The interpretation of temporal isolation effects

Figure 8.1 Serial position curves for all presentation schedules in both conditions in Experiment 1.

(p.141) schedule, F(2, 44) = 3.66, MSe = 0.01,p ‹ 0.05; and serial position, F(6, 132) = 132.87, MSe = 0.024, p ‹ 0.0001. Serial position also interacted with condition, F(6, 132) = 6.31, MSe = 0.024, p ‹ 0.0001, and, crucially, with presentation schedule, F(12, 264) = 9.59, MSe= 0.006, p ‹ 0.0001. No other interactions, including the overarching three-way interaction between all variables, were significant.

The interaction between serial position and presentation schedule was further explored by two separate within-subjects Presentation schedule × Serial position ANOVAs for the quiet and AS condition, respectively. The interaction between presentation schedule and serial position condition was significant for the quiet condition, F(12, 132) = 2.84, MSe = 0.007, p ‹ 0.002, as well as for the AS condition, F(12,132) = 8.53, MSe = 0.006, p ‹ 0.0001.

Discussion

The results of Experiment 1 are consonant with the predictions of temporal distinctiveness theories: irrespective of their serial position, items that were widely separated in time were remembered better than items that were temporally crowded. Experiment 1 thus replicated the results of Neath and Crowder (1996) and additionally extended their findings to longer lists (seven instead of five items), to a closed vocabulary set (letters instead of words), to significantly longer presentation durations and interitem intervals, and to situations when rehearsal at encoding was prevented by articulatory suppression.

The first experiment thus provided evidence against a possible role of rehearsal in producing temporal isolation effects. Moreover, contrary to the expectations of a rehearsal view, the magnitude of the isolation effect at early serial positions appeared to be greater in the AS condition than in the quiet condition. Figure 8.1 shows that performance at early serial positions for the decreasing schedule in the quiet condition was arguably close to ceiling, and this may have prevented the isolation effect from exhibiting its true magnitude. Experiment 2 explored this possibility by inserting a brief distractor task between list presentation and recall in the quiet condition.

Experiment 2

Experiment 2 was identical to the first study except for a brief distractor task between study and retrieval in the quiet condition. In addition, the constant presentation schedule was omitted, and participants were queried about their encoding strategies after completion of the experiment.

Method

Participants. Fourteen first-year students from the University of Western Australia participated voluntarily in exchange for course credit. Three participants were removed due to poor performance and one because the participant took almost three times as long as anyone else to complete the task. This left 10 participants, an equal number of whom were randomly assigned to the AS and quiet conditions.

Design and procedure. Lists were constructed in the same manner as for Experiment 1, except that the constant condition was not included. There were 40 trials of each presentation condition; increasing or decreasing. Presentation schedules were randomly intermixed.

In the quiet condition, participants repeated out aloud a random 3-digit number that was presented immediately after the list for 2,000 ms. In the AS condition, a blank screen of 100 ms followed by a mask of asterisks for 300 ms separated the last study item from the recall phase. After completion of the experiment, participants were queried about what strategies they used to perform the experiment.

(p.142) Results

Correct-in-position performance for individual participants in both groups ranged from 0.24 to 0.48 (averaged across serial positions). The serial position curves for both conditions and both presentation schedules are presented in Figure 8.2.

A 2 × 2 × 7 (Condition × Presentation schedule × Serial position) between-within ANOVA revealed a significant main effect of presentation schedule, F(1, 8) = 5.50, p ‹ 0.05, MSe = 0.019, and serial position, F(6, 48) = 29.10, p ‹ 0.0001, MSe = 0.03. In addition, the interaction of presentation schedule and serial position was significant, F(6, 48) = 7.81, p ‹ 0.0001, MSe = 0.008. No other effects reached significance.

Two separate 2 × 7 (Presentation schedule × Serial position) within-subjects ANOVAs within each condition confirmed the presence of the crucial presentation schedule × serial position interaction for the quiet condition, F(6, 24) = 3.34, p ‹ 0.02, MSe = 0.01, as well as the AS condition, F(6, 24) = 5.28, p ‹ 0.002, MSe = 0.006.

