Immediate and remote time estimation — A comparison

Acta Psychologica 57 (1984) 69-81

North-Holland

69

IMMEDIATE AND REMOTE TIME ESTIMATION - A COMPARISON

Dan ZAKAY and Eli FALLACH *

Tel- Aviv Uniuersity

Accepted August 1983

The influence of the length of time elapsing between the termination of an interval on its estimated

duration was tested in three experiments. In the first experiment, 89 subjects performed the W, C,

and CW tasks of the Stroop color-word test. The duration of each of these three tasks, which was

10 seconds in reality, was estimated twice by every subject. Once, immediately upon completion of

the task (IE), and a second time 90 seconds later (RE), both under prospective paradigm. The

nature of the relationship between task difficulty and its estimated duration was found to be

different in IE and RE. A negative relationship was found in IE while in RE no significant

difference was found between difficulty levels. In the second experiment it was found that RE’s

trend was not caused by estimation order. In the third experiment IE and RE were tested under

prospective and retrospective paradigms. In the perspective paradigm the results obtained in

experiment 2 were replicated. In the retrospective paradigm the relationship between task difficulty

and time estimation was, unlike the prospective paradigm, negative in both IE and RE. The significance of the results to time estimation theory was discussed.

Time estimation is a cognitive process which is sensitive to the condi- tions under which it is carried out. Hicks et al. (1976) listed the

following factors as influencing the process: (a) method of time estima-

tion - e.g., absolute time judgment by production, verbal estimation or

reproduction, or comparative time judgment; (b) duration of the inter-

val to be estimated; (c) the. nature of processing required of the subject during the interval to be estimated - e.g., empty or filled intervals; (d)

the nature of the test paradigm - e.g., a prospective paradigm in which

the subject knows in advance that he or she will be required to estimate the elapsed time or a retrospective paradigm in which the subject is told the nature of the task only after the interval to be estimated is over.

* Mailing address: D. Zakay, Dept. of Psychology, Tel-Aviv University, Ramat Aviv, 69978, Israel.

OOOl-6918/84/$3.00 0 1984, Elsevier Science Publishers B.V. (North-Holland)

70 D. Zakay, E. Fallach / Immediare and remote rime estimafion

One of the controversial issues in the literature on time estimation is the nature of the relationship between information processing load during an interval and the estimated duration of that interval. Accord- ing to Ornstein’s (1969) storage size metaphor, time estimation is a function of storage size which, in turn, is a function of the intensity of information processing required. Accordingly, the higher the intensity of processing required, the higher the resulting storage size and thus the higher the corresponding time estimate. For example, Ornstein (1969) found that time estimates of visual and auditory duration of complex stimuli were higher than those for simple stimuli. Other empirical supports for Ornstein’s model were obtained by Michon (1965), Avant et al. (1975), Lyman and Avant (1975), and Block (1978).

An opposing view is presented by the timer model (Frankenhaeuser 1959). According to this model, time estimation is based on the number of subjective units of time experienced during an interval where the subjective unit of time is an average mental content per unit of duration. Attentional models of time perception (e.g., Hicks et al. 1977) adopt the timer concept and claim that the estimate of duration increases with the observer’s attention to time, since the processing of the subjective units of time demands mental effort. This suggests that attention is divided between the processing of temporal and nontem- poral information. Supporting evidence for this view was provided by Curton and Lordahl (1974) who found that attentional focus was an important determinant of time estimation. Thus, a negative relation between task complexity and magnitude of time estimates is predicted by attentional models. This prediction was supported in several studies (e.g., Fraisse 1963; Vroon 1970; Burnside 1971; Sorkin et al. 1972; Devane 1974). Hicks et al. (1976) found support for that relationship only within the frame of a prospective paradigm.

