Recent studies with such stimuli, revealed a striking preservation of short-term, item recognition memory with aging (Della-Maggiore et al., 2000; Bennett, Sekuler, McIntosh, & Della-Maggiore, 2001; McIntosh et al., 1999). For example, Sekuler, Kahana, McLaughlin, Golomb, and Wingfield (2005) showed that young and older participants demonstrated equivalent short-term visual recognition memory, achieving equivalent proportions of correct “old”-“new” judgments, at each of three different, brief test delays. The present study adapted these basic methods to examine short-term temporal order memory with a new sample of participants. In addition, we exploited the metric properties of the grating stimuli in order to identify deterministic causes of observed errors in short-term temporal order memory.

The upper panels in Figure 1 show the proportion of correct recognitions and correct identifications of serial position for all three serial positions and for lure trials (trials on which p matched none of the study items). Results for young participants are shown in Panel A; results for older participants appear in Panel B. In addition, results are separated according to retention interval, 1 sec vs. 4 sec. There was no systematic difference in visual short-term recognition between the two retention intervals, 1 and 4 sec. In general, older participants achieved a somewhat higher proportion of correct recognitions than did their younger counterparts. Previous memory studies have shown that older participants' performance can be distorted by a criterion change (Harkins, Chapman, & Eisdorfer, 1979; Kosslyn, Thompson, Kim, & Alpert, 1995; Trahan, Larrabee, & Levin, 1986). Therefore we evaluated potential criterion changes, taking account not only of correct recognition responses, but also the correct rejection rate. When this was done, we found that the modest age-dependent superiority in recognition was accompanied by a corresponding decrease in the rate of correct rejection rate for a lure, that is for a p that matched none of the study items. Finally, when pairs of hits and false alarms were expressed as d' values (Macmillan & Creelman, 2005), the mean d's for the young and older participants were 1.01 and 1.16, respectively. Bootstrap resampling showed that in the absence of any actual difference between the two groups, a difference this large or larger would occur with p >.30. The nonsignificance between the groups' d's strengthens the claim that the two age groups had essentially equivalent recognition performance. Because neither the main effect of age nor any interaction involving age were statistically reliable, the following discussion ignores that variable.

Confirming what may be evident in the first and second lines of Table 1, Figure 1 shows that the proportion of correct recognitions was appreciably higher than the proportion of correct identifications of serial position (F(1,18)=395.13, p <0.01). This difference reflects the influence of errors in identifying the serial position of recognized items.

Although recognition responses showed no statistically significant serial position effect, such an effect was manifest with identification responses, that is, when participants' serial position judgments were taken into account. This serial position effect was considerably diminished at the longer of our two retention intervals (F(2,36)=6.22, p <0.01).

Errors in visual temporal order judgments can be exploited to identify the information that participants use to make successful judgments. This is especially true when, as is the case here, the metric properties of stimuli makes it possible to relate misidentifications to stimulus characteristics. For young participants, on 21% of trials when recognition was correct, the target was attributed to an incorrect serial position; for older participants, the corresponding value was 17%. The difference between the two age groups was not statistically significant (p>.40).

Basically, misidentifications could have arisen from either of two quite distinct sources. Some or all of the misidentifications could have been entirely stochastic, reflecting random guesses made when participants had no actual useable memory of what had been seen. Alternatively, misidentifications could have come from some deterministic process, for example, systematic errors associated with partial loss of serial position information. We set out to evaluate these alternative accounts of misidentifications.

To compare competing stochastic and deterministic accounts of misidentifications, each participant's misidentifications were sorted into the cells of a notional 2×2 table. In this sorting, we considered only trials on which p actually matched s₁ or s₃. The table's rows corresponded to two levels of a variable we call spatial similarity; the table's columns correspond to two levels of a variable we call temporal similarity. To generate the value of spatial similarity, we calculated the Euclidean distance in spatial frequency between (a) p and the misidentified study item, and (b) p and the remaining study item that did not match p. If the first of these two distances were the smaller, we categorized spatial similarity between p and misidentified item as “high”; otherwise, we categorized spatial similarity as “low.” For temporal similarity, we categorized misidentifications according to whether the error in identification represented a shift of one (high similarity) or two (low similarity) serial positions. For example, if s₂ were misidentified as matching p, when the actual matching study item was s₃, this error of one serial position was categorized as high temporal similarity; if s₁ were misidentified as matching p, when the actual matching study item was s₃, the error of two serial positions was categorized as low temporal similarity. A factorial cross of spatial and temporal variables produced four combinations of spatiotemporal differences between p and the misidentified study item.

The proportions of all serial position errors that fell into each of the four categories are shown in Figure 1C for young participants, and in Figure 1D for the older participants. On the horizontal-axis in each panel is the category, low or high, of spatial similarity; black bars show results with high temporal similarity, and gray bars show results with low temporal similarity. Because the distribution of misidentifications across the four categories was essentially the same for both age groups, for now we ignore the age variable.

