Memory for rewards guides retrieval

Abstract

Rewards paid out for successful retrieval motivate the formation of long-term memory. However, it has been argued that the Motivated Learning Task does not measure reward effects on memory strength but decision-making during retrieval. We report three large-scale online experiments in healthy participants ( N = 200, N = 205, N = 187) that inform this debate. In experiment 1, we found that explicit stimulus-reward associations formed during encoding influence response strategies at retrieval. In experiment 2, reward affected memory strength and decision-making strategies. In experiment 3, reward affected decision-making strategies only. These data support a theoretical framework that assumes that promised rewards not only increase memory strength, but additionally lead to the formation of stimulus-reward associations that influence decisions at retrieval.

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communications psychology Article
https://doi.org/10.1038/s44271-024-00074-9
Memory for rewards guides retrieval
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Juliane Nagel 1,2,3 , David Philip Morgan 1,2,3,NecatiÇağatay Gürsoy 1,2,3, Samuel Sander1,2,3,
Simon Kern 1,2,3 &GordonBenediktFeld
1,2,3,4
Rewards paid out for successful retrieval motivate the formation of long-term memory. However, it has
been argued that the Motivated Learning Task does not measure reward effects on memory strength
but decision-making during retrieval. We report three large-scale online experiments in healthy
participants (N=200, N=205, N=187) that inform this debate. In experiment 1, we found that explicit
stimulus-reward associations formed during encoding influence response strategies at retrieval. In
experiment 2, reward affected memory strength and decision-making strategies. In experiment 3,
reward affected decision-making strategies only. These data support a theoretical framework that
assumes that promised rewards not only increase memory strength, but additionally lead to the
formation of stimulus-reward associations that influence decisions at retrieval.
Rewards can enhance learning and memory (for a review, see Miendlar-
zewska et al.1). This occurs when they are experienced as a consequence of an
action (operant conditioning), but even the anticipation of a reward at
retrieval is sufficient to motivate encoding2–6. In this framework, items
associated with higher rewards are retained better, usually assessed with
a version of the “Motivated Learning Task”7–9. In this paradigm, participants
learn stimuli cued with varying amounts of reward, which is paid
out for later recognizing the studied stimuli (targets) among new
ones (lures).
Dopamine plays a key role in prioritizing memories10, presumably via
enhanced encoding11 and increased consolidation6. It determines which
information enters long-term memory via the hippocampal-VTA loop12.
Presenting reinforcers during learning elicits a dopaminergic response13,
which modulates neuroplasticity14 and thereby increases the memory
strength of the studied items15,16. Additionally, animal models suggest that
dopamine tags memory traces for preferential reactivation during sleep17,18.
In the Motivated Learning Task, researchers typically rely on the hit
rate (number of recognized targets) to investigate the impact of reward on
memory2,7. However, without correction for false alarms, (i.e., incorrectly
identifying a lure as target), the hit rate cannot be used to disentangle
memory strength (discriminability, the ability to discriminate between old
and new stimuli19) from decision-making strategies (response bias, the
tendency to respond “old”during recognition19). Memory strength and
decision-making strategies can be distinguished by considering the hit rate
and the false alarm rate together (calculating discriminability d’and
response bias C). However, in the standard implementation of the Moti-
vated Learning Task lures are not assigned a reward, which makes it
impossible to calculate those indices per reward level.
In three thoughtful experiments, Bowen et al.20 delineated the influence
of reward on memory strength and decision-making strategies. In their
modified version of the Motivated Learning Task, rewards were associated
with a category (indoor vs. outdoor scenes) rather than with individual
stimuli, i.e., lures had an implied reward level. In experiment 1, Bowen et al.20
found no effect of reward on memory strength, but participants were more
inclined to respond “old”to high reward items. In experiment 2 and 3, the
researchers eliminated the influence of reward on decision-making strate-
gies by penalizing false alarms contingent on their reward category. Simi-
larly, Marini et al.3presented reward information during study and test, and
show that reward information can bias decisions during retrieval, although
the study sample was small.