As for Experiment 1, the benefits for the decreasing interval were found at the beginning of the list for the first three serial positions, whereas the fifth and sixth serial positions benefited in the increasing condition. The crossover at serial position four is at roughly the same point as in Experiment 1 (see Figures 8.1 and 8.2). The apparent lack of difference between the decreasing and increasing condition for the terminal item in the quiet condition probably resulted from a suffix effect induced by the requirement to pronounce a random number at the end of the list. Suffix effects are a standard finding in serial recall (e.g., Greene and Crowder 1988; Hitch, Burgess, Towse et al. 1996) and this result is therefore not surprising.

The interview at the end of testing revealed that participants used a consistent encoding strategy. All participants, regardless of articulatory condition, reported that with decreasing presentation schedules they focused on remembering only the first three to four items. With increasing presentation schedules, all but two participants (both in the quiet condition) likewise reported that they focused only on the last three or four items during list presentation.

The interpretation of temporal isolation effects

Figure 8.2 Serial position curves for all presentation schedules in both conditions in Experiment 2.

(p.143) Discussion

Experiment 2 replicated the results of the first study even though performance in the quiet condition, including the first list item, could no longer be considered to be anywhere near ceiling. The results further weaken a rehearsal-based explanation for temporal isolation effects, and we give it no further consideration as a viable alternative explanation.²

The recall data are therefore compatible with a temporal distinctiveness notion, although the verbal reports by participants are supportive of the other alternative account of the data advanced at the outset; namely, that the predictability of intervals engendered selective encoding strategies. On this account, it was not temporal distinctiveness per se that produced the isolation effects at retrieval, but people’s choice to memorize well-separated items at the expense of others that they found more difficult to encode. In order to confirm the viability of this alternative explanation, we now model the data from the first two experiments in two ways; within a conventional temporal distinctiveness framework and within a nontemporal account augmented by selective encoding.

Temporal distinctiveness vs selective encoding: the SIMPLE theory

A powerful recent instantiation of the temporal distinctiveness hypothesis is the SIMPLE theory (ScaleInvariant Memory, Perception, and LEarning) of Brown et al. (2002). At an intuitive level, SIMPLE postulates that the confusability between any two memory traces is related to the ratio of the time that has elapsed between their encoding and the time of recall. The lower that ratio, the lower the confusability among items and hence the more likely it is that an item is recalled correctly. This mechanism favors recent items over more distant events. For example, items that were encoded 1 s and 2 s ago are less confusable (ratio of 0.5) than are items from 5 and 6 seconds ago (0.83). The mechanism also favors items that were separated in time over others that occurred in close succession. For example, items that occurred 5 s and 10 s ago (ratio 0.5) are less confusable than items that occurred 7 s and 8 s ago (0.88), notwithstanding the fact that the average retention interval is equal for both pairs of items. It follows that items from further in the past, and items that occurred near each other in time, will be more difficult to recall (see Brown et al. 2002 for further details).

More formally, SIMPLE rests on three principal assumptions:

1. Items are represented by their position within a potentially multidimensional psychological space, with one of those dimensions necessarily devoted to representing time. Here, the temporal dimension was accompanied by a second, positional dimension that corresponded to the list position of items.
2. The similarity between any two items in memory is a declining function of the distance separating them in psychological space.
3. The probability of recalling an item is inversely proportional to that item’s summed similarity to all other response alternatives, as just illustrated by the ratios between elapsed times of item pairs.

The SIMPLE architecture

Encoding in multidimensional space. Memory representations are organized along a primary temporal dimension that reflects the (logarithmically transformed) time since encoding. Retrieval can (p.144)be cued by the remembered location of an item along this dimension. In the present case, a second dimension represents within-list position, coded by ordinal numbers (i.e., position 1, 2,…). There is ample evidence that positional information – which can be decoupled from elapsed time – is relevant in serial recall (Henson 1999; Ng and Maybery 2002).

To illustrate, consider the representation of a two-item list after a 6 s retention interval (with items being separated by 1 s on the list): the two items would be in locations {log(7), 1} and {log(6), 2}, respectively, in the {time, position} space. The relative importance of the two dimensions at retrieval is determined by the parameter wt, which is the attentional weight paid to the temporal dimension. The weight given to the positional dimension is given by 1-wt, and therefore:

where d _i _, _j is the psychological distance between stimulus i and stimulus j, T _i is the temporal distance of stimulus i from the time of retrieval (logarithmically transformed to capture the fact that temporally distant events are more compressed than recent ones), and P _i is the ordinal position of item i. The attentional parameter wt (see, e.g., Nosofsky 1992) can be thought of as stretching (shrinking) the psychological space along the most (least) important dimension. In the present case, if wt is unity, the simulations implement an exclusively time-based representation (for the earlier two-item list, the representation reduces to {log(7)} and {log(6)}). Conversely, as wt approaches zero, the representation is no longer time-based but positional and the representation of the list becomes {1} and {2}.