The results shown in Figure 1C, D allow us to dismiss the hypothesis that all misidentifications resulted from a stochastic process. A process in which participants guessed randomly would on average have produced four bars of roughly equal height in Figure 1C and D. Monte Carlo simulations show that a stochastic process would generate results as biased as as those we observed in fewer than one in 100,000 replications of the experiment. Although we cannot rule out the possibility that random guesses produced some of the misidentifications, we can assert that many misidentifications arose from deterministic processes.

The distribution of misidentifications across the four categories in the notional 2×2 table suggests that both temporal and physical similarity induced temporal order errors, with physical similarity exerting a larger effect than temporal similarity (compare the pair of bars at the left side of Figure 1C or Figure 1D to the corresponding ones at the figures' right). The figure shows no evidence of an interaction between the two variables,for example, the black and gray bars at the left side of Panel C differ by about as much as the corresponding bars at the panel's right side. So, the same processes appear to be at work with both young and older participants, and have quite comparable effects on both groups.

To understand how spatial similarity might lead to errors in temporal order, we will use the basic structure of summed-similarity (or global-matching) memory models (Nosofsky, 1986; Clark & Gronlund, 1996; Kahana & Sekuler, 2002). We will work within this framework, because NEMo, one member of this class of models, has already accounted successfully for short-term memory with stimuli like those used here (Kahana & Sekuler, 2002). A summed similarity model assumes that the study items, s₁ … s₃, are stored in memory as corresponding noisy exemplars, m₁ … m₃, where the exemplars' subscripts signify the order in which the visual stimuli had been presented. When the probe, p, is presented, η₁ …η₃, the set of similarities between p and each of the noisy exemplars is computed. Again, subscripts signify the order in which study stimuli were presented. NEMo describes each similarity value as an exponentially decreasing function of the spatial difference between p and the corresponding values, m₁ … m₃. From the resulting similarity values, a summed similarity, Σ_η, is computed. Some criterion value of Σ_η > k is taken as evidence that at least one of the study items matched p, which makes p seem familiar. Over trials, the probability of a recognition response (that is, a “yes” response) corresponds to the proportion of trials on which Σ_η > k.

The central role that noise can play in summed similarity models brings to mind the role it occupies in some theories of cognitive aging. For example, Welford (1984) offered the influential proposal that various age-related changes in performance reflected older adults' relatively higher levels of internal neural noise (random variability). Researchers have developed and deployed powerful computational methods for testing detailed descriptions of noise's role in short-term memory, distinguishing between different sources of noise, such as internal vs. external noise, and different forms of noise, such as multiplicative vs. additive noise (Gold, Murray, Sekuler, Bennett, & Sekuler, 2005), but such analyses have as yet not been applied to results from older adults. Because we intentionally tailored stimuli to individual participants' visual discrimination, it is impossible to tell from our data whether age-related differences in internal noise accompany visual encoding. But we can exploit the summed similarity framework to generate useful propositions about age-related noise in the context of short-term recognition and temporal order memory.

First, consider how a summed similarity model could be extended to account for temporal order judgments. Such an extension requires that the model perform one additional operation on the set of similarities associated with a trial's study stimuli and p. In this additional operation, the similarities are processed with a max operator, which returns two values, the largest item {η₁ …η₃}, and the index (serial position) of that largest item. Hereafter, we refer to these returned quantities as value and index, respectively. The identification of the matching serial position is determined by the index, 1 … 3, returned by the max operator. Because of visual noise associated with each exemplar, there will be trials on which the index returned by max would not represent the serial position whose study item physically matched p, but would represent instead the serial position of another study item. On such trials, the model generates a temporal order error, in which the serial position of the matching item is misidentified. The probability of such errors will be some monotonically decreasing function of each study item's spatial frequency similarity to p. In other words, study items that did not match p but were spatially similar to it would be more likely misidentified as a match than would study items that were less spatially similar to p. Of course, this is the pattern of spatial similarity effects shown in Figure 1C and D, and suggests that once stimuli have been adjusted for small age-related differences in discriminability, there are little or no age-related differences in the internal noise in short-term memory that produces spatial-similarity based, temporal order lapses.

Second, consider how a different mechanism is required to motivate temporal similarity's influence on misidentifications of serial position. Drawing upon accounts of temporal effects in free recall (Howard & Kahana, 1999, 2002), we assume that the representation of each noisy exemplar is tagged in memory with a temporal code, and that each item's temporal tag could be misassigned at encoding, or degraded in memory by passage of time and/or interference. If this degradation were partial rather than complete (Dodson, Holland, & Shimamura, 1998), serially adjacent positions in a sequence would more likely be confused with one another than would be positions more widely separated in a sequence. In the case at hand, with partial loss of serial position information, s₁ is more likely misremembered as s₂ than as s₃, and s₃ is more likely misremembered as s₂ than as s₁. Again, this is the pattern of results seen in Figure 1C and D. We should note that this effect resembles Dodson et al.'s (1998) demonstration that even when individuals misidentify the source of information, they may retain partial information about that source. Clearly, our results suggest that young and older adults retain a form of such information in equal measure.