Although these studies suggest that the effects of reward on hit rate can
be explained by a shift in decision strategies, they supplied the participants
with perfect information about the reward contingencies at retrieval. To
identify the crucial involvement of stimulus-reward associations formed
during learning for decision-making at retrieval and independent effects of
rewards on memory strength, we conducted a series of three large-scale
online experiments.
Methods
Design
Generally, across all three experiments, methods and materials were highly
similar, and any deviations from the general methods between the three
experiments are detailed in the relevant sections. Participants underwent an
adapted version of the Motivated Learning Task (as e.g. reported in Adcock
et al.2) described below (also see Fig. 1). All tasks were programmed using
JsPsych, a collection of JavaScript plugins for browser-based experiments21.
1Clinical Psychology, Central Institute of Mental Health, Medical Faculty Mannheim, University of Heidelberg, Mannheim, Germany. 2Addiction Behavior and
Addiction Medicine, Central Institute of Mental Health, Medical Faculty Mannheim, University of Heidelberg, Mannheim, Germany. 3Psychiatry and Psychotherapy,
Central Institute of Mental Health, Medical Faculty Mannheim, University of Heidelberg, Mannheim, Germany. 4Department of Psychology, University of Heidel-
berg, Heidelberg, Germany. e-mail: juliane.nagel@zi-mannheim.de;gordon.feld@zi-mannheim.de
Communications Psychology | (2024) 2:31 1
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This study’s design and its analysis were preregistered on the OSF
(Experiment 1, April 26, 2021, https://osf.io/ufwmv; Experiment 2, August
4, 2021, https://osf.io/fhzqs; Experiment 3, February 28, 2022, https://osf.
io/nefud).
Participants
Participants across all three experiments were recruited via Prolific(https://
www.prolific.co/), an online work-sourcing site. The number of participants
and demographic information for each experiment are presented in Table 1.
In order to be included in the experiment and/or data analysis, participants
had to meet the inclusion and exclusion criteria presented in Supplementary
Tables 1 and 2 (see Supplementary Tables 3–5 for information about how
many participants were excluded for which reasons). Participants who did
not meet the exclusion criteria were re-sampled until the desired sample
sizes were achieved. Oversampling was permitted to facilitate the data col-
lection process. All participants provided informed consent prior to parti-
cipation, and all experiments were approved by the ethics committee of the
University Medical Faculty Mannheim, University of Heidelberg. For
experiment 1 and experiment 2, participants received £ 6.50 for completing
both parts of the study. At the end of the experiment, participants were
ranked according to their score (gems won in the task) and received a bonus
payment (rank 1-4: £ 25; 5-8: £ 20; 9-12: £ 15; 13-50: £ 7.50). In experiment
3, participants received £7.60 for completing both parts of the study.
Additionally, they earned a bonus based on their performance on the task:
They received the average reward they won across all trials of the test phase,
multiplied by 2, i.e., participants could additionally win between £ 0
and £ 10.20.
Procedure
All participants completed each experiment in a web browser using their
computer or laptop. The first part of the study began with a set of demo-
graphic questions (age, gender, highest level of education, native language).
They then completed the Stanford Sleepiness Scale22 (SSS) and the Psy-
chomotor Vigilance Task23 (PVT). Afterwards, participants were provided
with instructions for the Motivated Learning Task, which included a
description of both the learning and the test phase, and the reward and
punishment contingencies. Participants practiced both the learning and test
phase of the Motivated Learning task (3 targets, 3 lures), and then answered
a set of questions to ensure they understood the reward and punishment
contingencies of the task. The first part of the study ended with the learning
phase of the Motivated Learning Task. Participants returned for the second
Table 1 | Demographics for each of the three experiments
experiment 1 experiment 2 experiment 3
congruent incongruent
n200 103 102 187
sex (female/male) 106/94 54/49 48/54 103/84
gender (women/
men/non-binary/
undisclosed)
104/94/2/0 54/49/0/0 46/54/1/1 100/84/3/0
age M(SD) 24.34 (3.56) 22.91 (3.65) 22.89 (3.62) 26.91 (4.90)
mother tongue
English
73.00% 87.38% 90.20% 85.03%
very suresureguess
newold
1.5 - 2.5s
0.5 - 0.75s
3x
<1.51.5 - 2.5s1.5 - 2s2s1.5 - 2s
750
>>>>>
ready newold guess sure very sure Which reward?