The purpose of the present research is to explore the influence of an additional variable on the time estimation process, namely the influence of the ensuing time lapse after the termination of an interval on its estimated duration. We refer to Immediate Estimation (IE) as a paradigm in which duration of an interval is estimated immediately upon its termination, and to Remote Estimation (RE) as a paradigm in which duration of an interval is estimated only after a given period of time. The principal difference between IE and RE has been previously observed by James who wrote that “. . . in general, a time filled with varied and interesting experiences seems short in passing, but long as

D. Zakay, E. Fallach / Immediate and remote time estimation 11

we look back. On the other hand, a tract of time empty of experiences seems long in passing, but in retrospect short” (1890: 624). It is clear that by “looking back”, James meant what is referred to here as “RE”. However, it is claimed here that RE is different from IE even in regard to short intervals of delay. A confounding exists in the literature between prospective and retrospective paradigms and IE and RE paradigms. Hicks et al. (1976, 1977), for example, treat immediate retrospective time estimation as being identical to RE, which is not the case. It is important to note that both IE and RE are possible within the frames of a prospective or a retrospective paradigm. The need to explore the difference between IE and RE is important for several reasons: (a) to clarify the existing confounding between IE and RE, and between prospective and retrospective time estimation in order to specify a condition which hitherto has been overlooked and which should be taken into account in time estimation studies; (b) to test an hypothesized explanation for the phenomena pointed out by James (1890); and (c) to achieve a better understanding of the general mechanism of time estimation by comprehending the nature of the difference between IE and RE, and testing an hypothesized mechanism for its explanation.

We suggest that the accessibility of the temporal information accumulated in the cognitive timer during an interval decreases as a function of the time elapsing from the termination of the interval, as does the relevancy of that information for estimating the duration of specific interval. This hypothesized relationship reflects the nature of the mechanism which underlies the cognitive timer (Frankenhaeuser 1959; Thomas and Brown 1974; Thomas and Weaver 1975) which is activated by some signal interpreted as the commencement of a specific interval and is stopped upon receiving another signal interpreted as its termination. The timer is reset upon receiving a new starting signal. Until then, information is stored in the timer, but it is probably subjected to some decay processes similar to those characterizing working memory (Allan and Rousseau 1976). On the other hand, during any interval some information is retained in short-term storage and some of it is trans- ferred later on to long-term storage where, although it might be further changed as a function of elapsing time (Bartlett 1961), it nevertheless remains accessible. It is assumed that the cognitive system draws on the most accessible information in order to perform a specific task. This is exemplified in the anchoring and availability heuristics (Tversky and Kahneman 1974). Hence, it is suggested that in IE, time estimation has

12 D. Zakay, E. Fallach / Immediate and remote time estimation

the highest probability of being based on the temporal information stored in the cognitive timer, while in RE, time estimation has the highest probability of being based on the information stored in memory. Hence, it is hypothesized that within the framework of an IE prospective paradigm, a negative relationship should be found between magnitude of time estimation of intervals and complexity of the task performed during it, as predicted by attentional models. On the other hand, within the framework of RE prospective paradigm, that relationship should be found to be positive, as predicted by the storage size model.

Experiment 1

Method

Subjects

Twenty-one males and 68 females, all of whom were first year social science

students at Tel-Aviv University, ranging in age betwen 19 and 30 years, participated in

the experiment in partial fulfillment of course requirements.

Experimental task

The Stroop color-word test (Stroop 1935) was used with the following three

subtasks: (a) a W task in which a name of a color is to be read; (b) a C task in which a

color patch is to be named; and (c) a CW task in which color names written in

incongruent colored inks are presented to Ss who are required to name the color of the

ink and to ignore the color name. The Stroop task was chosen as the difficulty order of

the subtasks is well established, with W the simplest task and CW the most difficult in

terms of reaction time and number of errors (Dyer 1973). The fact that naming a

stimulus takes more time and is more difficult than reading the name of this stimulus is

well established (e.g., Fraisse 1979), as well.

Procedure

Each S was tested individually and performed all three subtasks. The order of the

subtasks was counter-balanced across Ss. Each subtask was administered separately,

and its time interval was deliminated for the S by the experimenter saying “Start” and

“Stop”. The interval was measured by an electronic timer. The duration of each of the

three intervals was estimated twice by each S. The first estimate was made immediately

after the experimenter said “Stop”. The second estimate was made 90 set afterwards.

