize the number of judgments used in eaoh category.

If this

is true, constant errors will tend to be underestimated and

75

this tendency toward underestimation will increase with increase in the magnitude of the "true" constant error. Since only two categories of Judgment were used in this ex­ periment, the possibility was suggested that such a factor might be operative in Experiments I and II of the present study - particularly in Experiment II in which only one stimulus magnitude was used.

It was thought that if this

factor was present, the use of equal Judgments in providing an "escape" category might minimize its influence.

Therefore,

it was decided to use three categories of Judgments rather than two in the present experiment. Statement of the Problem The purpose of this experiment was to determine with three categories of Judgment, the time-error function for outline circles at 1-, 4-, 8- and 18-second interpolated in­ terval at 1-second stimulus duration. Procedure The procedure was the same as in Experiment II, except in the following respects: 1*

Thirty five Judgments were made in each session.

2*

There were four sessions for each subject, at each

of which an interpolated interval of 1, 4, 8 and 12 seconds was used* The sessions were given once each day to each subject and were attended for four consecutive days by all subjects* 3*

The four intervals were rotated among the four

76

sessions so that each was presented an equal number of times each day.

Twelve students in an elementary psych­

ology course, who knew nothing about the purpose of the experiment, were used as subjects. 4*

The instructions were changed to read as follows:

Please keep your head in the headrest at all times. Look directly ahead of you and move your eyes as little as possible. This is 'VBRY important. This is an experiment to determine how well you can detect differences in size. A short time after I give the ready signal, a circle will appear on the screen. Keep looking at this circle and remember to move your eyes as little as possible. After the circle dis­ appears, there will be a pause, and then a second circle will appear. Tell me as soon as you can after you see the second circle whether it is larger, small­ er or equal to the first circle. Simply say larger, smaller or equal. After this there will be another pause, and then we start over again. In each case you are to tell me whether the second of the pair is larger, smaller or equal to the first. Any questions? Ready? Results and Discussion The time-errors in this experiment were measured by si£. The use of this measure required the equal division of the equal judgments between the two categories.

£$ in this way

provides a measure of the time-error directly comparable to those obtained in Experiments I and II, and to measures of 6 the time-error used in other experiments. Table I shows the time-errors by interpolated interval and experimental session.

In Table XI these data are re­

arranged by subject and interpolated interval.

Eigure 11 is

based on the mean values in Table X and shows the time-error "61 Lauenstein’s familiar DJfc is twice in this manner. See footnote 5, p.49.

when 2$ is computed

77

Table X Time-error (&>) by Interpolated Interval and Sxperimental Day

Day

1

Interval (sec.) 4 8

12

-24.3

-11.4

-17.1

-14.3

-8.6

1.4

5.7

-1.4

-25.7

4.3

-12.9

2.9

2.9

4.3

0.0

-14.3

-4.3

-2.9

0.0

-5.7

1.4

-7.1

-11.4

-7.1

5.7

-12.9

-7.1

-2.9

-14.3

-2.9

-4.3

-18.6

-12.9

1.4

4.3

2.9

0.0

1.4

-21.4

1.4

14.3

2.9

11.4

-5.7

2.9

*8.6

-10.0

-24.3

Mean

-5.7

-2.5

-5.2

-7.3

SD

11.5

5.9

9.5

8.4

S£

3.5

1.8

2.9

2.5

t*

1.6

1.4

1.8

2.9

1

2

3

4

* t .02 = 2.78; t.01= 3.11

Mean

SD

-8.4

10.5

-3.7

5.7

-5.1

7.7

-3.0

11.2

78

Table XI

%) by

Time-error (E

Interpolated Interval and Subject

Interval (sec.) 1

4

8

12

Ca

-24*3

1.4

0.0

-2.9

-6.5

10.4

Ce

5.7

4.3

5.7

1.4

4.3

1.7

Co

-8.6

2.9

0.0

2.9

-0.7

4.7

Di

0.0

-11.4

-7.1

-14.3

-8.2

5.4

Ei

-14.3

-2.9

•17.1

-5.7

-10.0

5.9

He

•12.9

•7.1

-12.9

-24.3

•14.3

6.2

Ki

2.9

-12.9

-21.4

*14.3

-11.4

8.9

Li

14.3

1.4

-4.3

-5.7

1.4

7.9

Lo

1.4

1.4

11.4

-1.4

3.2

4.9

Pe

2.9

4.3

4.3

-7.1

1.8

3.6

So

-25.7

•8.6

•11.4

•18.6

-16.1

6.6

St

•4.3

-2.9

-10.0

2.9

—3.6

4.6

xb ject

Mean -

SD

79

Interval in Seeonda Fig. 11.

llaan Time-error(IJt) aa a Function of Interpolated Interval

laeh point ia the M a n of It obaerrationa•

•10

Fig. It.

Mean TlM~error(IJl) aa a Function of Practice

laeh point la the aaan of If-obaerrationa.

80

as a function of interpolated interval.

Figure IS is

based on the mean daily values in Table XI and shows the praotice curve for the four sessions. Figure 11 confirms and extends the results obtained in Experiments I and II for the time-error function at 1second stimulus duration.

The shape is the same, with the

"maximum** point still at four seconds. ourve are negative.

All points on the

The time-error for the 12-second in­

terpolated interval continues the trend in the same direct­ ion.

This value is significantly different from zero.

A

comparison of the _t values shown in Table XII for all three experiments gives convincing evidence of the trend.

In Ex­

periment III, the jfc values increase with increasing inter­ polated interval after four seconds until significance is achieved at 12 seconds.

This suggests that the time-error

may become increasingly negative with increasing interpol­ ated interval while other factors remain relatively const­ ant.

