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Encoding, maintenance, and retrieval processes in the lag effect: A multinomial processing tree analysis

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Short-term studies on repeated learning of verbatim material have typically revealed an overall benefit of long lags compared to short lags between repetitions. This has been referred to as the lag effect. On educationally relevant time scales, however, an inverted-U-shaped relation between lag and memory performance is often observed. Recently, Cepeda et al. (2009) showed that the optimal lag for relearning depends heavily on the time interval between the last learning session and the final memory test (i.e., the retention interval; RI). In order to explore the cognitive mechanisms underlying this result in more detail we independently manipulated both the lag and the RI in a 3×2 experimental design and analysed our data using a multinomial processing tree model for free-then-cued-recall data. Our results reveal that the lag effect trends are mainly driven by encoding and maintenance processes rather than by retrieval mechanisms. Our findings have important implications for theories of the lag effect.
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Encoding, Maintenance, and Retrieval Processes 1
Running head: ENCODING, MAINTENANCE, AND RETRIEVAL IN THE LAG EFFECT
Encoding, Maintenance, and Retrieval Processes in the Lag Effect:
A Multinomial Processing Tree Analysis
Carolina E. Küpper-Tetzel and Edgar Erdfelder
University of Mannheim, Germany
Corresponding author’s address:
Carolina E. Küpper-Tetzel
University of Mannheim
L9, 7, room 209
68131 Mannheim, Germany
Phone: +49-621-181 3569
Fax: +49-621-181 3997
Email: kuepper-tetzel@psychologie.uni-mannheim.de
PublishedinMemory:
http://www.tandfonline.com/doi/abs/10.1080/09658211.2
011.631550#.Ul1aAVD2hak
Encoding, Maintenance, and Retrieval Processes 2
Abstract
Short-term studies on repeated learning of verbatim material have typically revealed an
overall benefit of long lags compared to short lags between repetitions. This has been referred
to as the lag effect. On educationally relevant time scales, however, an inverted-U-shaped
relation between lag and memory performance is often observed. Recently, Cepeda et al.
(2009) showed that the optimal lag for relearning heavily depends on the time interval
between the last learning session and the final memory test (i.e., the retention interval (RI)).
In order to explore the cognitive mechanisms underlying this result in more detail, we
independently manipulated both the lag and the RI in a 3 by 2 experimental design and
analysed our data using a multinomial processing tree model for free-then-cued-recall data.
Our results reveal that the lag effect trends are mainly driven by encoding and maintenance
processes rather than by retrieval mechanisms. Our findings have important implications for
theories of the lag effect.
Encoding, Maintenance, and Retrieval Processes 3
Acknowledgements
The authors are grateful to Kerstin Mertz and Jana Scheible for their considerable help with
data collection and to Pia Sue Helferich for editing the Multinomial Processing Tree graph.
We thank David Riefer and an anonymous reviewer for helpful comments on this manuscript.
Encoding, Maintenance, and Retrieval Processes 4
Encoding, Maintenance, and Retrieval Processes in the Lag Effect:
A Multinomial Processing Tree Analysis
The lag between initial learning (i.e., when new information is acquired for the first
time) and relearning (i.e., when this information is repeatedly studied) has a strong effect on
memory performance on a final test. The finding that memory performance benefits from
increasing lags between study episodes has been referred to as the lag effect. Past studies,
however, have profoundly challenged this simple lag effect finding (e.g., Ausubel, 1966;
Glenberg & Lehmann, 1980; Cepeda, Vul, Rohrer, Wixted, & Pashler, 2008). They have
shown that the retention interval (RI) (i.e., the time between the last study episode and the
final test) plays a crucial role in the modulation of the lag effect function. Glenberg and
Lehmann (1980), for instance, found that, given a 7-day RI, memory performance increased
between the massed practice condition and a 1-day lag condition, but decreased again for a
lag of 7 days between learning sessions. In other words, memory performance on the final
test administered after one week followed an inverted-U-shaped trend with increasing lag.
Recently, Cepeda et al. (2008) and Cepeda et al. (2009) investigated this effect at
educationally relevant time scales. Cepeda et al. (2009) conducted two experiments with RIs
of 10 and 168 days, respectively, combined with six different lags between initial learning
and relearning. They also found that memory performance on the final test followed an
inverted-U-shaped trend with increasing lag. The maximum of the lag effect function,
however, depended on the length of the RI. More precisely, the optimal lag between study
episodes increased as the RI increased. On the basis of an extensive web study, Cepeda et al.
(2008) formalised and reinforced this systematic relationship between lag and RI. Taken
together, these findings suggest that memory performance follows a nonmonotonic trend with
increasing lag, but that the optimal point in time for relearning increases with RI. We use the
term “lag effect” in a way that includes these recent findings.
Encoding, Maintenance, and Retrieval Processes 5
An important aspect that has not been examined yet is the contribution of encoding,
maintenance, and retrieval processes to the lag effect trends. Basically, improved memory in
the optimal lag condition compared to other study conditions could emerge from any
combination of three different influences: (1) enhanced encoding during repeated practice
leading to a strengthening of the memory trace, (2) improved maintenance leading to
enduring memory traces and resistance to forgetting until the time of testing, and (3) better
retrieval during the final test phase. The answer to the question about the exact contributions
of these memory processes to the lag effect is – to date – not only unknown, but also has
fundamental impact on the evaluation of lag effect explanations. All theories of the lag effect
proposed so far aim at explaining the emergence of the lag effect by focussing on different
memory processes.
The contextual variability theory (Glenberg, 1976, 1979) states that with increasing
lag more different context components are stored along with the to-be-learned information.
This boosts the probability of successful retrieval at final test because more effective retrieval
cues are available due to increased overlap between context components at test and at study.
Hence, retrieval should benefit from the increase in context variability associated with longer
lags. However, Glenberg (1976) also points out that longer lags must not always translate to
increased memory performance. If the RI is short compared to the lag between study sessions
inverted-U-shaped memory functions may occur because the retrieval cues at test are biased
towards the second learning occurrence, and thus, share less contextual components with the
stored memory trace which also contains contextual features from the first learning session.
According to the study-phase retrieval theory (Thios & D’Agostino, 1976), memory
performance improves when during the second occurrence of an item its first occurrence is
retrieved from memory. The second occurrence serves as a cue initiating automatic study-
phase retrieval. Successful study-phase retrieval is assumed to strengthen the stored memory
Encoding, Maintenance, and Retrieval Processes 6
trace. The benefit of successful retrieval during practice increases with lag because
successful study-phase retrieval is more effortful which, in turn, increases performance on the
test. However, lags may become too long and lead to a failure in study-phase retrieval
decreasing later memory performance.
The Multiscale Context Model (MCM) (Mozer, Pashler, Cepeda, Lindsey, & Vul,
2009) combines the Search of Associative Memory (SAM; Raaijmakers, 2003) and the
predictive utility theory (Staddon, Chelaru, & Higa, 2002). SAM encompasses assumptions
of the contextual variability and the study-phase retrieval theory. The novel aspect in MCM,
however, is the predictive utility assumption. It states that the time that elapses before the
reencounter of information (i.e., the lag) determines for how long this information will be
maintained in memory for the future. More precisely, if the to-be-learned material is
relearned after a long lag our memory system will store and, importantly, maintain the
material for a longer period of time. By contrast, if the lag is short the material will be
available for a short time only.
Taken together, the contextual variability theory, the study-phase retrieval theory, and
MCM offer plausible theoretical explanations for the lag effect. They can be distinguished,
however, with respect to the underlying memory processes they put forward to explain the
lag effect trends. The contextual variability theory emphasises the role of retrieval processes
during testing. The study-phase retrieval theory focuses on the importance of encoding
processes during repeated practice. MCM advances an adaptive feature of the memory
system and introduces the importance of maintenance processes. Thus, in order to evaluate
which theory makes the most plausible assumptions in terms of the underlying memory
processes it would be crucial to disentangle contributions of encoding, maintenance, and
retrieval processes to the lag effect.