During these 90 set, Ss were asked to memorize simple geometrical figures which were

projected in front of them by a slide projector. This was done in order to prevent

memorization of the previous time estimate and in order to ensure a “reset” of the

cognitive timer. Time estimates were done within a prospective paradigm by using a


reproduction method, which was chosen over verbal estimation since a verbal response is easily remembered. Ss were told in advance that they would have to estimate the

duration of an interval in which they performed each task and were asked to perform the task as fast and accurately as possible. Upon finishing each task, Ss were asked to

press a button for the same duration which they felt corresponded to the duration of the task. Afte 90 set, Ss were asked to do this again. By pressing the button, a hidden

electronic timer was activated and the time recorded was taken as the time estimates. The objective time of all the intervals was 10 sec.

Subjective evaluation of the tasks’ difficulty

In order to measure the perceived difficulty of each task, 11 Ss, who did not

participate in the experiment itself but represented the same population from which Ss were sampled, were asked to perform all three tasks. The order of tasks was randomly

decided for each S. After performing all three tasks, each S was asked to give each task a score of relative difficulty on a 7-point scale where 1 stood for ‘I very easy” and 7 for

“very difficult”. The average score of each task was taken as its score of subjective

difficulty. The rank means of the difficulty levels of the three tasks were 1.40 for the W tasks, 1.74 for the C task, and 3.72 for the CW task. These subjective ranks validated the order of objective difficulty levels.

Results

Analysis according to objective difficulty

The time estimates (TE) obtained were subjected to a 4-way ANOVA of estimation

paradigm (IE and RE), objective task difficulty (3 levels) sex, and presentation order.

However, since presentation order and sex were not found to have any significant

effect, the TE scores were analyzed for clarity by a 2 (estimation paradigm) X 3 (task difficulty) ANOVA with repeated measurements. The means of the TE scores are

presented in table 1.

A significant interaction between the factors of estimation paradigm and task difficulty was found (F(2,176) = 6.72; p < 0.01). The interaction is presented in fig. 1.

Specific comparisons were carried out by ScheffC tests. Significant differences were

found in the IE paradigm between the low and high difficulty tasks (F(5,176) = 4.18;

Table 1 TE means (in seconds) in the experimental tasks (n = 89).

Estimation delay

IE RE

Task difficulty (objective) Low(W) Medium (C) High (CW)

6.32 6.19 6.30 6.09 5.54 6.25

14 D. Zakay, E. Fallach / Immediate and remote time estmation

- Immediate estimation

__-- Remote estimation

Law Medium High

Task Difficulty (Objective)

Fig. 1. Interaction between estimation paradigm and objective task difficulty in the Stroop tasks.

p < 0.01) and between the medium and high difficulty tasks (F(5,176) = 5.70; p < 0.01). No significant differences were found between the three difficulty levels in the RE

paradigm.

Analysis according to subjective difficulty Scheffe tests which followed a one-way ANOVA with repeated measures performed

on the subjective ranks obtained by the 11 judges revealed that the W and C tasks were not significantly different, whereas each was significantly different from the CW tasks. Hence, another analysis was done, this time with only two difficulty levels: low, which

included the W and C tasks, and high which included the CW tasks. The corresponding TE’s means were computed for each S. A 2 (estimation paradigm)X 2 (subjective difficulty level) ANOVA with repeated measurements was performed and a significant interaction between estimation paradigm and subjective difficulty level (F&88) = 12.74; p < 0.01) was found. This interaction is presented in fig. 2.

Significant differences were found by means of Scheffe tests between the low and high subjective difficulty levels in IE (F(3,88) = 23.66; p < 0.01). However, no similar significant difference was found in RE. A significant difference was found between RE and IE in the high difficulty level (F(3,88) = 2.72; p < 0.05) while no similar significant difference was found in the low difficulty level.

TE's Means (seconds)

6.4.

6.3.

6.2.

6.1.

6.0.

5.9.

5.8.

5.7.

5.6.

D. Zakay, E. Fallach / Immediate and remole time estimation

Immediate estimation

_____ Remote estimation

15

I 1

Low High

Task Difficulty (Subjective)

Fig. 2. Interaction between estimation paradigm and subjective task difficulty in the Stroop tasks.

Discussion of experiment 1

The experimental hypotheses were supported by the results. However, since RE was always after IE, it was confounded with estimation order. This was unavoidable as it was necessary to test the relationship between IE and RE within subjects. Hence, a second experiment was performed in order to examine the influence of estimation order

on the results obtained.