Thus, significance is achieved when the magnitude of

the effects tending to produce the negative time-error is great enough. It is noted that two of the three .t's in Experiment III are greater than those obtained in Experiments I and II; this fact may provide further indication that the changes in procedure in this experiment were effective in improving experimental precision. That the use of an equal category may have had the

81

Table XII Comparison of Results Obtained In Experiments I, II and III

Experiment

______ 1 BE

Interval_(sec.)__________ 8' BE " S P " t K SB

'

t

I

-2.8

17.8

.44

-0.4

15.5

.07

-3.5

13.2

.75

II

-3.7

13.9

.75

-1.9

11.7

.45

-7.4

10.6 1.98

III

-5.7

11.5 1.63

-2.5

5.9 1.39

-5.2

9.5 1.79

82

anticipated effect is indicated by the fact that the time-errors in this experiment for two out of three comparisons are more negative than those obtained in Experi­ ment II.

It should be noted further that the E$ values,

as calculated, were based on an equal division of the equal Judgments.

This measure provides the most conservative

(least negative) estimate of the time-error.

It may be

that a proportionate division of the equal Judgments be­ tween the two categories would provide time-error values more comparable to those obtained in Experiment II.

TS$>

value8 determined from such a proportionate division of the equal Judgments are shown in Table XIII.

It is apparent

that there is a considerable difference between the values in this Table and those obtained in Experiment II.

It may

be noted also that neither method of determining E$ changes the shape of the curve.

The relationships among time-errors

are about the same, except that the function obtained when E#

determined on a proportionate basis resembles the

function obtained in Experiment II even more closely than does the function shown in Figure 11. It should be noted also that each condition was deter­ mined over four days rather than three days as in Experiment II.

The additional day as indicated in the disoussion below

may have further minimized the difference between the timeerrors obtained in the two experiments. .

The results indicate then that the use of forced Judgments

83

Table XIII Time-error (E£) by Interpolated Interval as Computed by Proportional Division of Equal Judgments

_____________ Interval_(sec.)_________________ ~ EJb

1 -10.0

4 ' -2.6

SD

28.0

13.4

22.9

13.7

SE

8.4

4.0

6.9

4.1

t*

1.2

.7

1.5

3.4

*t.05 = 2.20; t.01= 3.11

8 -10.6

12 -14.0

in Experiment II may hare been a factor in minimizing the measured value of the time-errors obtained* Figure 12 provides additional evidence to shoe that the time-error decreases in negativity with Increase in prac­ tice*

It is Interesting to note the similarities in the prac­

tice trends of Experiment I and III by comparing the timeerrors for the first four days in Figure 5 with the results plotted in Figure 12* Summary and Conclusions 1*

It was demonstrated that the time-error becomees in­

creasingly negative for intervals of from 4 to 12 seconds when the stimulus duration is constant at one second* 2*

It was indicated also that the time-error changes

from 1 to 4 seconds, becoming slightly less negative at four seconds* 3*

There is a tendency for the time-error to become

less negative with practice. 4*

These results confirmed in almost all respects the

eomparable results of Experiments I and II* 5*

Adding an equal category seems to yield time-errors

which are more negative than those obtained in Experiment II in which no equal category was used. Experiment IV The time-error as a function of interpolated interval stimulus duration, and practice for "filled-in" circles*

85

Introduction In this experiment, Interest was focused on the effect of changing the type of stimulus*

In the first three exper­

iments, outline circles had been used as the stimuli.

There

was reason to believe, however, that the use of filled-in circles might yield more clear cut results.

It was felt that

this stimulus, because it covered a greater area, might mag­ nify the effects of stimulus duration (see p.

).

In investi­

gations of figural after-effects (22) which depended on the same parameters explored in this study, namely, stimulus duration and interpolated interval, a definite difference was found in these two types of stimuli.

This suggested the use

of this stimulus because it might provide some clue to a re­ lationship between figural after-effects ana the time-error. It may also be noted that line thickness is eliminated in this type of stimulus.

This point was relt to be another

consideration justifying its use, since it was a change to­ ward greater simplification. Statement of the Problem ▲long with ihe changes suggested by the results of ISxperiment I, II, and III» as well as the considerations stated above, it was decided to use the design of jsxperiment I and de­ termine, in the same experimental situation, the effects of stimulus duration, interpolated interval and practice on the time-error for filled-in circles.

86

Procedure The procedure was the same as in Experiment ill, ex­ cept for the following modifications: 1,

A filled-in circle of uniformly dense black, 92.0

mm. in diameter, was the stimulus. 2.

There were nine experimental conditions corres­

ponding to the nine combinations of the following: (a) (b)

Stimulus duration - 1,5, and 5 seconds. Interpolated interval - 1,4, and 8 seconds.

These conditions were rotated among the nine subjects over a nine day period according to the scheme described in Ex­ periment I.

The stimulus durations above are for the first

stimulus in each pair.

The duration of the second stimulus

was constant at one second. 5.

Nine naive subjects, elementary psychology students,

were used. Results and Discussion In general, the results are similar to those obtained in Experiment I.

A major difference is that the time-errors

for this stimulus are preponderantly negative.

Apart from

this difference, a comparison of the functions in Figure 13 with those obtained in Experiment I (Figure 4) discloses many similarities.

In both experiments, an inflection point

is noted at three seconds.

In both experiments, the time-error

generally becomes less negative (or more positive) from one to three seconds.

It was noted in Experiment I that the time-

errors at five seconds duration were all less negative or

87

-I

10IS Duration in Saeonds Fig. 13.

Maan Time-error aa a Funetlon of Stimulus Duration For Bach Intarpolatad Interval

Bach point la tha maan of nlna observations.