If participant
says “old”:
Learning
Test
EXPERIMENT 1
0.5 - 0.75s
3x
<1.51.5 - 2.5s1.5 - 2s2s1.5 - 2s
750
>>>>>
ready newold guess sure very sure
Learning
Test
EXPERIMENT 2
2150
0.5 - 0.75s
3x
<1.51.5 - 2s2s1.5 - 2s
>>>>>
ready
Learning
Test
EXPERIMENT 3
10 £
0.20 £
Fig. 1 | Motivated Learning Task. Example trials of the Motivated Learning Task for
the learning and test phases of experiment 1, 2 and 3. During the learning phase,
participants had to memorize 128 images. Each image was associated with a reward
presented before the image (gems in a treasure chest in experiments 1 and 2, or cash
(GBP), displayed as pictures of a bank note/coin in experiment 3). Trials of the
Motivated Learning Task were separated by three trials of a flanker task to prevent
rehearsal. During the test phase, participants had to determine whether the image
they were presented with was “old”(i.e., shown during the learning phase) or “new”
(i.e., not shown during the learning phase) and indicate their confidence in their
choice on a 3-point likert scale (i.e., “guess”,“sure”,“very sure”). In experiment 1, if
participants said that an image is “old”they were asked to indicate which reward they
thought the image was associated with. In experiments 2 and 3, the reward was
shown before the picture also in each trial of the test phase. In experiment 2, the
reward was either congruent or incongruent to the reward shown to the participant
during the study phase. In experiment 3, rewards shown during the test phase were
always congruent to the reward shown during the study phase. In all experiments,
participants who made a hit were rewarded the amount associated with the image.
For a correct rejection, they received the mean value of all possible rewards and if
they made an incorrect decision, they lost the mean value of all possible rewards. The
example stimuli shown for experiments 1 and 2 have been uploaded under the Public
Domain Mark 1.0 Universal license by Bureau of Land Management California and
Jeff Hollet on Flickr. The example stimuli shown for experiment 3 are photographs
taken by Gordon Feld. The graphics used as fixation markers and reward displays
were drawn by the Juliane Nagel.
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 2

part of the study ~22–26 h later. Due to a coding error, the retention interval
varied slightly for some participants (for each experiment, 4.00%, 2.94%,
0.54% of participants deviated by >60 min from the planned retention
interval), but for each participant, the two sessions were separated by at least
one night of sleep and the results were not affected by excluding these
participants. When participants returned for the second session, they
completed the SSS and the PVT again, and had the opportunity to read the
instructions for the test phase of the Motivated Learning Task again. Once
again, they had to pass the questions about the reward contingencies. Par-
ticipants then completed the test phase of the Motivated Learning Task, and
were debriefed afterwards.
Stimuli
For experiment 1 and 2, we collected landscape images from the Creative
Commons online repository and assessed them in terms of aesthetics,
composition, familiarity, memorability, and whether or not the participants
knew the images in a pilot study. Participants rec ruited via Prolific(N= 152)
provided ratings on these aspects (each participant rated 73 pictures out of a
stimulus pool of 975 pictures, resulting in M= 11.38 ratings per picture) and
additionally completed a subsequent recognition memory test to collect a
measure of memory accuracy for each picture. Based on the measures
collected in the pilot study, we divided the images into small subsets (to
achieve the required number of final stimuli, we removed the stimuli that
received the highest “known”ratings) with properties that were as similar as
possible using the R package anticlust24. The sets were then balanced across
task variables (reward level, exposure duration, image category (target/lure)
and in experiment 2, experimental group). This way, each participant was
presented with a unique stimulus set in the Motivated Learning Task, but
variance in stimulus properties across sets was minimized. In experiment 3,
we used the stimulus set previously used in Feld et al.8and Alizadeh
Asfestani et al.25, consisting of indoor scenes, outdoor scenes and buildings.