Encoding, Maintenance, and Retrieval Processes 7
A paradigm that has often been used in the past to determine the role of storage (i.e.,
encoding or maintenance) versus retrieval processes makes use of two memory tests: one test
that depends highly on retrieval processes (e.g., free recall) followed by one that depends less
on retrieval processes (e.g., cued recall) (see, e.g., Drachman & Leavitt, 1972; Hogan &
Kintsch, 1971; Thomson & Tulving, 1970). Consequently, finding a memory effect in free
recall, but not in cued recall, suggests that retrieval processes play a major role for the
phenomenon. In contrast, if the effect emerges in both memory tests alike, this hints at the
conclusion that the phenomenon is rather driven by storage processes (i.e., encoding,
maintenance, or both).
Although performance profiles in the free-then-cued-recall paradigm provide valuable
information, a more fine-grained analysis of the memory processes involved would be
preferable. Multinomial processing tree (MPT) models (Batchelder & Riefer, 1999; Erdfelder
et al., 2009) offer such an analysis by providing separate estimates of the cognitive processes
underlying performance scores. In the past, MPT models have been used successfully to
disentangle storage and retrieval contributions to well-known memory phenomena, for
example, the bizarreness effect (Riefer & Rouder, 1992), the recognition failure effect (Riefer
& Batchelder, 1995), retroactive inhibition (Bäuml, 1991, 1996), and, more recently, the
enactment effect (Steffens, Jelenec, Mecklenbräuker, & Thompson, 2006; Steffens, Jelenec,
& Mecklenbräuker, 2009).
Thus, in order to evaluate prevailing theories of the lag effect, we examined the role
of encoding, maintenance, and retrieval processes by assessing memory performance with
both free and cued recall tests and by analysing the data with an extended1 version of Rouder
and Batchelder’s (1998) storage-retrieval MPT model for a free-then-cued-recall paradigm.
In our study, we assessed joint effects of different lags and RIs on memory
performance. Critically to our approach, memory performance was assessed by a free recall
Encoding, Maintenance, and Retrieval Processes 8
test on weakly associated cue-target word pairs immediately followed by a cued recall test for
the target word given the cue word. Based on the performance on the cued recall test at the
end of practice combined with the performances on the free and cued recall final tests
administered after the RI, 12 observable events can occur for each word pair (Table 1).
(Table 1 about here)
Based on the observed frequencies of these 12 events, MPT modelling allows
estimation of seven parameters representing underlying memory processes: one probability of
associative encoding (e), two probabilities of associative maintenance in memory until the
final test (ms and mu for maintenance following successful vs. unsuccessful initial cued recall,
respectively), two probabilities of successful retrieval in free and cued recall (rf and rc,
respectively), and, finally, two probabilities of single word retrieval in free recall in case of
successful vs. unsuccessful associative encoding or maintenance (s and u, respectively).
(Figure 1 about here)
To facilitate the understanding of this method, the extended MPT model is presented
as a processing tree diagram in Figure 1. It has 32 branches, each terminating in one of the 12
events summarized in Table 1. Each of these branches represents a possible sequence of
encoding, maintenance, and retrieval processes underlying performance in free and cued
recall. Specifically, a word pair is either encoded as an association with probability e or is not
encoded as an association with the complementary probability 1-e. In case of successful
associative encoding, cued recall at the end of practice may be successful with probability rc
or fail with probability 1-rc. Hence, parameter rc represents the probability of successful
associative retrieval in a cued recall test and is likely to be close to one whenever the cue-
target association is stored in memory at the time of testing. Associative maintenance to the
time of testing occurs upon encoding and successful initial cued recall with probability ms. If
associative maintenance of the word pair is successful (ms), associative retrieval during final
Encoding, Maintenance, and Retrieval Processes 9
cued recall may be successful with probability rc or unsuccessful with the complementary
probability 1-rc. In either case, the intact word pair may be retrieved during free recall with
probability rf resulting in event E1 (in case of successful final cued recall) or E4 (in case of
unsuccessful final cued recall). Associative retrieval during free recall, however, may fail
with probability 1-rf, so that the intact word pair cannot be retrieved as association.
Nevertheless, each word of a pair may be independently retrieved during free recall with
probability s or not retrieved with probability 1-s, so that both words of a pair (E1 or E4,
depending on successful vs. unsuccessful final cued recall, respectively), exactly one word
(E2 or E5, depending on successful vs. unsuccessful final cued recall, respectively), or neither
word is recalled (E3 or E6, depending on successful vs. unsuccessful final cued recall,
respectively). In contrast, if maintenance of the word pair association in memory fails (1-ms),
the final cued recall will also fail. However, items may be retrieved (u) or not retrieved (1-u)
as nonassociated single words during free recall, so that both words of a pair (E4), exactly one
word (E5), or neither word is recalled (E6)2. Moreover, successful associative maintenance
may also occur following unsuccessful cued recall at the end of learning, albeit with
probability mu that may, in principle, differ from ms. From there, the MPT tree progresses as
described above except that the branches terminate in event categories E7 to E12 instead.
Finally, associative encoding can fail altogether with probability 1-e. This implies a failure of
both cued recall at the end of practice and final cued recall. However, items may be retrieved
(u) or not retrieved (1-u) independently as nonassociated single words during free recall, so
that both words of a pair (E10), exactly one word (E11), or neither word is recalled (E12).
Summing up the branch probabilities that terminate in the same observable event, we obtain
the following set of model equations for the 12 possible events:
p(E1) = e rc2 ms [rf +(1-rf) s2]
p(E2) = 2 e rc2 ms (1-rf) s (1-s)
p(E3) = e rc2 ms (1-rf) (1-s)2
p(E4) = e rc [ms (1-rc) (rf + (1-rf) s2) + (1-ms) u2]
Encoding, Maintenance, and Retrieval Processes 10
p(E5) = 2 e rc [ms (1-rc) (1-rf) s (1-s) + (1-ms) u (1-u)]
p(E6) = e rc [ms (1-rc) (1-rf) (1-s)2 + (1-ms) (1-u)2]
p(E7) = e (1-rc) rc mu [rf + (1-rf) s2]
p(E8) = 2 e (1-rc) rc mu (1-rf) s (1-s)
p(E9) = e (1-rc) mu rc (1-rf) (1-s)2
p(E10) = e (1-rc) [mu (1-rc) (rf + (1-rf) s2) + (1-mu) u2] + (1-e) u2
p(E11) = 2 [e (1-rc)2 mu (1-rf) s (1-s) + e (1-rc) (1-mu) u (1-u) + (1-e) u (1-u)]
p(E12) = e (1-rc) [mu (1-rc) (1-rf) (1-s)2 + (1-mu) (1-u)2] + (1-e) (1-u)2
On the basis of the observed event frequencies, the seven model parameters (e, ms, mu,
rc, rf, s, and u) are then estimated using standard maximum likelihood techniques (Hu &
Batchelder, 1994) as implemented in freely available software for MPT models (e.g.,
Moshagen, 2010). The parameters of Rouder and Batchelder’s original free-then-cued-recall
MPT model have previously been validated experimentally by applying specific
manipulations that were assumed to influence one parameter (e.g., retrieval) while leaving
others (e.g., storage) unaffected (see Rouder & Batchelder, 1998). Thus, it has been
established that the model not only fits empirical data but also provides parameters that
capture the intended memory processes selectively. Our MPT model keeps all the basic
assumptions of Rouder and Batchelder’s (1998) model and represents a straightforward
extension by (1) differentiating between processes of encoding and processes of maintenance
to the time of testing and by (2) providing an estimate of associative retrieval during cued
recall in addition. Therefore, it seems appropriate to use our extended MPT model to measure
encoding, maintenance, and retrieval contributions to the trends in the lag effect and, more
importantly, to evaluate theoretical explanations of the lag effect.
Method
Participants
Sixty-two persons participated in this experiment. Two participants were excluded
from all analyses because they severely underperformed during the relearning session (cued
Encoding, Maintenance, and Retrieval Processes 11
recall performance < 40%). The remaining 60 participants were current students or alumni of
the University of Mannheim. Thirty-seven were female, mean age 22.45 (range, 18-33).