88

Table XIV Time-error (E?fc) by Experimental Condition and Day

Condition* Day

1-1

1-4

1

•8.6

•4.3 -30.0

2

1.4

•2.9

•17.1 -14.3

4

7.1 -18.6

•7.1

1.4

-7.1 -15.7

-20.0

•2.9

-5.7

6

0.0

-5.7

4.3

7

-10.0

8

•20.0

3-4

10.0

3-8

5-1

5-4

5—8

Mean

SD

-4.3 -14.3

-8.4

10.3

7.1 -11.4 -24.3 -14.3 *22.9

•7.6

11.4

2.9 -12.9 -20.0

—8.6

7.9 7.2

8.6 -11.4

8.6 -10.0

5

9

3-1

1.4 -12.9

0.0 -10.0

-8.6 -14.3

-7.1 -14.3

. in «

3

1-8

-9.4

2.9 -20.0

17.1 -20.0

-1.4

-4.4

12.8

-5.7

-2.7

9.6

0.0 •10.0

-1.4 -21.4

-4.3 -27.1

5.7

5.7

-4.3

8.6

0.0 -10.0

-4.0

10.3

1.4 -15.7

-8*6

17.1

0.0

18.6

1.4 -22.9

-3.2

14.1

1.4 -18.6

-8.6

10.0

-1.4

-4.3

-2.1

10.6

15.7 •15.7

2.9

15.7

Mean

-5.7

•7.5

-8.5

-.8

-1.4

-7.9

-3.5

-4.1 -10.8

SD

11.9

6.5

12.8

8.3

10.7

7.0

16.2

10.2

7.4

SE

4.2

2.3

4.5

2.9

3.8

2.5

5.7

3.6

2.6

t**

1.4

3.3

1.9

•3

•4

3.2

.6

1.1

4.2

*The first digit in the number for each condition is the stimulus duration in seconds and the second digit is the interpolated interval in seconds. ♦♦t.0 5 = 2.31* t.02=2.90* t.01* 3.36

89

Table XV Time-error (E%) by Subject end Experimental Condition

Condition*

Go Ha

3-8

5-1

5-4

5-8

2.9

-4.3

18.6

15.7

-1.4

5.1

9.2

0.0

7.1

0.0

10.0

-4.3

-5.7

-2.5

7.3

-8.6

5.7

1.4 -21.4 -14.3 -10.0

-5.1

8.5

5.7 -18.6 -12.9 -24.3 -20.0 *22.9 -15.7

11.0

1-4

1-8

15.7

-2.9

-7.1

8.6

-10.0 -14.3

-5.7 2.9

Ho

1.4

Mic

0.0 -18.6 -30.0

-2.9

-8.6

-4.3

Ow

-17.1

1.4

Po

7.1

-4.3

Mil

3-1

1-1

8.6

Sh

-20.0 -15.7 -15.7

Si

■*20.0

SD

0.0

-5.7

1.3

10.4

-8.6

-7.1

0.0 -14.3

•5.4

7.4

10.0 -10.0 -11.4

8.6

-4.3

-1.1

7.7

-1.4 -12.9 -14.3 -10.0 -10.8

6.6

1.4

17.1 -14.3

Mean

17.1

1.4

4.3 -10.0 -7.1

3—4

2.9

-8.6

-5.7 -27.1 -15.7 -11.4

l w o • o

Subject

-eo«o

1.4

#1.4 -22.9 -16.0

*The first digit in the number for eaeh condition is the stimulus duration in seconds and the second digit is the interpolated interval in seoonds.

7.9

more positive than at one second duration.

In this ex­

periment, this is true also, except for the function at eight seconds interpolated interval.

It should be empha­

sized, however, that an inflection point at three seconds appears to be the rule in both experiments since it was ob­ tained in a total of five out of six functions. The time-error functions for interpolated interval at the various durations present a more regular picture in Fig­ ure 14 than do the corresponding curves in Experiment I (Figure 3).

There is general agreement in both experiments

for the 4- and the 8-second intervals.

In the six functions

of both experiments the time-error generally becomes more negative or less positive with increasing interpolated in­ terval.

In this experiment, no "maximum" point is found at

four seoonds as in Experiment I.

For the three functions

of Figure 14, the picture is one of considerable agreement; they all indicate increasingly negative time-errors with in­ creasing length of interpolated interval. The variance analysis in Table XVII of the mean values shown in Table XVI indicates that the interval variance is significant but that the duration variance is not.

In view

of the regularity of the duration trends, further analysis is suggested.

Inspection of Figure 13 discloses that the

duration function at 8-second interpolated interval while similar in general shape does not follow the same course as the other two curves.

This suggests some kind of interaction

91

I* -6

10

*

It Interval 1b teoonda

Fig. 14.

Mean Time-error(ljt) aa a Function of Interpolated Interval for tach Stimulus Duration Sach point Is the mean of nine observations.

9£ Table XVI Mean Time-error (EjG) by Stimulus Duration and Interpolated Interval

Duration (sec.)

Interval (seo.) a

l

o

Mean

1

-5.7

-7.5

-8.5

cv? . c*1

3

-0.8

-1.4

-7.9

-3.4

5

-3.5

-4.1

-10.8

—6.1

Mean

-3.3

-4.3

-9.1 ■ — ---1—

—

—

—

— ——

—

— f

The time-error for each condition is the mean of nine time-errors*

Table XVII Analysis of Variance of Means* by Stimulus Duration and Interpolated Interval

Source Of Variation

D.7.

Sum of Squares

Durations

£

Intervals

Mean Square

7 Ratio

7.05

7.01

23.28

11.64

3.72

6.94

18.00

2

55.65

28.33

9.06

Residual

4

12.51

3.13

Total

8

92.44

11.56

*These means are the means of the rows and columns in Table XVI.

of interval with duration not present with the shorter intervals*

The net effect in this case seems to be to

increase the interaction variance disaproportionately and reduce the variance for the duration averages*

This

conclusion is confirmed by the results of the variance analysis summarized in Table XVIII.

These results demon­

strate that with omission of the 8-second duration func­ tion, the variation due to durations is significant.

On

the other hand, it is noted that the interpolated inter­ val is now not significant.