Similarity-distance metric. Following much precedent in the categorization literature, SIMPLE assumes that the similarity of any two items in memory is a reducing exponential function of the distance between them in psychological space:

$The interpretation of temporal isolation effects$

where η _i,jis the similarity between items i and j and d _i,j the distance between them. It follows that items that are very close have a similarity approaching unity, whereas items that are more psychologically distant have a similarity that, in the extreme, approaches zero. The parameter cgoverns the rate of decline of similarity with distance. In conjunction with the logarithmic transformation of time, this similarity metric gives rise to the di $The interpretation of temporal isolation effects$ stinctiveness ratios mentioned earlier.

Similarity determines recall. The third assumption is that the probability of recalling item i is inversely proportional to the summed similarity of that item to every other potentially recallable item. Specifically, the discriminability of the memory trace for item i, D _i, is given by:

$The interpretation of temporal isolation effects$

where n is the number of available response alternatives, which in the present case is assumed to be equal to the number of list items.

Discriminability translates into recall probability by taking into account the possibility of omissions. Omissions arise from thresholding of low retrieval probabilities by a sigmoid function: if Di is the discriminability given by the preceding equation, the recall probability P_i is derived as:

$The interpretation of temporal isolation effects$

(p.145) where t is the threshold and s the slope (or noisiness) of the transforming function. Any D_i that falls below the threshold engenders an omission.

Model parameters. For the present simulations, we used a basic version of SIMPLE that did not incorporate mechanisms for extra-list intrusions or response suppression and that ignored possible phonological or semantic similarity between items. All of these mechanisms are necessary for modeling of a wider range of paradigms; however, they are not needed for (and indeed could potentially obscure) the core predictions that are of interest here.

The present basic version of SIMPLE thus has five free parameters:

1. c governs the rate at which the psychological similarity of two items decreases as a function of the distance between them in psychological space.
2. wt specifies the amount of attention paid to the temporal dimension (at the expense of attention paid to the positional dimension).
3. s (for ‘slope’) and
4. t (for ‘threshold’) relate to omissions as described above.
5. An additional parameter o is required to accommodate output interference. It is assumed that the memories of to-be-recalled items become progressively less distinctive as recall proceeds due to interference caused be each successive recall. The output interference parameter, o, reduces the value of c for the nth item recalled by multiplying it by o ^n-1. Thus with o = 1, there is no output interference; as o reduces below 1 there is increasing output interference.

Two rival accounts for the data

All simulations implemented the exact presentation regime of the experiment(s) being modeled, using the experimental presentation duration, interitem intervals, and retention intervals. The best-fitting parameter estimates and R² values for all simulations reported in this article are summarized in Table 8.1.

Time-based account. The time-based account for Experiment 2 was straightforward, with the parameters being estimated from the data using the experimental presentation regime. Parameter values were estimated separately for the quiet and suppression conditions, but were held constant for the increasing and decreasing schedules within each articulation condition. The results are shown in the left panel of Figure 8.3, where it is evident that a good fit was obtained. Moreover, the parameter estimates were meaningful and consistent with a time-based interpretation of the

Table 8.1 SIMPLE parameter values used in all simulations

Experiment	Cond	c	wt	o	t	s	R²
One	Quiet	9.37	0.74	0.75	0.56	3.79	0.960
(temporal)	Suppress	9.16	0.73	0.84	0.83	9.45	0.992
Two	Quiet	12.1	0.86	0.79	0.74	5.45	0.978
(temporal)	Suppress	5.49	0.67	0.91	0.84	9.78	0.988
One	Quiet	15.6	0	0.21	0.01	2.79	1.00
(encoding)	Suppress	9.87	0	0.40	0.68	21.0	0.990
Two	Quiet	5.36	0	0.50	0.61	4.18	0.990
(encoding)	Suppress	2.78	0	0.85	0.85	11.1	0.991