Materials
The word material consisted of 30 weakly associated cue-target word pairs from 30
common categories. All words were concrete German nouns taken from German production
norms (Hager & Hasselhorn, 1994). Both words of a pair always came from the same
category (e.g., foods). The cue word was a weakly associated word of the category (e.g.,
candy, production index < 0.02) and the respective target word was one of the four most
frequently produced words for that category (e.g., bread). Weakly associated word pairs were
used to avoid inferential processes during recall. In order to ensure that significant effects
would not be due to word list characteristics, we constructed four word lists, each containing
30 target words with high associations to their respective category and to each other (e.g.,
category: foods, target words: bread, meat, butter, vegetables). These four target word lists
were counterbalanced across participants. Thus, the same cue word was combined with one
target word that varied depending on the active word list.
Design
The experiment consisted of two learning sessions separated by a lag and one final
test session occurring after the RI. The lag between learning sessions was either 0 days, 1
day, or 11 days and the RI was either 7 or 35 days. This resulted in a 3 x 2 between-subjects
design. These intervals were chosen on the basis of Cepeda et al. (2008), who suggest an
inverted-U-shaped memory trend in the 7-day RI group (i.e., peak at a 1-day lag) and a
positive linear trend in the 35-day RI group for lags increasing from 0 to 11 days. Participants
were randomly assigned to their experimental condition, subject to the constraint of their
Encoding, Maintenance, and Retrieval Processes 12
availability for attending sessions on different days. Four experimental conditions contained
10 participants each and two conditions contained 9 and 11 participants, respectively.
Procedure
Participants attended two learning sessions and one test session. During the first
learning session, participants worked on two study-test trials. The 1-day lag and 11-day lag
group were dismissed after these trials and returned after the respective lag to their second
learning session. The 0-day lag group worked for five minutes on an unrelated distractor task
and continued with the second learning session on the same day. The second learning session
contained one more study-test trial. After the second learning session, all participants were
dismissed and returned after a RI of either 7 or 35 days to the final test session.
A study-test trial consisted of a study phase, a distractor task, and a test phase. During
the study phase, each word pair was presented for three seconds separated by a 750
milliseconds interstimulus interval. Word pairs were presented in a different random order in
each study phase. After the study phase, participants worked for two minutes on an unrelated
arithmetic task. Afterwards, participants were administered a free recall test immediately
followed by a cued recall test. Both memory tests were self-paced. For the free recall test,
they were instructed to write all word pairs they could remember on a lined recall sheet. It
was pointed out to them that if they could only remember one word of a pair, they should
nevertheless write it down. For the cued recall test, participants were presented with the cue
word and asked to recall and type the correct target word. They were asked to recall all 30
target words given the cue. The cues were presented sequentially in random order.
Participants could skip to the next cue word if they could not remember the target word. They
were not provided with feedback about their performance during the memory tests.
On the final test session, participants worked on a free recall test immediately
followed by a cued recall test. Afterwards, they were compensated for their participation and
Encoding, Maintenance, and Retrieval Processes 13
debriefed. The whole experiment lasted about 1.5 hours divided over three sessions. All
participants were required to attend three sessions on three different days. Participants in the
0-day lag condition who completed the experiment within two sessions worked for 15
minutes on an unrelated experiment during their third session. This was done to establish
comparable motivational conditions for all participants.
Results
Learning performance
Participants showed good learning performances in both memory tests at the end of the
first learning session after two study-test trails, 52% free-recall accuracy and 83% cued-recall
accuracy. Moreover, as expected, free and cued recall performances assessed by the end of
the first learning session were not affected by lag, F(2,57) = 1.31, p = .279, p2 = .04 and
F(2,57) = 1.24, p = .297, p2 = .04, respectively.
Memory performance in the relearning session (i.e., after the lag) showed the expected
decline in free and cued recall as a consequence of increasing lag. We performed multiple
comparisons and adjusted the α-level of .05 using the Holm-Bonferroni correction method
(Holm, 1979). All significance tests are reported with p-values corresponding to two-tailed
tests even when directed hypotheses were imposed. The Welch test was applied whenever
Levene’s test indicated unequal variances at = .05. Memory performance on both memory
tests was significantly lower during practice after an 11-day lag compared to a 1-day lag
(free-recall accuracy: 48% vs. 69%; cued-recall accuracy: 78% vs. 96%), t(32.76) = 3.51, p =
.001, 2 = 0.27 and t(20.80) = 3.74, p = .001, 2 = 0.40 for free and cued recall, respectively.
Also, the decrease between a 0-day lag and an 11-day lag was significant (free-recall
accuracy: 70% vs. 48%; cued-recall accuracy: 92% vs. 78%), t(38) = 3.52, p = .001, 2 = 0.25
and t(23.98) = 2.81, p = .010, 2 = 0.25 for free and cued recall, respectively. There was no
Encoding, Maintenance, and Retrieval Processes 14
significant difference in memory performance between the 0-day and the 1-day lag condition,
all ts 1.69, ps .10.
Final test performance
An initial analysis of the final test performance revealed that there was no systematic
effect due to the counterbalance factor word list neither for free recall nor for cued recall,
F(3,56) = 1.16, p = .332, p2 = .06 and F(3,56) = 1.05, p = .376, p2 = .05, respectively. Thus,
for further analyses, data were collapsed across the four word lists. An α-level of .05 was
used for all statistical tests. Again, significance tests are reported as two-tailed tests even in
case of directed predictions.
Not surprisingly, participants recalled more word pairs on both memory tests after a
7-day RI (free recall: M = 41%, SD = 20; cued recall: M = 74%, SD = 23) than after a 35-day
RI (free recall: M = 19%, SD = 17; cued recall: M = 43%, SD = 23), t(58) = -4.43, p < .001,
2 = 0.25 and t(58) = -5.12, p < .001, 2 = 0.31 for free and cued recall, respectively.
Of greatest interest, however, were the different trends in the two RI conditions as a
function of increasing lag. To revisit, we expected that with increasing lag (0-day < 1-day <
11-day) memory performance would follow an inverted-U-shaped trend (i.e., negative
quadratic trend) in the 7-day RI group and a positive linear (or at least monotonically
increasing) trend in the 35-day RI group. Descriptively, the data fit our expectations nicely
(see Figure 2). In fact, a significant negative quadratic trend emerged in the 7-day RI
condition for cued recall, t(27) = 2.08, p = .048, 2 = 0.14, and a marginally significant
quadratic trend occurred for free recall, t(27) = 1.71, p = .099, 2 = 0.10. In contrast, the
linear trend was neither significant for free recall, t(27) = 1.07, p = .292, 2 = 0.04, nor for
cued recall, t(27) = -0.25, p = .807, 2 < 0.01. In the 35-day RI condition, however, a
significant positive linear trend was detected for both free recall, t(27) = 2.24, p = .033, 2 =
Encoding, Maintenance, and Retrieval Processes 15
0.16, and cued recall, t(27) = 2.79, p = .010, 2 = 0.22. The quadratic trend was not
significant in this condition, neither for free recall, t(27) = 0.71, p = .482, 2 = 0.02, nor for
cued recall, t(27) = 0.52, p = .606, 2 = 0.01.