The reason for this result

is disclosed on examination of the curves in Figure 14. The indicated trend with interpolated interval is slight from one to four seconds and this variation is all that is reflected in the variance analysis in Table XVI.

Ap­

parently the uniform but slight trend from 1 to 4 seconds is not large enough to yield significance with this test. Table XV indicates the significance of the trends from another point of view.

The V s in this table are arranged

by stimulus duration and interpolated interval, and were obtained for the difference between each time-error and a hypothetical one of zero.

In general, we note the same

trend as in the previous experiments.

The trend toward

significance increases with increasing interpolated inter­ val.

The one exception is found at 1-second duration and

8-second interval.

This value is smaller than the 4-seoond

Table XVIII Analysis of Variance of Means* by Stimulus Duration and Interpolated Interval

Source of Variation

D.F.

Sum of Squares

Durations

2

Intervals

Mean Square

F Ratio

F.05

F.01

30.25

15.13

63.04

19.00

99.01

1

1.50

1.50

6.25

18.51

98.49

Residual

2

0.48

.24

Total

5

32.23

6.45

*The means for the three durations at the 8»second interval are not included in this analysis* In all other respects this table provides the same kind of analysis as in Table XVII•

95

value, but it is still larger than the 1-second value. this oase the

t value

In

at four seconds is significant at the

•02 level of significance*

Inspecting the table in terms

of varying duration, the maximum point attained at the 3second duration is indicated by the fact that all the t^’s are smallest at the 3-second duration.

The trend toward in­

creasing significance, then, takes place on either side of the 3*seoond duration in all three functions.

The general

point of these observations is to reaffirm the conclusion that time-errors vary systematically with both duration and interval. The practice curve in Figure 15 indicates the same kind of trend as before, namely, a general tendency toward a de­ crease in negativity with increasing practice. Summary and Conclusions 1*

A negative time-error was obtained on the average

for all nine experimental sessions and also when the data were rearranged for all nine conditions. 2.

The time-error varies systematically with stimulus

duration, becoming decreasingly negative from 1 to 3 seconds and increasingly negative from 3 to 5 seoonds. 3.

The time-error becomes increasingly negative with

increasing interpolated interval for all stimulus durations. 4.

Practioe effects are shown in this experiment similar

to those previously found.

In general, the time-error be­

comes decreasingly negative with increasing practice.

96

-

8-

-4-

6-

-0

-

-10 Day Pig. 15.

Mean Time-error as a Function of Practice

£ach point le the mean of nine observations. Inter­ vening holidays are indicated on the abclssa as an ”x?

97

Experiment Y The time-error for filled-in circles as a function of four interpolated intervals, with stimulus duration constant. Introduction It was desired in Experiment V to determine the manner in which the interpolated interval function differed for the two kinds of stimuli when other conditions were the same. Therefore this experiment was identical with Experiment III

exeept for the fact that here a filled-in circle was used as the stimulus.

In addition, a check could be obtained on

one of the functions obtained in Experiment IV arid the trend further explored beyond the range of interpolated intervals used in Experiment IV. Statement of the Problem To determine the relationship between time-error and in­ terpolated interval for 1-, 4-, 8- and 12-second interpolated intervals at one second stimulus duration. Procedure 1.

The stimulus used in this experiment was the same

as that used in Experiment IV. 2.

Only eight subjects, students in an elementary psych­

ology course, were used in this experiment; all of them were ignorant of the experimental purpose. In all other respects, the conditions and procedure were identical with those in Experiment III.

98

Results Table XIX summarizes the results by interpolated interval and session*

Table XX rearranges these results by

subject and experimental session*

In figure 16,the time*

error is plotted as a function of interpolated interval. Although the trend is generally negative, the timeerror at four seconds represents a slight deviation from the trend.

That this is not serious is indicated when the

comparable curve at 1-second duration in Experiment IV (Figure 14) is considered.

This curve is different from

the other two curves in Experiment IV in that the decrease in time-error from four to eight seconds is relatively slight.

In the light of this evidence it may be that the

inversion in Figure 16 does not represent a marked devi­ ation from trend. The time-error for the 12-second interval as in Exper­ iment III is very significant, thus confirming the overall trend.

The comparison of these two curves indicates that

the lack of a maximum point at the 4-second interpolated in­ terval may constitute a reel difference in the functions for the two kinds of stimuli.

Further comparison (Table XXI)

discloses that negative time-errors for the filled-in circle as compared to those for the outline circle are generally more negative.

Inspection of Table XXI discloses a general

trend for the £ values of both functions to increase with increasing Interpolated interval.

The comparison of

t values

99

Table XIX Time-error (E%) by Interpolated Interval and Experimental Day

Interval (sec.) Day

1

4

8

12

-4.3

-15.7

-2.1

-2.9

4.3

-18.6

-5.7

-14.3

-4.3

-2.9

-20.0

-5.7

•*2*9

-1.4

1.4

-12.9

-15.7

0.0

-5.7

-11.4

10*0

•21.4

4.3

-14.3

4*3

-10.0

-1.4

-11.4

-11.4

2.9

-8.6

-10.0

-2.5

-8.4

-4.7

-10.4

SD

8.0

8.7

7.0

3.7

SE

3.0

3.3

2.6

1.4

t*

•8

2.6

1.8

7.4

1

2

3

4

Mean

*t.05*2.37j t.01~3.5

Mean

SD

-7.4

7.4

-6.1

6.5

-6.8

10.2

— 5.7

6.2

1 00

Table XX Time-error (Efr) by Subject and Interpolated Interval

Interval (sec*) 4 5

Subject

1

Co

-4.3

0*0

-1*4

-2.9

-2.2

1.5

Ka

-15.7

-2.9

-2.1

-11.4

-8.0

5.8

flu

4.3

-15.7

-5.7

-5.7

-5.7

7.1

Sea

-11.4

-18.6

4.3

-12.9

-9.7

8.4

Seh

10.0

-1.4

-5.7

**10.0

-1.8

7.4

Sp

—4.3

—10.0

-20.0

-11.4

—11.4

5.7

St

4.3

2.9

1.4

-14.3

-1.4

7.5

We

-2.9

-8.6

-14.3

-11.8

6.9

-21.4

Is_

Mean_______ SD

101

Table XXI Comparison of Results for Experiments III and V

Interval (sec.)