Motivated Learning Task
Because memory tasks with a lot of trials can be quite exhausting for par-
ticipants, we wanted to increase motivation and reduce attrition rates using a
gamified version of the Motivated Learning Task. We embedded the task in
a cover story, where participants were recruited as crew members on a pirate
ship. As part of their duties on the pirate ship, their goal was to scout for
treasure at different locations (corresponding to the learning phase). The
treasures were chests containing varying amounts of gems (i.e., different
reward magnitudes). Participants navigated between the locations via the
Flankers Task, which was stylized as arrows on a treasure map. When
participants returned the next day, they went out to retrieve the treasures
with their crewmates (corresponding to the test phase), visiting both old
locations (targets) and new locations (lures). When participants correctly
recognized an old location, they could collect the treasure (i.e., they received
the reward associated with the target). If they missed an old location, the
crew’s captain punished them by taking gems away from them. Other pirate
crews inhabited new locations, so if participants mistakenly identified a new
location as old, the rival pirate crew would steal some of their gems. This is
why the crew’s captain rewarded pirates who prevent such a situation, i.e.,
participants received gems if they correc tly identified a new location as new.
Our cover story is highly similar to the interrogative cover story
described by Sinclair et al.26, who found that participants who received
interrogative instructions (as compared to imperative instructions) per-
formed better in a recognition memory task, had better memory for rewards
associated with the studied items, and demonstrated greater effects of
memory-enhancing reward effects.
The Motivated Learning Task was split into two phases, the learning
phase and the test phase. In the learning phase, participants were asked to
memorize 128 landscape images for a later memory test. Four additional
images at the beginning and at the end of the task, which did not appear in
the later memory test, buffered primacy and recency effects. Each trial
started with a fixation (a spyglass; 1500–2000 ms), followed by a reward
(2000 ms). There were different reward amounts (see description of each
experiment for specific amounts) which corresponded to the amount par-
ticipants could win if they correctly identified the subsequent image as old
during the recognition test 24 h later. After a second fixation
(1000–1500 ms), a landscape image was presented, for one of four possible
exposure durations (see description of each experiment) to control for
encoding strength effects unrelated to reward. This was done as a positive
control of our paradigm as well as to prepare future studies that will
intervene during the retention period, because exposure duration has pre-
viously been found to incre ase hit rate, without interacting with reward (Feld
et al.)8. After each image, participants completed three trials of a flanker task,
where they were shown a serie s of arrows and had to press the arrow key that
corresponded to the direction of the middle arrow highlighted in b old. Trials
in this task were either congruent (e.g., >>>>>) or incongruent (e.g., >><>>).
Halfway through the learning phase, participants were offered a short break
lasting a maximum of 2 min and a minimum of 30 s.
In the test phase, participants were shown the landscape images they
had learned previously (i.e., targets; 128 images) and new images (i.e., lures;
128 images). In each trial, participants were shown a fixation (a shovel;
500–750 ms) followed by a “ready”button which participants clicked before
seeing the image. This ensured that participants’mouses were in approxi-
mately the same position before seeing the image, to make reaction times
comparable across trials. Whilst the image was shown participants had to
decide whether the image was “old”(i.e., they did see the image during the
learning phase) or “new”(i.e., they did not see the image during the learning
phase). Identifying a target as old was a hit and participants won the reward
associated with the image, and identifying a lure as new (correct rejection)
was rewarded with the average of all possible rewards. Making a mistake
(false alarm: identifying a new image as old; miss: identifyingan old image as
new) resulted in the loss of the average reward. Afterwards, participants
were asked to rate their confidenceintheirold/newdecisionona3-point
scale (“guess”,“sure”,“very sure”). See Fig. 1for a description of the task for
all three experiments.
In the first experiment (N= 200), we attempted to disentangle memory
strength and decision-making strategies by adjusting the paradigm in such a
way that the false alarm rate per reward level could be calculated without
using categories or showing the reward during recognition testing. Parti-
cipants learned several pictures associated with different amounts of points
(gems), which were earned for correctly identifying the pictures in a
recognition memory test 24 later. After identifying a picture as either old or
new, we asked participants for their confidence in their decision (“guess”,
“sure”,“very sure”). Previous studies using the Motivated Learning Task
have found that high confidence responses are sensitive to reward, but found
no evidence for (or against) a reward effect in low confidence items2.