(Figure 2 about here)
Model-based analyses
Our extended MPT model for free-then-cued-recall was used to disentangle encoding,
maintenance, and retrieval contributions to free and cued recall in the final memory test. For
model-based analyses, the frequencies of the 12 event categories were calculated for each
participant and aggregated separately for each of the 3 x 2 = 6 experimental conditions,
resulting in N = 1,800 data points in total. The Type I error level was set to α = .05 for all
model-based analyses. A sensitivity analysis was performed using G*Power 3.1 (Faul,
Erdfelder, Buchner, & Lang, 2009). This analysis showed that with a sample size of N =
1,800 data points, a significance level of α = .05, and a desired power of 1-β = .95, the
detectable effect size for G2 goodness-of-fit tests based on df 30 is ω 0.14 (i.e., a small
effect; cf. Cohen, 1988). Thus, all G2 tests reported below allowed detecting already small
deviations from the model. The multiTree software (Moshagen, 2010) was used for all MPT
model analyses reported here. To revisit, our extended free-then-cued-recall MPT model
contains seven parameters (e, ms, mu, rc, rf, s, and u) per condition (see Figure 1), that is, 6 · 7
= 42 parameters across all six conditions. Hence, the overall goodness-of-fit test has 6 · (12-
1) – 42 = 24 degrees of freedom. This general model fitted the data well (G2(24) = 19.65, p =
.716). To specify our model as parsimoniously as possible and to increase the precision of
parameter estimates, we tested the additional restriction that the maintenance probabilities ms
and mu can be set equal in each condition. A priori, we hypothesised that ms > mu, because
success in associative cued recall at the end of practice is likely to have positive effects on
subsequent maintenance. However, as revealed by a G2 difference test, this effect was not
Encoding, Maintenance, and Retrieval Processes 16
significant in our data, G2(6) = 1.44, p = .964. Consequently, we report results based on the
more parsimonious version of our extended model that contains a single maintenance
parameter m only.3 The overall goodness-of-fit test for this restricted model has 6 · (12-1) –
36 = 30 degrees of freedom and indicates an excellent fit to the data (G2(30) = 21.09, p =
.885).
Parameter Estimates. Of greatest interest for our research question are the probability
estimates for associative encoding e, associative maintenance m, and associative retrieval rf
presented in the upper, middle, and lower chart of Figure 3, respectively.
(Figure 3 about here)
The associative encoding parameter e followed an inverted-U-shaped trend with
increasing lag in both RI conditions (Figure 3, upper chart). More specifically, the probability
of associative encoding increased significantly between the 0-day and the 1-day lag
condition, ΔG2(1) = 6.60, p = .010 and ΔG2(1) = 5.90, p = .015, and decreased between the 1-
day lag and the 11-day lag condition, ΔG2(1) = 57.12, p < .001 and ΔG2(1) = 27.36, p < .001,
for the 7- and 35-day RI group, respectively. In line with our expectations, associative
encoding was not affected by the length of the RI, ΔG2(3) = 4.28, p = .233. This result is
important because it shows that the additional associative encoding parameter e in our
extended MPT model can be considered as a valid measure of encoding processes at practice
that is not affected by the length of the RI.
The parameter for associative maintenance m, however, was affected differently by
the length of the RI (Figure 3, middle chart). In the 7-day RI group, associative maintenance
increased between the 0-day lag and the 1-day lag as well as the 11-day lag, ΔG2(1) = 20.49,
p < .001 and ΔG2(1) = 17.25, p < .001, respectively. There was no difference in associative
maintenance between the 1-day and the 11-day lag, ΔG2(1) = 0.06, p = .813. In the 35-day RI
condition, associative maintenance increased significantly between the 0-day lag and the 1-
Encoding, Maintenance, and Retrieval Processes 17
day lag, ΔG2(1) = 15.44, p < .001, and increased further between the 1-day and the 11-day
lag, ΔG2(1) = 18.20, p < .001.
In addition, we tested the difference in m between the two RI conditions for each lag.
As expected, better associative maintenance of the material emerged in the 7-day RI
condition than in the 35-day RI condition for all lag conditions, ΔG2(1) = 104.60, p < .001,
ΔG2(1) = 112.51, p < .001, and ΔG2(1) = 30.52, p < .001, for 0-, 1-, and 11-day lag,
respectively. Again, this validates the current MPT model because the length of the RI should
have a strong negative impact on maintenance of the to-be-learned material to the time of
testing.
The parameter estimates for associative retrieval rf during free recall are presented in
the lower chart of Figure 3. In the 7-day RI condition, associative retrieval increased
significantly between the 0-day lag and the 1-day lag as well as the 11-day lag, ΔG2(1) =
6.79, p < .009 and ΔG2(1) = 7.51, p = .006, respectively. We found the same results in the 35-
day RI group, for the comparison between 0-day and 1-day lag, ΔG2(1) = 4.45, p = .035, and
for the comparison between 0-day and 11-day lag, ΔG2(1) = 4.12, p = .043. Importantly, the
probability of associative retrieval did not differ significantly between the two distributed
learning conditions, neither for the 7-day RI, ΔG2(1) = 0.15, p = .695, nor for the 35-day RI,
ΔG2(1) = 0.04, p = .849.
In addition, we analysed the difference in associative retrieval between the two RI
groups for each lag condition. Not surprisingly, the probability of associative retrieval in free
recall was significantly smaller after a 35-day RI than after a 7-day RI for all lag conditions,
ΔG2(1) = 5.49, p = .019, ΔG2(1) = 4.91, p = .027, and ΔG2(1) = 7.46, p = .006, for a 0-, 1-,
and 11-day lag, respectively.
Last but not least, estimates of the associative cued recall probability rc (not shown in
Figure 3) differed significantly between conditions, G2(5) = 24.25, p < .001. However, as
Encoding, Maintenance, and Retrieval Processes 18
expected, all six rc parameter estimates were very close to 1, ranging between .96 and 1.00
with a mean of .99. This result is roughly in line with the original free-then-cued-recall MPT
model (Rouder & Batchelder, 1998) which is based on the simplifying approximation rc = 1.
Discussion
Our data convincingly show that different lags of relearning can affect memory
performance either in a linear or in a negatively accelerated quadratic manner depending on
the length of the RI. More precisely, in the 7-day lag condition, we revealed an inverted-U-
shaped trend with increasing lag. Memory performance in this condition peaked at a 1-day
lag and decreased for shorter or longer lags. In contrast, in the 35-day RI condition, memory
performance increased with lag, thereby suggesting that memory performance improves from
a 0-day to an 11-day lag. Thus, we successfully replicated the lag effect trends detected by
Cepeda et al. (2008).
The model-based analyses contribute to a better understanding of the underlying
cognitive processes. Our extended MPT model for free-then-cued-recall based on Rouder and
Batchelder (1998) fit the empirical data successfully. Not surprisingly, associative retrieval
decreased with the length of the RI. The lag effect trends, however, were particularly driven
by processes captured by the associative encoding parameter e and the associative
maintenance parameter m. We found a systematic interplay between encoding and
maintenance processes that influenced memory performance in the final test and that was
mediated by the length of the RI.
More precisely, associative encoding revealed an inverted-U-shaped trend in both the
7-day and the 35-day RI condition alike. This result represents the drop in learning
performance after a long lag (i.e., 11 days) compared to a short lag (i.e., 1 day) – a result that
is in line with earliest findings in memory research (Ebbinghaus, 1885/1964). Memory
performance after a short RI of 7 days was particularly affected by this inverted-U-shaped
Encoding, Maintenance, and Retrieval Processes 19
trend in associative encoding. In this condition, associative maintenance and associative
retrieval (captured by rf) both increased between the massed and the spaced conditions, but
there was no further significant difference between the two spaced conditions. In contrast, in
the long 35-day RI condition, the detrimental effect of poor encoding after a long lag of 11
days was outweighed by better associative maintenance processes. Thus, the positive effect of
increasing lag for memory performance after a RI of 35 days was most certainly due to
enhanced associative maintenance processes. Note that retrieval processes cannot explain this
effect because the associative retrieval parameter rf reflected the advantage of spaced practice
over massed practice only and was not sensitive to lags of different lengths. However, the
latter finding is consistent with previous research suggesting that spaced practice, in general,
leads to enhanced retrieval compared to massed practice (e.g., Batchelder & Riefer, 1980).
Taken together, encoding processes dictated the inverted-U-shaped memory
performance in the 7-day RI condition, whereas maintenance processes to the time of testing
were responsible for the linear increasing memory performance in the 35-day RI condition
with increasing lag. Thus, given a long RI, the detrimental effects of decreased encoding as a
consequence of a long lag are outweighed by better maintenance processes of the encoded
memory traces.
Consequently, a theory that attempts to explain the lag effect must emphasise the
crucial roles and interplay of encoding and maintenance processes for this learning effect.