Experiment III* y

**

S%

4 ... t

1 t

8

12 **

t

-5.7

1.7

-2.5

1.4

-5.2

1.8

—7.3

2.9

—2.5

.8

-8.4

2.6

-4.7

1.8

-10.4

7.4

*t.05*2.20; t.01» 3.11 **t.05*2.37; t.01*3.50

102

-4* E

%

-6-

-

-

8-

10-

-12 Interval in Seconds Fig. 16.

Mean Time-error as a Function of Interpolated Interval

isach point is the mean of eight observations.

B*

-4

-8 Day Fig. 17.

Mean Time-error(E%) as a Function of Practice

Each point is the mean of eight observations.

for the 1- and 4-seoond intervals in both curves supports the point made above; the trend is different for both fig­ ures in the neighborhood of four seconds.

For both curves

however, the trend is clearly one of increasing reliability as the interval increases from 4 to 12 seconds.

Comparison

of results for the 12-second interval further indicates that the time-error for the filled-in circle is reliably differ­ ent from zero at a much higher level of significance then the outline cirole.

This may be attributed not only to the

fact that the time-error for the filled-in circle is more negative at this interval but also to the fact that varia­ tion due to individual differences is less.

Evidence for

this point is provided by comparison of the standard errors of the mean at 12 seconds for the two stimuli.

The stand­

ard error for filled-in circles (1.4) is less than that for outline circles (2.5) despite the fact that the number of degrees of freedom used in determining each standard error is, respectively, 7 and 11. Summary and Conclusions 1*

The results obtained in this experiment confirm

the general finding, aamely, that at 1-second stimulus dura­ tion the time-error becomes increasingly negative with in­ creasing interpolated interval* 2*

Time-errors obtained with filled-in circles tend

to be more negative than those obtained with outline circles.

3.

The results of this experiment, combined with

those of Experiment IV suggest that the interpolated in­ terval function for the solid circles does not have a max­ imum at four seconds as do the outline circles. 4.

The effect of practice is similar to the effects

observed as in previous experiments, namely, a general de­ crease in negativity with an increasing amount of practice.

105

YI

DISCUSSION

The combined results in the present study support the conclusion that the time-error for circles varies system­ atically with stimulus duration and interpolated interval. Despite the large variability due to individual differences, systematic variation in the time-error is observed under the various conditions employed.

This is indicated in Table XXII

which summarizes the comparable results for all five experi­ ments.

The table shows that the mean time-error is negative

for all conditions and indicates also a general trend for the time-error to become increasingly negative with increasing length of interpolated interval.

As noted previously, the trend

may be complicated by a reversal up to four seconds in the case of outline circles.

Apart from the results in this table, the

results of Experiment's I and IV indicate that systematic vari­ ation exists as a function of stimulus duration and that the shapes of the functions are similar for both outline and filledin circles. It was also demonstrated that changing the experimental situation in the direction of increasing simplicity reduced variability among individuals and increased the reliability of the results.

In addition, the results indicate that when in­

terpolated interval was increased sufficiently (to 12 seconds) obscuring individual differences tended to diminish and a negative time-error was obtained for each individual almost without exception.

This is true for the time-error function

1 06

Table

nil

Uean Time-error (£%) by Interpolated Interval With Stimulus Duration Constant at One Second (Experiments 1 - 7 )

Experiment

N______ 1

IntervalEsee.) 4 8

12

I

9

-2.8

-0.4

-3.5

II

9

-3.7

-1.9

-7.4

Ill

12

-5.7

-2.5

-5.2

-7.3

IV

9

-5.7

-7.5

-8.5

mm

V

8

-2.5

-8*4

-4.7

-10.0

*0 7

when stimulus duration is constant, at one second.

Further

study is required for interpolated interval functions at other stimulus durations. Theoretical Interpretations The major objective of the present study was to deter* mine whether or not time-error functions existed for size com­ parisons.

One reason for such determination was to check on

the nature of the time-error function for extensive stimuli. The theoretical point of such determination centered in part around Kfihler’s trace theory.

It was noted (pp. 8f) that no

specific predictions within the meaning of this theory could be made for extensive stimuli such as those used in the present study.

However, the consideration of trace theory from a broad­

er point of view suggested that the present study would be of interest since the course of changes in the distribution of trace "potential" could be investigated with the use of the time-error as a "probe." Consistent with this point of view, the attempt to explain these results is based on the general hypothesis that the after­ effects of stimulation are embodied in a trace having a central locus and which, following Kohler, results from electrochemical change.

The comparison judgment, as explained previously, is

also considered to arise from a gradient of potential created by the trace of previous stimulation and a present process. In this case the spatial aspects of the gradient are important. Strict spatial isomorphism, however, is not assumed between

108

perceptions and traces but general topological relationships are assumed.

Furthermore, following the theory of figural

after-effects (discussed below), the central representation of perceived size or distance is not strictly spatial in a physical sense but depends on functional properties of the corresponding cortical processes.

For example, in the theory

of figural after-effects any boundary is assumed to set up figure currents (electrical) in the cortex.

The distance between any

two boundaries is assumed to correspond to the strength of figure currents between the two boundaries in the intervening medium; in general, the weaker the intervening currents the greater will be the perceived distance between the two bound­ aries. Specifically, in explaining these results, a three-factor theory is offered.