Whenever a participant identified an image as old during recognition, we
asked them how many gems they expected to win for their answer - irre-
spective of whether the image was in fact a target or a lure (see Fig. 1). This
gave us information about which reward participants expected to receive
whenever they made a false alarm. Note that this experiment also had other
pre-registered goals, and the associated analyses can be found in Supple-
mentary Note 4. Disentangling memory strength and decision-making
strategies was not an explicit goal of the preregistration for experiment 1,
because we assumed our modification to the paradigm would enable us to
calculate a false alarm rate per reward level based on our previous studies8,25.
This turned out to be wrong, which led to experiments 2 and 3. Descriptive
performance measures for the different tasks and control tasks can be found
in Supplementary Table 6. Reward levels were 50, 750, 1450 and 2150 gems,
and exposure durations were 1500, 1833, 2167 and 2500 ms.
In experiment 2 (N= 205), we explicitly assigned a reward to lures by
presenting the reward information not only during the learning phase, but
also during the test phase (see Fig. 1). Participants were informed that the
reward presented before each image during the learning and the test phase
corresponds to the amount of reward that is paid out according to the same
contingencies as in experiment 1. We did not mention whether the reward
presented during the test phase matched the reward presented during the
learning phase. However, reward congruency between learning phase and
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Communications Psychology | (2024) 2:31 3

test phase was manipulated between two groups: In the congruent group
(n= 103), the reward presented for targets during the test phase (shown
reward) always corresponded to the reward presented during the learning
phase (true reward). In the incongruent group (n= 102), the reward pre-
sented for targets was completely orthogonal to the true reward the picture
was associated with during the learning phase (i.e., in 25% of target trials,
true and shown reward matched). In both groups, lures were presented with
a pseudo-random reward level (each reward level appeared equally often
across all lures). As in experiment 1, we asked participants for their con-
fidence in their old/new decision (“guess”,“sure”,“very sure”), but since
rewards were presented during the test phase, we did not ask about their
reward expectations. We expected reward to exert its influence on memory
because it strengthens encoding during and consolidation after learning, not
because it changes decision-making strategies during test. That is, in both
the congruent and incongruent group, we preregistered to find an effect of
true reward on hit rate. In the congruent group, we expected to find an effect
of reward on memory strength (d’). In the incongruent group, we expected
to find no effect of shown reward on memory strength, but hypothesized the
shown reward to affect criterion. We also preregistered an effect of true
reward on memory strength and possibly criterion in the incongruent
group, but later realized that this part of the preregistered model could not be
calculated as planned (for details, see Supplementary Note 5). We further
predicted that the previously observed reward effect in the Motivated
Learning Task mainly reflects improved memory strength, i.e., we did not
expect to find an effect of true reward in decision-making strategies (cri-
terion). However, we acknowledged in our preregistration that shown
reward may influence hit rate and decision-making strategies. In the con-
gruent group we hypothesized to replicate the effect of reward on hit rate
from the previous experiment to ensure that the presentation of reward
information during the test phase per se does not influence performance in
the Motivated Learning Task. Reward levels were 50, 750, 1450 and 2150
gems, and exposure durations were 1500, 1833, 2167 and 2500 ms.
Experiment 3 (N= 187; we aimed to recruit 200 participants, however,
a coding error led to additional exclusions after finalizing data collection)
mainly corresponded to the congruent group of experiment 2 (i.e., corre-
sponding rewards were presented during learning and test, and confidence
ratings in the old/new decision were collected), but was changed in key
features. First, we changed the stimulus material. In an effort to make the
task easier for participants and increase overall memory for the task con-
tents, we used more distinct pictures of interior scenes, exterior scenes and
buildings (which were more similar to Adcock et al.2and previously used in
Feld et al.8and Alizadeh Asfestani et al.25). Furthermore, we used two instead
of four exposure levels (1500 and 2000 ms), and two instead of four reward
levels (also more similar to previous research). Most importantly, reward
was changed to monetary values instead of gems/points (£ 0.20 or £ 10).
Since images of money should act as a secondary reinforcer that has already
been strongly learned by participants, we assumed that this would maximize
any cue related dopamine reaction27. The entire study was still embedded
into the pirate cover story, but instead of gem-filled treasure chests, parti-
cipants saw pictures of the monetary reward before eac h stimulus during the
learning and test phase (see Fig. 1). These changes were implemented to
increase the effect of rewards on memory strength found in experiment 2. At
the same time, experiment 3 served as a replication.