Thus, the contextual variability theory, which conceives retrieval processes at test as most
important, cannot be considered as a potential candidate for explaining the processes
producing the curvilinear lag effect trend. Nevertheless, the MPT results show that the
contextual variability theory can account for the spacing effect since the advantage of spaced
over massed practice was reflected in the associative retrieval parameter.
Encoding, Maintenance, and Retrieval Processes 20
Our model findings suggest that both the study-phase retrieval theory and the
predictive utility assumption of MCM provide the most plausible explanations for the lag
effect trends. In accordance with the study-phase retrieval account, better encoding occurred
after a lag of 1 day compared to the massed condition. However, if the lag becomes too long
(e.g., 11-day lag), successful study-phase retrieval may fail, which leads to decreased
encoding. This, in turn, has negative effects on the later memory performance. The inverted-
U-shaped memory performance on the final test after a 7-day RI is consistent with this
explanation. MCM endorses the crucial role of forgetting and proposes that more enduring
memory traces are stored after a long lag compared to a short lag between study episodes.
Using MPT modelling, we were able to find that the linear increasing lag effect in the 35-day
RI condition was specifically affected by the model parameter that captures maintenance of
the material to the time of testing. Thus, consistent with MCM, the memory traces that were
encoded after an 11-day lag were maintained better than memory traces that were encoded
after a 1-day lag. This proved to be particularly beneficial if memory performance was
assessed after a long 35-day RI.
Taken together, our MPT analyses showed that the study-phase retrieval theory and
the predictive utility assumption of MCM offer the most plausible assumptions in regard to
the underlying cognitive mechanisms for the lag effect. The current findings suggest that the
shift of optimal lag with RI is not due to a single mechanism, but rather to a systematic
interplay of encoding and maintenance processes that is moderated by the length of the RI.
References
Ausubel, D. P. (1966). Early versus delayed review in meaningful learning. Psychology in the
Schools, 3, 195-198. doi: 10.1002/1520-6807(196607)3:3<195::AID-
PITS2310030302>3.0.CO;2-X
Encoding, Maintenance, and Retrieval Processes 21
Batchelder, W. H., & Riefer, D. M. (1980). Separation of storage and retrieval factors in free
recall of clusterable pairs. Psychological Review, 87, 375-397. doi: 10.1037/0033-
295X.87.4.375
Batchelder, W. H., & Riefer, D. M. (1999). Theoretical and empirical review of multinomial
process tree modeling. Psychonomic Bulletin & Review, 6, 57-86. doi:
10.3758/BF03210812
Bäuml, K.-H. (1991). Experimental analysis of storage and retrieval processes involved in
retroactive inhibition – The effect of presentation mode. Acta Psychologica, 77, 103-
119. doi: 10.1016/0001-6918(91)90026-V
Bäuml, K.-H. (1996). A Markov model for measuring storage loss and retrieval failure in
retroactive inhibition. Acta Psychologica, 92, 231-250. doi: 10.1016/0001-
6918(95)00018-6
Cepeda, N. J., Coburn, N., Rohrer, D., Wixted, J. T., Mozer, M. C., & Pashler, H. (2009).
Optimizing distributed practice: Theoretical analysis and practical implications.
Experimental Psychology, 56, 236-246. doi: 10.1027/1618-3169.56.4.236
Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008). Spacing effects in
learning: A temporal ridgeline of optimal retention. Psychological Science, 19, 1095-
1102. doi: 10.1111/j.1467-9280.2008.02209.x
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2. ed.). Hillsdale, NJ:
Erlbaum.
Drachman, D. A., & Leavitt, J. (1972). Memory impairment in the aged: Storage versus
retrieval deficit. Journal of Experimental Psychology, 93, 302-308. doi:
10.1037/h0032489
Ebbinghaus, H. (1885/1964). Memory: A contribution to experimental psychology. Oxford
England: Dover.
Encoding, Maintenance, and Retrieval Processes 22
Erdfelder, E., Auer, T.-S., Hilbig, B. E., Aßfalg, A., Moshagen, M., & Nadarevic, L. (2009).
Multinomial processing tree models: A review of the literature. Zeitschrift für
Psychologie – Journal of Psychology, 217, 108-124. doi: 10.1027/0044-
3409.217.3.108
Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). Statistical power analyses using
G*Power 3.1: Tests for correlation and regression analyses. Behavior Research
Methods, 41, 1149-1160. doi: 10.3758/BRM.41.4.1149
Glenberg, A. M. (1976). Monotonic and nonmonotonic lag effects in paired-associate and
recognition memory paradigms. Journal of Verbal Learning and Verbal Behavior, 15,
1-16. doi: 10.1016/S0022-5371(76)90002-5
Glenberg, A. M. (1979). Component-levels theory of the effects of spacing of repetitions on
recall and recognition. Memory & Cognition, 7, 95-112. doi: 10.3758/BF03197590
Glenberg, A. M., & Lehmann, T. S. (1980). Spacing repetitions over 1 week. Memory &
Cognition, 8, 528-538. doi: 10.3758/BF03213772
Hager, W., & Hasselhorn, M. (1994). Handbuch deutschsprachiger Wortnormen [Handbook
of German word norms]. Göttingen: Hogrefe.
Hogan, R. M., & Kintsch, W. (1971). Differential effects of study and test trials on long-term
recognition and recall. Journal of Verbal Learning and Verbal Behavior, 10, 562-567.
doi: 10.1016/S0022-5371(71)80029-4
Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian
Journal of Statistics, 6, 65-70.
Hu, X. & Batchelder, W. H. (1994). The statistical analysis of general processing tree
models with the EM algorithm. Psychometrika, 59, 21-47. doi: 10.1007/BF02294263
Encoding, Maintenance, and Retrieval Processes 23
Moshagen, M. (2010). multiTree: A computer program for the analysis of multinomial
processing tree models. Behavior Research Methods, 42, 42-54. doi:
10.3758/BRM.42.1.42
Mozer, M. C., Pashler, H., Cepeda, N. J., Lindsey, R., & Vul, E. (2009). Predicting the
optimal spacing of study: A multiscale context model of memory. In Y. Bengio, D.
Schuurmans, J. Lafferty, C. K. I. Williams, & A. Culotta (Eds.), Advances in neural
information processing systems (p. 1321-1329). La Jolla, CA: NIPS Foundation.
Raaijmakers, J. G. (2003). Spacing and repetition effects in human memory: Application of
the SAM model. Cognitive Science: A Multidisciplinary Journal, 27, 431-452.
doi:10.1016/S0364-0213(03)00007-7
Riefer, D. M., & Batchelder, W. H. (1995). A multinomial modeling analysis of the
recognition-failure paradigm. Memory & Cognition, 23, 611-630. doi:
10.3758/BF03197263
Riefer, D. M., & Rouder, J. N. (1992). A multinomial modeling analysis of the mnemonic
benefits of bizarre imagery. Memory & Cognition, 20, 601-611. doi:
10.3758/BF03202710
Rouder, J. N., & Batchelder, W. H. (1998). Multinomial models for measuring storage and
retrieval processes in paired associate learning. In C. E. Dowling, F. S. Roberts, & P.
Theuns (Eds.), Recent progress in mathematical psychology: Psychophysics,
knowledge, representation, cognition, and measurement. (pp. 195-225). Mahwah, NJ:
Lawrence Erlbaum Associates Publishers.
Staddon, J. E. R., Chelaru, I. M., & Higa, J. J. (2002). Habituation, memory and the brain:
The dynamics of interval timing. Behavioural Processes, 57, 71-88. doi:
10.1016/S0376-6357(02)00006-2
Encoding, Maintenance, and Retrieval Processes 24
Steffens, M. C., Jelenec, P., & Mecklenbräuker, S. (2009). Decomposing the memory
processes contributing to enactment effects by multinomial modelling. European
Journal of Cognitive Psychology, 21, 61-83. doi: 10.1080/09541440701868668
Steffens, M. C., Jelenec, P., Mecklenbräuker, S., & Thompson, E. M. (2006). Decomposing
retrieval and integration in memory for actions: A multinomial modelling approach.