Experiment 2

Method

Subjects

Eight males and 22 females sampled from the same population as that of the first experiment who did not participate in the first experiment participated in the second

one.

Experimental tasks and procedure

The experimental tasks were identical to those used in the first experiment. The procedure was similar as well. The only difference was that each S was asked to give RE only. This was done 90 set after the termination of each experimental task. During


these 90 set, Ss were asked to memorize simple geometrical figures, as in experiment 1. Order of experimental tasks was counterbalanced.

Results and discussion of experiment 2

Order of presentation and sex were found to have no influence on time estimation. Hence, the time estimates (TE) obtained were subjected to a one-way ANOVA with 3

levels of objective task difficulty with repeated measurements. The means of the TE scores were: W task - 6.58 set; C task - 6.76 set; CW task - 7.61 sec. The effect of task difficulty was significant (F(2,58) = 3.20, p < 0.05). This finding clearly indicates

that the pattern of relationship between TE and task difficulty level was not caused by estimation order, as the trend obtained here is similar to that obtained for RE in the first experiment, and is even more clear. The fact that the only difference between this

experiment and the first one was that, in the first one, Ss were tested on both IE and RE, indicates to the high influence of IE on RE. A possible explanation for this might

be that in performing RE after IE Ss are trying to behave consistently and to replicate their IE behavior.

Experiment 3

The purpose of the third experiment was to test IE versus RE under a retrospective time estimation paradigm and to compare it to the prospective time estimation

paradigm. As for the prospective paradigm a replication of the second experiment was expected. However, predictions for the retrospective paradigm are not so clear and

obvious. Hicks et al. say that: “Attention to passing time would not normally be a

factor in retrospective judgments because the interval the subject is judging has already elapsed before he gets his instructions for judgment. The judgment should be more dependent on his memory for events that occurred during the interval.. . It may be that these judgments are made proportional to the amount of content retrieved from an interval, rather than to memory of the amount of processing performed during it”

(1976: 725). Hence, it is not possible to state definitely the type of trend to be expected between TE and task difficulty in IE and RE under a retrospective paradigm. It should also be remembered that Hicks et al. (1976) found no significant function between

judged time and response uncertainty under the retrospective paradigm. However, one solid hypothesis which can be made is that, contrary to prospective paradigm, the relationship between TE and task difficulty in IE and RE under a retrospective

paradigm should be of the same type and trend. The reason for that is that based on Hicks et al’s (1976) analysis there is no basis to expect different mechanisms of time

estimation in IE and RE under retrospective paradigm.

Method

Subjects Forty males and 40 females sampled from the same population as that of the former

experiments but who did not participate in them, served as Ss in the third experiment.


Table 2

TE means (in seconds) in the third experiment (10 subjects in each cell).

Paradigm Estimation

delay

Task difficulty

Low (W) High (CW)

Prospective IE 9.69 5.98

RE 8.64 10.45

Retrospective IE 6.93 5.58

RE 8.91 7.49

Experimental tasks and procedure

In light of the subjective difficulty levels revealed in the first experiment only the W

and the CW tasks were used. The Ss were randomly assigned to one of eight

experimental groups: (1) Retrospective, IE, W task (RIW); (2) Retrospective, IE, CW

task (RICW); (3) Retrospective, RE, W task (RRW); (4) Retrospective, RE, CW task (RRCW); (5) Prospective, IE, W task (PIW); (6) Prospective, IE, CW task (PICW); (7)

Prospective, RE, W task (PRW); (8) Prospective, RE, CW task (PRCW).

The duration between termination of the target interval and the remote estimation was 60 sec. The procedure for the prospective groups was identical to that utilized in experiment 2. The procedure for the retrospective groups differs only in that Ss were not told in advance that they would be asked to estimate the interval’s duration.

Results

As in the former experiment, order of presentation and sex were found to have no influence on time estimation. The time estimates (TE) obtained were subjected to a 3-way ANOVA of Paradigm (prospective versus retrospective) X estimation delay (IE

versus RE) x task (W versus CW). The means of the TE scores are presented in table 2. Significant main effects were obtained for estimation delay (F(1,72) = 4.17; p < 0.05).