It is believed that this theory will pro­

vide a convenient set of working hypotheses in terms of which future research in this area may be structured. this theory may be defined as: (Faotor Y), (2)

(1)

The factors in

a vector rield factor

an adaptation factor (Factor A), and (3)

a

figural after-effect factor (Factor F ) . In the following formulation of this theory it will be assumed that Factors Y and F are central and Factor A is peripheral in locus. Faotor Y describes the fate of the trace in terms of the vector field hypothesis (pp. 31f). of this theory to the trace,

It is a special application

and postulates

that trace shrinkage

1 09

constitutes a change in the direction of cohesive equilib­ rium.

This shrinkage| other things equal, increases with

increasing time after stimulation, although the curve describ­ ing this shrinkage is probably not linear. i'actor

A refers

to the after-effect of previous stimulat­

ion, not in terms of a cortical trace, but to the changed char­ acter or the sensory surface rollowing stimulation.

In brief,

it is hypothesized that there is a decrement in response of the sensory surface to the second stimulus because it is adapt­ ed (possibly fatigued) by pre-exposure to the rirst one.

This

a.

decrement in response is assumed to result in diminution of 7 perceived size for the second figure. The effects of factor A will increase with increasing stimulus duration and decrease vith increasing interpolated interval. Factor F is based on relatively recent research involv­ ing figural after-effects.

As in the present study, the para­

meters which govern the magnitude of rigural after-effects are stimulus duration and interpolated interval (13). According to the theory of figural after-effects, any contour in the visual field sets up "figure currents."

These

currents "satiate" the conducting medium and thus counter 7. Of interest in this connection is the phenomenon of gamma movement. The basis for this phenomenon has been attributed by some to cortically localized expanding and contracting excitations. This theory has oeen noted in connection with time-error hypotheses by McClelland (27) and provides a possible link between intensity and distribution of excitation, since it is well known (8) that the magnitudes of expansion and contraction in gamma movement vary with object intensity or degree of contrast between figure and ground. Gamma movement phenomenons apply equally to light objects on a dark field or the reverse.

110

processes are generated which tend to increase resistance to the further flow of figure currents.

The counter-processes

are related by Kohler (21) to the phenomena of electrical polarization.

After exposure to a figure the corresponding

area on the cortex is satiated.

The strength of this satia­

tion depends upon exposure time and time after inspection of a given figure.

Since the cortical medium following exposure

is satiated, it will resist the flow of figure-currents set up by a new figure.

On this basis it is asserted that figure, or

part of figures, will recede from satiated areas.

If a circle

then be exposed inside the area satiated by a larger circle it will shrink, since that is- the only way it can recede from the area which has been most intensely satiated.

This area corres­

ponds approximately to the contour of the previous figure.

On

the other hand, for the same reason, the circle will expand when its contour falls uniformly outside an area that has been maximally "satiated."

It is important to note that if the

contour of the second figure coincides with the contour of the first figure no displacement effects may occur.

There is in

this case usually an equilibrium position in which the second figure can neither shrink nor expand away from a satiated zone since it is surrounded equally by it on both sides of its contour. Although exposure times for the inspection figure are usually for periods of 40 seconds and more, figural after­ effects have been noted when exposure times have been as short as five seconds (13,21).

In the present study this factor could

Ill

result in either positive, zero-or negative time-errors, depend­ ing on the relationship of the second stimulus to the satiated area. In brief, three factors are postulated to account for the variation in time-error with stimulus duration and interpolated interval: 1*

A vector-fleld factor (Factor V) which will generally

result in negative time-errors. 2.

An adaptation factor (Factor A) which will result in

positive time-errors. 3*

A figural after-effect (Factor F) which may result

in either positive or negative time-errors depending on whether the second stimulus falls outside or inside the area of maximal satiation. The integrated application of these three factors may be illustrated first by reference to Experiment IV. ment IV, an overall negative time-error is noted.

In Experi­ In addition,

there is a general tendency for the time-error to become in­ creasingly negative with increasing interpolated interval (Figure 14).

This situation would be predicted by Factor V.

On the other hand in Figure 13 it is noted that the time-error becomes decreasingly negative when stimulus duration increases from one to three seconds. by Factor A.

This situation would be predicted

However, the fact remains that when stimulus

duration increases from three to five seconds, all three ourves reverse in direction.

This fact is inconsistent with predict-

Ilk ions made only on the basis of Faotor (A) but could be predicted by simultaneous operation of the three factors. Let us reconsider Figure 13 in terms of the three fact­ ors simultaneously. are negative.

At one second duration all three points

This faot may be attributed to Factor V.

In

addition, it is noted that the points are arranged in such order that as the interval increases, the time-error becomes increasingly negative.

This is true also for the points at

both three and five seconds stimulus duration.

This aspect

of the situation is assumed to be due to both increase in effect of Factor V and decrease in effect of Factor A. The uniform increase in negativity from three to five seconds is attributed to the increasing influence of Factor F. Assuming that the locus of maximum satiation shrinks with the trace as a result of Faotor V, then the operation of Factor F will generally be such as to produce a negative error.

Accord­

ingly, the inflection at three seconds duration in Figure 13 may be considered a result of Factor F becoming important en­ ough to offset the influence of Factor A. Inspection of Figure 14 extends this description further. The curve for the 5-second duration is generally below the 3-second curve due to the action of Factor F cancelling the action of Factor A. A comparison of results obtained with outline and filledin circles in terms of this theory should be made with caution because of the difference in conditions between Experiments I

113

and IV.

However, the results obtained in Experiment I are

in general similar to those obtained in Experiment IV and lend themselves to an explanation similar to that stated above• It has been reported that figural after-effects differ somewhat for the two types of figure (21).

It may be that

the greater degree of negativity for time-errors obtained with filled-in circles is due in part to the mere intense figural after-effects obtained with this kind of figure. On the basis of these three factors it may be possible to make general predictions about trends for the time-error function at varying values of stimulus duration and interpolated interval.