Quarterly Journal of Experimental Psychology, 59, 557-576. doi:
10.1080/02724980443000764
Thios, S. J., & D'Agostino, P. R. (1976). Effects of repetition as a function of study-phase
retrieval. Journal of Verbal Learning & Verbal Behavior, 15, 529-536.
doi:10.1016/0022-5371(76)90047-5
Thomson, D. M., & Tulving, E. (1970). Associative encoding and retrieval: Weak and strong
cues. Journal of Experimental Psychology, 86, 255-262. doi: 10.1037/h0029997
Encoding, Maintenance, and Retrieval Processes 25
Footnotes
1 Rouder and Batchelder’s (1998) original MPT model for free-then-cued-recall differs from
our extended model mainly by using a single storage parameter that combines encoding and
maintenance processes. For our research question, however, it was crucial to differentiate
between encoding and maintenance processes. Inclusion of cued recall performances at the
end of practice (i.e., in the relearning session after the lag) enabled us to introduce an
additional encoding parameter and to decompose Rouder and Batchelder’s associative storage
parameter a into associative encoding and maintenance parameters, e und m, respectively.
Keeping the basic assumptions of Rouder and Batchelder’s MPT model unchanged, our
extension provides separate estimates for associative encoding, maintenance, retrieval in cued
recall, and retrieval in the final free recall test.
2 One reviewer pointed out correctly that the MPT model does not distinguish between the
probability to recall the cue and the probability to recall the target. Rather, a single parameter
s or u is assigned to the independent retrieval of one word of the pair, irrespective of whether
it is a cue or target. This model assumption, most certainly, represents an approximation that
allows us to keep the model as simple and parsimonious as possible. Nevertheless, we
checked whether cues and targets were recalled equally often. This was indeed the case for all
but one experimental condition: Only in the 11-day lag group that was tested after a 35-day
RI, participants recalled slightly more targets (M = 11, SD = 5.9) than cues (M = 9, SD = 5.7)
in the final free recall test, t(9) = 3.35, p = .008. In all other five conditions differences were
even smaller and not significant (all ts 2.06, all ps .067). Thus, for the sake of simplicity
and model parsimony, since the difference in cue and target recall in our experiment was
small and the s and u parameters were not of major interest for the current research question,
we decided not to distinguish between cue and target retrieval.
Encoding, Maintenance, and Retrieval Processes 26
3 We would like to point out that the restriction ms = mu= m has negligible effects on
estimates of the other parameters. Estimates for m reported in the present paper resemble
those for ms in the unrestricted version of the extended model. In other words, substantive
conclusions are not affected by the version of the extended model used for data analyses.
Encoding, Maintenance, and Retrieval Processes 27
Figure Captions
Figure 1. Extended MPT model for a free-then-cued-recall paradigm to disentangle encoding,
maintenance, and retrieval processes based on Rouder and Batchelder (1998). The processing
tree presents the latent cognitive processes leading to 12 observable event categories:
Successful cued recall at the end of practice, successful final cued recall and free recall of the
complete word pair (E1), exactly one word of the pair (E2), or neither word of the pair (E3) or
successful cued recall at the end of practice, unsuccessful final cued recall and free recall of
the complete word pair (E4), exactly one word of the pair (E5), or neither word of the pair
(E6) or unsuccessful cued recall at the end of practice, successful final cued recall and free
recall of the complete word pair (E7), exactly one word of the pair (E8), or neither word of
the pair (E9) or unsuccessful cued recall at the end of practice, unsuccessful final cued recall
and free recall of the complete word pair (E10), exactly one word of the pair (E11), or neither
word of the pair (E12). The transition probabilities between cognitive states (rounded
rectangles) are represented by the model parameters (e = probability of associative encoding
during study, ms, mu = probability of associative maintenance to the time of testing upon
successful encoding (following successful or unsuccessful cued recall at the end of practice,
respectively), rc = probability of associative retrieval during cued recall, rf = probability of
associative retrieval during free recall, s = probability of associated single word retrieval
during free recall, u = probability of nonassociated single word retrieval during free recall).
Figure 2. Mean and standard errors of correctly recalled word pairs on the final free recall
(upper chart) and final cued recall test (lower chart) as a function of lag and retention
interval.
Figure 3. Parameter estimates and standard errors for the probability of associative encoding
e (upper chart), for the probability of associative maintenance m (middle chart), and for the
probability of associative retrieval rf (lower chart) as a function of lag and retention interval.
Encoding, Maintenance, and Retrieval Processes 28
Table 1. Twelve event categories for a memory paradigm that combines cued recall
performance at the end of practice with final free and cued recall performances.
Cued recall at
end of practice Final cued
recall Final free recall
Both words Exactly one word Neither word
Correct Correct E1 E
2 E
3
Incorrect E4 E
5 E
6
Incorrect Correct E7 E
8 E
9
Incorrect E10 E
11 E
12
Encoding, Maintenance, and Retrieval Processes 29
Figure 1
Encoding, Maintenance, and Retrieval Processes 30
0
10
20
30
40
50
60
70
80
90
100
0days 1day 11days
InterstudyInterval
0
10
20
30
40
50
60
70
80
90
100
0days 1day 11days
InterstudyInterval
RI=7days
RI=35days
Figure 2
Correctlyrecalledwordpairsin%
FreeRecall
CuedRecall
Encoding, Maintenance, and Retrieval Processes 31
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0days 1day 11days
Probability estimate for
associative encoding e
InterstudyInterval
RI=7days RI=35days
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0days 1day 11days
Probability estimate for
associative maintenance m
InterstudyInterval
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0days 1day 11days
Probability estimate for
associative retrieval rf
InterstudyInterval
Figure 3
... Several studies indicate that the optimal spacing interval durationproviding maximal memory performancedepends on and changes with the retention interval duration. As a consequence there is no overall best spacing interval duration, but instead the optimal spacing interval duration, but also the U-shape pattern, described above, depend on the time point the learner is finally tested (e.g., [17,[20][21][22]). In a comprehensive meta-analysis, Cepeda et al. [5] already provided evidence for the relation between spacing and retention intervals. ...
... Memory formation can roughly be subdivided into three major steps (e.g., [24]): Encoding (transformation of environmental information into working memory), consolidation (transfer of working memory content into longer term memory stores) and retrieval (reactivation of memory contents stored in the brain). Evidence from recent studies even indicate a fourth major step, namely maintenance [20][21][22]26]. Of course, test performance reflects a mixture of all three or four major steps and we cannot claim that our analysis of the Learning Period purely reflects encoding and consolidation and the analysis of the Final Test Period purely retrieval (but see [20] for a nice way of disentangling). ...
... Evidence from recent studies even indicate a fourth major step, namely maintenance [20][21][22]26]. Of course, test performance reflects a mixture of all three or four major steps and we cannot claim that our analysis of the Learning Period purely reflects encoding and consolidation and the analysis of the Final Test Period purely retrieval (but see [20] for a nice way of disentangling). In future studies it may be interesting to combine a spacing paradigm as in the present study or as in Küpper-Tetzel and Erdfelder's work [20] with physiological measures (e.g., EEG, fMRI) and/or with odor cueing paradigms (e.g. ...
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Spaced learning produces better learning performance than extended learning periods without or with little interruptions. This “spacing effect” exists on different time scales, ranging from seconds to months. We recently found large spacing effects with a hithero rarely investigated 12-hours spacing interval. The present study tested for potentially larger learning effects in the temporal vicinity of 12 hours and analyzed spacing effects separately for learning and forgetting. 102 participants learned 40 German-Japanese vocabulary pairs in separate conditions with 7.5 minutes and 4-, 8-, 12-, and 24-hours spacing intervals. Two final tests were executed after retention intervals of 24 hours and 7 days. The 7.5-min spacing interval produced a steeper initial learning curve than all other spacing intervals. 24 h after the last learning unit, we found almost no forgetting in the 4-, 8- and 12-hours spacing conditions, but about 9.3 % and 3.6 % forgetting in the 7.5 min and 24 hours spacing conditions. After 7 days, forgetting was in the range of 13 % for all conditions between 4 and 24 hours. The 7.5 minutes condition produced 34 % forgetting. Our results indicate that spacing intervals in the range of 8 hours ± 4 hours provide high learning performance and can be easily integrated in our daily schedules.