The main effect of paradigm was close to significance (F(1,72) = 3.34; p -C 0.07). The

specific comparison between PRW and PIW was not significant, while that between PRCW and PICW was highly significant (Scheffe test, F(7,72) = 3.30; p < 0.01). The

trends obtained are presented in fig. 3.

Discussion of experiment 3 & General discussion

The results obtained in the third experiment clearly indicate that IE and RE have different influences on time estimation under prospective and retrospective paradigms. In the prospective paradigm a strong replication of the second experiment was obtained and thus the original hypotheses of this study were further supported. As for the retrospec-

78 D. Zakay, E. FaNach / Immediate and remote time estimatron

TE's Means (seconds)

11.0.

10.5.

10.0’

9.5.

9.0.

PI

2 _-_---_ pR /

/ / -x-x-x- RI

/ -o-o-o- RR

8.0.

7.5

7.0 -

6.5 .

6.0 .

5.5 .

5.0 .

Low High

Task Difficulty

Fig. 3. Trends of IE and RE under prospective and retrospective paradigms. PI - Prospective, immediate estimation PR - Prospective, remote estimation RI - Retrospective, immediate estimation RR - Retrospective, remote estimation

tive paradigm, the hypothesis about similar trends of the relationship between time estimation and task difficulty in RI and RR was supported. This is in support of the assumption that the time estimation’s mechanisms are different under PI, PR and retrospective paradigms. As for the finding that the trend was negative, this is hard to explain, although it is not surprising on the basis of Hicks et al.‘s (1976) assumption that time judgments under retrospective paradigm are made proportional to the amount of content retrieved from an interval, rather than to amount of processing performed during it. Content can be very

D. Zakay, E. FaNach / Immediate and remote time estimation 19

task specific and hence only after testing IE and RE under retrospective paradigm with several filler tasks the exact nature of the relationship would be known. However, it is suggested here that under a retrospective paradigm, both IE and RE reflect the memory of the content of the cognitive timer at the end of the target interval, According to that hypothesis, the relationship between task difficulty and time estimation under retrospective paradigm should always be negative. This should, of course, be validated empirically.

As for the prospective paradigm, the results obtained in the present study indicate that the nature of the relationship between the magnitude of the estimated duration of an interval and the difficulty levels of the tasks performed during that interval is influenced by the factor of immediate versus remote estimation. It was found as hypothesized that this relationship was negative in IE while a tendency toward a positive relationship was obtained in RE. This was true for objective difficulty levels as well as for subjective difficulty levels. According to Logan and Zbrodoff (1979) and Logan (1980), in the Stroop CW task much attention is required for the analysis of each stimulus as there is a need to divide attention between reported and unreported dimensions, and hence much more attention is devoted to the CW stimulus than for the C or W stimulus. This is in support of the hypothesis that in PI the reason for time estimates being higher for the low difficulty tasks than for the high difficulty tasks is that estimation was based on temporal information which was accumulated to a smaller degree in the cognitive timer in the difficult task, as most of the attentional resources were needed for its performance. A further empirical support for this was obtained by Fraisse (1979) who found that durations were more over- estimated while reading the name of stimuli as compared to naming the stimuli. That finding was explained in that the easier the processing the subject will be more attentive to duration itself. In the PR paradigm, however, no significant difference was found between the estimated duration of the easy and difficult tasks, a finding which indicates that a different mechanism for time estimation had been employed. This assumption is supported by the findings of Guay and Bourgeois (1981), who found that when subjects hold time lengths of 4, 8, 16, and 32 set in memory for a period of 20 set of rest or 20 set of interpolated activity, they become more variable than if they recall the item immediately. It is suggested here that in PRE, time estimation is based on storage size.


The results obtained in the present study clearly indicate that the differences between the IE and RE paradigms cannot be explained in

terms of prospective and retrospective paradigms. However, other tasks

in addition to the Stroop test should be incorporated in future research, as should other objective task durations. It is also important to vary the

delay between the termination of the estimated interval and the actual

estimation in order to test further the findings of the present study.

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Immediate and remote time estimation — A comparison