As a check on such predictions, there is a need for

further studies which would find interpolated and extrapolated points for the functions obtained in this study.

The use of

other types of figures will also be of interest.

It has been

noted, for example, that figural after-effects are greater with squares than In this

with circles. connection it is interesting to reconsider Tress-

elt*s study in which square outline figures were used.

It was

noted (po23)

that the results were difficult to explain in

terms of the

hypotheses offered.

However, a reinterpretation

of these results in terms of figural after-effects is suggestive. Thus the significantly positive error obtained with the large square could be explained in terms of the proximity of taehistoscope contours.

Since these contours were present all the

114 time, while the squares were present intermittently for only one second exposures, relatively large satiation effects in the neighborhood of the tachistoscope contours might have accumulated.

The positive time-error could be attributed to

the action of figural after-effects on the second stimulus, causing it to shrink since it was located inside a satiated area.

These effects of course would act on the first stimulus

as well if subjects were required to fixete the tachistoscope*s contours during the rest periods between pairs; but judging from the description of the procedure in this experiment such was not the case. The theory outlined above is concerned with the explana­ tion of time-error functions for extensive stimuli.

But in

certain respects it may be applicable to results obtained with intensive stimuli.

This possibility is suggested by the re­

sults of Vada's study (see footnote 1, p.3).

The purpose of

this study was to determine the relationship between the timeerror and stimulus duration for auditory intensities.

The

stimulus durations used varied from .25 to 2.5 seconds with 8 interpolated interval constant at 1.5 seconds. He found under these conditions that positive time-errors decreased and nega­ tive time-error decreased with increasing length of stimulus duration.

These results agree with those found in the present

study for the appropriate range of durations (one to three seoonds)• FI In Wada's study the stimulus durations of both stimuli in a pair were varied together.

115

Explanation of those results may be made In terms of Factors A and F.

It is not difficult to see in terms of pre­

vious description (p.109) that increasing strength of Factor A could result in more positive errors for both intensive and extensive stimuli.

In the case of Factor F, its applicability

to intensive stimuli may be noted in other observations of KShler and Wallach (22) in connection with the study of figural after-effects.

According to their observations not only did

figures tend to recede from satiated areas but they also appear9 ed "paler." This effect was consistent with their notion that the intensity of figure processes was weakened by "satiation." The central locus of the phenomenon was indicated by the fact that the same effeots were observed when the second stimulus stimulated the corresponding area of the non-satiated eye. According to this discussion, increasing length of stim­ ulus duration will produce more positive time-errors due to the simultaneous operation of Factors A and F.

Further com­

parison is not possible since Wade's durations do not cover the range used in the present study.

However, on the basis of the

above argument no reversal in trend, as was found in the present study, ought to be found for intensive stimuli as stimulus dura­ tion is increased beyond 2.5 seoonds. Although this 3-factor theory goes considerably beyond the 97 ttfhe troublesome question of black as an intensity is implicit here, but ampy modern investigators (4) agree in considering the possibility of a medium gray as a "neutral" point for brightness intensity changes. It is possible that the intensive changes pro­ duced by figural after-effects may be thought of in terms of a re­ duction in "contrast" between figure and ground.

1 16

data, Its worth can he assessed by future experiments design­ ed specifically to test Its predictions*

With this in mind

the following predictions are made: 1.

Time-errors for circles will increase in negativity

when stimulus duration is increased from 5 to 10 seconds. The increase will be greater for an interpolated interval of eight seconds as compared to an interval of one second.

This

prediction is based on the assumption that Factor F will in­ crease in strength and that its operation in conjunction with Factor V will yield increasingly negative time-errors (p.iiz). 2.

If two interpolated interval functions be determined

such that stimulus durations are held constant at one-half second in one and 10 seconds in the other, the following re­ sults ought to be obtained: (a)

Negative time-errors at all points in each funct­

ion (p. 108), (b)

The time-error for the 10-second function will

increase in negativity at a faster rate than will the timeerror for the one-half second function (p.M2 ). 5.

Time-errors for squares ought to be more negative than

those for circles.

The differences will probably be more reliable

at the longer stimulus durations (p.io). 4.

The time-error for the broken outline circle will in­

crease in negativity at a faster rate than will the time-error for the closed outline circle (p.3>).

117

VII

SUMMARY a n d c o n c l u s i o n s

Summary The present study consisted of fire experiments.

The

first experiment (Experiment I), was designed to investigate simultaneously the influence of practice, stimulus duration and interpolated interval on the time-error and precision of size judgments.

To accomplish this purpose, a factorial design

was employed in which nine subjects were tested over a period of nine days. The results obtained suggested that the time-error was in­ fluenced by stimulus duration and by practice.

However, these

results were not conclusive, particularly with regard to the re­ lationship between time-error and interpolated interval.

It was

felt that the complexity of the design provided considerable opportunity for the operation of obscuring interaction effects. The nine repetitions required by this design, for example, in­ troduced practice effects which undoubtedly tended to make timeerrors less negative.

It was considered that the differential

effects of nine repetitions on such factors as individual moti­ vation, the development of absolute impressions and individual differences in indifference points required further study under simplified conditions. No definite tendency was revealed in Experiment I for vari­ ation in precision as a function of either stimulus duration or interpolated interval.

It was felt that the number of judgments

per stimulus magnitude was too few to provide reliable determine-

118

tions of precision.

Since prolonging the sessions would have

been impractical and might also have interfered with the ad­ equate determination of time-errors, it was decided to study only the time-error in this experiment, and to change the ex­ perimental situation to salt this purpose when necessary. Accordingly, Experiment II was designed to provide a simpler situation in which time-error relationships could be studied.

In this experiment, stimulus duration was held con­

stant and interpolated interval was varied among the three in­ tervals of Experiment I.