... The idea that different memory tests tap into different memory processes (i.e., free recall: retrieval; cued recall/ recognition: storage), has been systematically used by many researchers already decades ago and has since then advanced to an established method to estimate the contribution of retrieval and storage processes in item memory (e.g., Drachman & Leavitt, 1972;Hirshman et al., 1989;Hogan & Kintsch, 1971;Küpper-Tetzel & Erdfelder, 2012;Nadarevic, 2017;Riefer & Rouder, 1992;Schonfield & Robertson, 1966;Tulving & Pearlstone, 1966). For example, based on the finding that the bizarreness effect on item memory (i.e., better memory for bizarre than common sentences) occurs on free but not cued recall, Hirshman et al. and Riefer and Rouder concluded that there is an advantage in retrieval, but not storage, of bizarre items. ...
... Following previous research contrasting free recall with cued recall and recognition to infer about storage versus retrieval (Batchelder & Riefer, 1986;Danckert & Craik, 2013;Küpper-Tetzel & Erdfelder, 2012;Riefer et al., 2002;Riefer & Batchelder, 1995;Tulving & Pearlstone, 1966), we propose a similar two-test procedure with the standard source memory test followed by our novel source recognition test. This allows us to not only measure source storage via the source recognition test but also to assess the role of retrieval processes by comparing source memory performance between both tests: As elaborated earlier, in contrast to our novel source recognition test, source memory in the standard test (no reinstatement of source features) additionally depends on self-initiated, successful source retrieval, rather than source storage only. ...
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The present research aimed to devise a test of source recognition that facilitates access to source information stored in memory. Therefore, we extended the standard source-monitoring paradigm, in which items are presented in a source-neutral manner during test, by a second, subsequent test with source reinstatement. In this second test, items (i.e., words) were presented with both study sources (i.e., two speakers) consecutively such that for originally studied words, one test presentation was the exact reinstatement of the original source. To validate our assumption that the test with reinstatement primarily assesses source storage, we manipulated source storage by varying encoding frequency between-participants (repetition vs. no repetition of each item-source-pair). Additionally, we varied source similarity between-participants (similar vs. dissimilar speakers). Data analyses (N = 146) based on multinomial and signal detection models showed a source memory enhancement in the second test with reinstatement compared to the first standard test, especially for similar sources. Additionally, repetition selectively benefited source memory in the second test, validating our interpretation of the second test as a measure for source storage. Altogether, our novel source recognition test offers a promising method for investigating various well-known source memory phenomena more comprehensively.
... Learning over longer retention intervals seems to benefit from longer inter-study intervals (Cepeda et al., 2006(Cepeda et al., , 2008Glenberg, 1976). Different processes might account for the spacing and the lag effect (Cepeda et al., 2006;Küpper-Tetzel & Erdfelder, 2012). Retrieval processes during retention tests have been discussed as explanations for the spacing effect, whereas the lag effect may be explained by different encoding strategies (e.g., retrieval of the first encoding of an item) during learning or maintenance after learning. ...
Thesis
Full-text available
Distributed practice is a well-known learning strategy whose beneficial effects on long-term learning are well proven by various experiments. In learning from texts, the benefits of distribution might even go beyond distributed practice, i.e. distribution of repeated materials. In realistic learning scenarios as for example school or university learning, the reader might read multiple texts that not repeat but complement each other. Therefore, distribution might also be implemented between multiple texts and benefit long-term learning in analogy to distributed practice. The assumption of beneficial effects of this distributed learning can be deduced from theories about text comprehension as the landscape model of reading (van den Broek et al., 1996) in combination with theories of desirable difficulties in general (R. A. Bjork & Bjork, 1992) and distributed practice in particular (Benjamin & Tullis, 2010). This dissertation aims to investigate (1) whether distributed learning benefits learning; (2) whether the amount of domain-specific prior knowledge moderates the effects of distribution, (3) whether distributed learning affects the learner’s meta-cognitive judgments in analogy to distributed practice and (4) whether distributed practice is beneficial for seventh graders in learning from single text. In Experiment 1, seventh graders read two complementary texts either massed or distributed by a lag of one week between the texts. Learning outcomes were measured immediately after reading the second text and one week later. Judgements of learning were assessed immediately after each text. Experiment 2 replicated the paradigm of Experiment 1 while shortening the lag between the texts in the distributed condition to 15 min. In both experiments, an interaction effect between learning condition (distributed vs. massed) and retention interval (immediate vs. delayed) was found. In the distributed condition, the participants showed no decrease in performance between the two tests, whereas participants in the massed condition did. However, no beneficial effects were found in the delayed test for the distributed condition but even detrimental effects for the distributed condition in the immediate test. In Experiment 1, participants in the distributed condition perceived learning as less difficult but predicted lower success than the participants in the massed condition. Experiment 3 replicated the paradigm of Experiment 1 with university students in the laboratory. In the preregistered Experiment 4, an additional retention interval of two weeks was realized. In both experiments, the same interaction between learning condition and retention interval was found. In Experiment 3, the participants in the distributed condition again showed no decrease in performance between the two tests, whereas participants in the massed condition did. However, even at the longer retention interval in Experiment 4, no beneficial effects were found for the distributed condition. Domain-specific prior knowledge was positively associated with test performance in both experiments. In Experiment 4, the participants with low prior knowledge seemed to be impaired by distributed learning, whereas no difference was found for participants with medium or high prior knowledge. In the preregistered Experiment 5, seventh graders read a single text twice. The rereading took place either massed or distributed with one week. Immediately after rereading, judgements of learning were assessed. Learning outcomes were assessed four min after second reading or one week later. Participants in the distributed condition predicted lower learning success than participants in the massed condition. An interaction effect between learning condition and retention interval was found, but no advantage for the distributed condition. Participants with low domain-specific prior knowledge showed lower performance in short-answer questions in the distributed condition than in the massed condition. Overall, the results seem less encouraging regarding the effectiveness of distribution on learning from single and multiple texts. However, the experiments reported here can be perceived as first step in the realistic investigation of distribution in learning from texts.
... Many papers argue that spacing effects could arise from some combination of two processes: encoding variability, which determines the amount of strengthening, and study-phase retrieval, which determines the likelihood of strengthening (Benjamin & Tullis, 2010;Küpper-Tetzel & Erdfelder, 2012;Landauer, 1969;Mozer et al., 2009;Raaijmakers, 2003;Smolen, Zhang, & Byrne, 2016;Walsh et al., 2018). Recall that encoding variability theory asserts that re-encoding benefits increase with more variable encoding contexts (such as after greater temporal lags) because there will be a greater diversity of contextual elements added to the memory, resulting in more routes to retrieval (Estes, 1955;Maddox, 2016;Mozer et al., 2009;S. ...
Preprint
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Some neural representations change slowly across multiple timescales. Here we argue that modeling this "drift" could help explain the spacing effect (the long-term benefit of distributed learning), whereby differences between stored and current temporal context activity patterns produce greater error-driven learning. We trained a neurobiologically realistic model of the entorhinal cortex and hippocampus to learn paired associates alongside temporal context vectors that drifted between learning episodes and/or before final retention intervals. In line with spacing effects, greater drift led to better model recall after longer retention intervals. Dissecting model mechanisms revealed that greater drift increased error-driven learning, strengthened weights in slower-drifting temporal context neurons (temporal abstraction), and improved direct cue-target associations (decontextualization). Intriguingly, these results suggest that decontextualization -- generally ascribed only to the neocortex -- can occur within the hippocampus itself. Altogether, our findings provide a mechanistic formalization for established learning concepts such as spacing effects and errors during learning.