There were thus three experimental

conditions as compared with the nine conditions of Experiment I and only three sessions were required for appropriate rotation of these conditions. ulus magnitude.

It was decided also to use only one stim­

Theoretically, if a time-error existed, one mag­

nitude would be sufficient to reveal it.

Since the use of one

magnitude would also make for a greater number of judgments effective in measuring the time-error the number of judgments per session was cut to 30. Thus in Experiment II only one function was to be determin­ ed - the time-error for interpolated interval with stimulus dura­ tion constant at one second.

Its basic purpose was to determine

whether, when certain changes were made, it would substantiate the corresponding results in Experiment I.

The changes intro­

duced in Experiment II when compared to Experiment I are summarized as follows: 1.

Number of sessions reduced from nine to three days.

119

2.

Number of judgments per session reduced from 60

to 30. 3.

Number of stimulus magnitudes reduced from five to

4.

Stimulus duration held constant at one second thus

one.

reducing the number of experimental conditions from nine to three. The function obtained in Experiment II confirmed the shape of the function obtained in Experiment I.

The rationale under­

lying the changes described above was confirmed, since the timeerror for each condition was consistently larger and the corres­ ponding standard deviation consistently smaller than those ob­ tained in Experiment I. Since the changes introduced in this experiment did not change functional relationships and further since they increased the reliability of time-8rror determinations and the magnitude of the time-errors obtained, it was decided to adhere to these changes as closely as possible in the subsequent experiments. The combined results of experiments I and II suggested that a prediction might be made for the value of the time-error at an interpolated interval larger than those already used.

In

addition, certain inferences from experimental data suggested that the effect of using only two categories of judgment ought to be evaluated.

There was evidence indicating that the two-

category situation might underestimate the magnitude of the time-error.

1 20

On this basis Experiment IIL was performed, substantially as a modification of Experiment II.

The same function was

studied but with the additional interval of 12 seconds making a total of four interpolated intervals.

In addition three

categories of judgment were used rather than two.

The results

of this study provided a third confirmation of the 1-second function.

With the largest interval an "extrapolated" point

on the curve was obtained as expected.

This experiment showed

also that the shape of the function is not distorted by the use of two or three categories.

It was indicated that three categ­

ories of judgment provided larger estimates of the time-error than did two categories of judgment. Experiments IV and V were concerned with time-error deter­ minations for a different type of stimulus, viz a "filled-in" circle.

This type of circle was used because its comparison

with the outline circle had theoretical import.

In addition,

the use of this circle was of interest because in one sense it constituted a simplification of the outline circle - no line thickness was involved. Experiment IV employed the procedures of Experiment III and investigated the same variables as did Experiment I.

This

experiment then had nine conditions and rotated these over a period of nine days. periment I.

Its purpose was the same as that of Ex­

It was hoped however, that the changes in procedure

and the use of the filled-in circle would make it possible to obtain more clear cut results than had been obtained in Experiment

181

I.

Similar results were obtained for the effects of stimulus

duration, interpolated interval and practice.

While the re­

sults were not alike in all respects they were similar enough to reinforce general conclusions made in the first three experi­ ments. Experiment V was performed to extend the investigation and to compare the functions for the two types of stimuli under more comparable conditions.

Therefore, in this experiment the pro­

cedure of Experiment III was followed exactly, except of course for the difference in the two types of stimuli.

The results ob­

tained in this experiment agreed with those of Experiment III, in that a significantly negative time-error was obtained at the largest interpolated interval. what in shape.

The two functions differed some­

An evaluation of these differences in terms of

the results of Experiment IV suggested that the differences were "real."

It was concluded also that the time-error was generally

more negative for filled-in circles than for outline circles. Conclusions The combined results of the five experiments indicate that the time-errors for both outline and filled-in circles tend to vary systematically as a function of stimulus duration,inter­ polated interval and practice.

In general, the following con­

clusions may be made: 1.

Time-errors become decreasing^ negative (or increas­

ingly positive) when the stimulus duration increases from one* to three seconds.

This trend changes when stimulus duration In­

creases from three to five seconds so that time-errors tend to

1 22

become increasingly negative (or decreasingly positive). 2.

Time-errors tend to become increasingly negative

(or decreasingly positive) over an interpolated interval of from one to eight seconds.

This trend obtain generally for

stimulus durations of 1, 3 and 5 seconds.

Reversals have been

consistently noted in this trend for outline circles at inter­ polated intervals of from one to four seconds.

Time-errors for

an interpolated interval of 12 seconds at one second stimulus duration, are negative at very high levels of statistical signif­ icance. 3.

At one second stimulus duration the time-error is, on

the average negative for the range of interpolated intervals in­ vestigated in this study. 4.

Time-errors exhibit an irregular tendency to become

decreasingly negative (or less positive) with increasing pract­ ice.

While the trend contains large fluctuations, it has been

noted clearly in four out of the five experiments. 5.

The various changes in procedure introduced suggest

that the time-error in this situation can be conveniently stud­ ied with only one stimulus magnitude and with approximately 30 to 50 judgments per session.

Larger time-errors seem to be ob­

tained with three ettegories of judgment than with two.

How­

ever, further study is needed before any definite decision can be made concerning the superiority of one or the other technique for the determination of time-errors in this situation. 6.

For short interpolated intervals (less than 3 seconds).

1£3

the time-error as a function of stimulus duration varies in a similar manner for both extensive and intensive stimuli. This similarity is attributed to the joint operation of two factors:

a peripheral adaptation factor and a figural after­

effect factor. 7.

The time-error functions obtained in the present

study for both stimulus duration and interpolated interval have been discussed in terms of a theory employing three hypo­ thetical factors.

Evidence from this and other studies suggests

that this theory provides a more adequate experimental approach to the study of the time-error for extensive stimuli than does Kohler’s original trace theory of the time-error.

124

VIII

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