... 30 However, longer spacing schedules can be less effective when information is not yet well-learned, likely due to learners forgetting the information across sessions. 40,41 Because spacing increases the risk of forgetting between learning sessions, spaced learning activities should provide sufficient practice with the material to permit any forgotten information to be re-learned. Although it is not possible to anticipate the perfect spacing schedule, effective spacing schedules typically involve providing sufficient practice with the learning material during the learning sessions and enough time between sessions such that the information is still familiar but not fresh in mind. ...
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[Full text link: https://rdcu.be/cSXY3] Research on the psychology of learning has highlighted some straightforward ways of enhancing learning. However, effective learning strategies are underutilized by learners. In this Review, we discuss key research findings on two specific learning strategies: spacing and retrieval practice. We focus on how these strategies enhance learning in a variety of domains across the lifespan, with an emphasis on research in applied educational settings. We also discuss key findings from research on metacognition—learners’ awareness and regulation of their own learning. Learners’ underutilization of effective learning strategies could stem from false beliefs about learning, lack of awareness of effective learning strategies, or the counter-intuitive nature of these strategies. Findings in learner metacognition highlight the need for improving learners’ subjective mental models of how to learn effectively. Overall, the research discussed in this Review has important implications for the increasingly common situations in which learners must effectively monitor and regulate their own learning. [Nature Reviews Psychology, August 2022]
... Other studies also failed to reveal a benefit of distributed practice for foreign language acquisition, including vocabulary, grammar, listening and reading (e.g., Lapkin et al., 1998;Collins et al., 1999;Serrano and Munoz, 2007). However, when the learning addressed the recall of verbal material, not the application of procedures, distributed practice did yield quite reliably positive effects, even in a test after 1 week (e.g., Cepeda et al., 2008, using trivia facts;Küpper-Tetzel andErdfelder, 2012 andKüpper-Tetzel et al., 2014a, using word pairs or vocabulary; for a review see Cepeda et al., 2006). ...
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We investigated the effect of distributed practice and more specifically the “lag effect” concerning the retention of mathematical procedures. The lag effect implies that longer retention intervals benefit from longer inter-study intervals (ISIs). University students (N = 235) first learned how to solve permutation tasks and then practiced this procedure with an ISI of zero (i.e., massed), one, or 11 days. The final test took place after one or five weeks. All conditions were manipulated between-subjects. Contrary to our expectations, the analyses revealed no effect of distributed practice and therewith also no lag effect, even though the sample size was sufficiently large. The only significant effect was that test performance was poorer after 5 weeks than after 1 week. In view of the present results and those of other studies, we assume that distributed practice works differently for declarative and procedural knowledge, with less robust of even absent effects when procedural skills are practiced with ISIs compared to massed practice.
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Research has produced mixed findings regarding the effects of spacing L2 study. In order to know how this potentially very powerful learning tool can be useful, it is important to understand the cognitive mechanisms that drive the effects in L2 learning and how the operation of these mechanisms may be affected by variables relevant for SLA contexts. In this study, I examine the contribution of the dual mechanism of successful effortful retrieval during study to the lag effect in foreign vocabulary learning from L2-L1 retrieval practice. I additionally investigate the effects of feedback study time on the operation of the two cognitive mechanisms under investigation. Native speakers of English studied Finnish vocabulary during L2-L1 retrieval practice in paired-associate learning while their response latencies and accuracy were recorded. Results suggest that: (a) successful effortful retrieval underlies benefits of spacing L2-L1 retrieval practice: even with immediate feedback study, the benefits of effort are conditional on retrieval success; (b) successful retrieval is more beneficial than unsuccessful retrieval, contrary to proposals where this was not directly tested; and (c) imposing longer study time externally has little benefit, unlike what has been previously found with learner-regulated longer study time. Implications for L2 learning and teaching are discussed.
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The present study investigated the effect of distributed versus crammed practice before a course deadline on the retention and transfer of knowledge, and whether learner characteristics moderate the effect. In Experiment 1, only 41% (N = 38) of the initially enrolled students worked the voluntary but recommended practice tasks. Moreover, markedly fewer students did so in the distributed condition (12%) than the crammed practice condition (29%). In Experiment 2, working the practice tasks was mandatory and more students completed them (N = 105, i.e., 81%). Students who distributed practice clearly outperformed students who crammed practice on tests of knowledge retention and transfer five weeks after the practice deadline. No moderating effects of learner characteristics emerged. The study shows that distributed practice following knowledge acquisition is a powerful learning tool for fostering long-term retention and transfer with adults in authentic educational contexts.
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This study is a conceptual replication of Rogers and Cheung's (2018) investigation into distribution of practice effects on the learning of L2 vocabulary in child EFL classrooms in Hong Kong. Following a pretest, treatment, delayed posttest design, 66 primary school students (Cantonese L1) studied 20 vocabulary items over three training episodes under spaced-short (1-day interval) or spaced-long (8-day interval) learning conditions. The spacing of the vocabulary items was manipulated within-participants, and learning was assessed using crossword puzzles following a 4-week delay. While Rogers and Cheung (2018) resulted in minimal overall learning with a slight advantage for the spaced-short group, this study found large learning gains across the experimental conditions with no significant differences between the two learning schedules. Taken together, these results provide evidence that the results from previous research examining input spacing with adult populations in laboratory contexts might not generalize to authentic child learning contexts.
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Evidence-based design guidelines for formative testing from the retrieval practice literature.
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Typically, symbolic enactment increases memory for verb-object phrases. When investigating which processes constitute this enactment effect, a difficulty is that observable effects in standard memory tests are ambiguous. The present work presents a multinomial model that decomposes memory performance into (a) a retrieval parameter, (b) a parameter for integration of a verb-object phrase, and (c) one for item-specific processing. We tested whether enactment strengthens the item-specific processing of the object in addition to that of the verb, and whether enactment strengthens the integration of verbs and objects on top of item-specific processing. Memory after enactment was compared to that after verbal learning and after imagery. Our findings show that, indeed, all three processes are increased after enactment as compared to verbal learning. In addition, retrieval is hindered by enactment.
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Reports data from 3 experiments in support of the encoding specificity hypothesis of retrieval: the effectiveness of retrieval cues depends upon the specific format of encoding of the to-be-remembered (TBR) words at the time of their storage, regardless of how strongly the cues are associated with the TBR words in other situations. In the critical experimental conditions, TBR words were studied in presence of weakly associated cue words. 180 female undergraduates served as Ss. Recall of the TBR words in the presence of these cues was greatly facilitated in comparison with noncued recall; recall of the TBR words in presence of their strongest normative associates, which had not been seen at input, did not differ from noncued recall. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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97 STUDENTS FROM THE SALESIAN UNIVERSITY OF ROME WERE USED TO ASSESS THE VALUE OF EARLY AND DELAYED REVIEW. THE FOLLOWING CONCLUSION WAS MADE: "THE PRINCIPAL ADVANTAGE OF EARLY REVIEW WOULD APPEAR TO BE ITS SUPERIOR CONSOLIDATING AND "SENSITIZING' EFFECTS ON MORE HIGHLY AVAILABLE MATERIAL; WHEREAS THE PRINCIPAL ADVANTAGE OF DELAYED REVIEW PROBABLY INHERES IN SUPERIOR RELEARNING OF FORGOTTEN MATERIAL, BOTH ON MOTIVATIONAL AND COGNITIVE GROUNDS." (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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Spacing repetitions generally facilitates memory for the repeated events. This article describes a theory of spacing effects that uses the same principles to account for both facilitatory and inhibitory effects of spacing in a number of memory paradigms. Increasing the spacing between repetitions is assumed to result in the storage of greater amounts of information of three types or levels: contextual, structural (associative), and descriptive. Contextual information is encoded automatically, while the encoding of the structural and descriptive information depends on control processes utilized. Remembering involves accessing the stored information using retrieval cues containing information on any level that matches the stored information. The ultimate effectiveness of the spacing is controlled by this matching between the retrieval cues and the stored information. Previous experiments demonstrating the operation of these principles on the structural and descriptive levels are reviewed. Three new experiments are reported that illustrate interactions between stored information and retrieval cues based on contextual information.