Stanford Sleepiness Scale (SSS)
The SSS is a subjective measure of an individual’s current level of
sleepiness22. Participants rate their sleepiness on a 7-point scale ranging
from “1 - Feeling active and vital; alert; wide awake”to “7 - Almost in reverie;
sleep onset soon; lost struggle to remain awake”. Low scores indicate a low
level of current sleepiness, whereas high scores indicate a greater level of
current sleepiness.
Psychomotor Vigilance Task (PVT)
The PVT is a sustained attention task, which measures an individual’s
objective vigilance. We used a 3 min version of the PVT23. In this reaction
time task, participants pressed the space bar as soon as a millisecond clock
appeared on the screen. The following measures were analyzed: median
reaction speed (1/reaction time in ms) and percentage of lapses (number of
lapses (reaction time ≥500 ms) divided by the number of valid stimuli,
excluding premature responses (reaction time ≥100 ms)). Reaction times
<100 ms were regarded as premature responses and treated as errors of
commission. These analysis thresholds are based on Basner & Dinges28;note
that exclusion criteria for participants were more lenient (see Supplemen-
tary Table 2).
Statistics and reproducibility
All t-tests are reported as Welch’st-test, which does not assume equal
variance. Effect sizes are reported as Cohen’sd. (Generalized) linear mixed
models were calculated using the R package lme4 (version 1.1.3429). Unless
reported otherwise, two-sided tests are reported at α= .05. We report p-
values for these models using Satterthwaite’s degrees of freedom method.
Unless reported otherwise, the linear mixed models were run on the trial-
wise (i.e., unaggregated) data. For linear mixed models, t-values and degrees
of freedom are reported. For generalized linear mixed models, z-values and
the number of observations are reported, and β-weights are reported in log-
odds. In experiment 1 and 2, the predictor reward was transformed as
reward / 1000, expressing any effects of reward in units of 1000 gems.
Likewise, the predictor duration was transformed as duration / 1000,
expressing any effects of duration in units of 1 s. Confidence was coded as
0=“guess”,1=“sure”,2=“very sure”. Image type was coded as lure= -0.5
and target = 0.5. In experiment 2, group was coded as incongruent = -0.5
and congruent = 0.5. In our model equations, (…|participant) and (…|
image) denote random effects by participant and individual image,
respectively (for details on model notation, see Singman & Kellen30). For
each analysis, we first tried to fit a maximal model, as recommended by Barr
et al.31.Whenamodeldidnotconvergeorresultedinasingularfit, we
reduced it by first removing correlations between random slopes and
intercepts. If convergence was still not achieved, we next removed random
slopes. The full outputs for each model are reported in the Supplementary
Note 7. Sensitivity (d’) was calculated as z(hit rate)-z(false alarm rate) and
criterion Cwascalculatedas-.5*(z(hit rate)+z(false alarm rate)) according
to Macmillan & Creelman19. A reviewer suggested drift diffusion models as
an alternative analysis strategy, because drift diffusion models take into
account reaction times. This allows for a quantification of “cautiousness”
(in form of the parameter “boundary separation”), which could e.g. be
expected to increase with reward. Drift diffusion models (DDM) were fit
separately for each participant. Given that maximum-likelihood methods
for estimating DDM parameters can be particularly sensitive to outliers, we
opted to exclude trials outside the 150 ms –5000 ms range. Furthermore,
only participants with a minimum of 10 trials per condition were
considered32. For each model, we compared a complex model to a simple
model. For the simple model, α(boundary separation), τ(non-decision
time), β(starting point or bias) and δ(drift rate) were estimated based on
the entire data range, regardless of any variables of interest. In the complex
model, we let the parameters α,β,δ,andτdiffer by a variable of interest
(e.g., reward; see respective model descriptions), resultingin an α,β,δ,and
τestimate for every level of the variable of interest per participant. Model
comparisons were based in the BIC (Bayesian Information Criterion) and
AIC (Akaike Information Criterion), where we regarded the complex
model to be preferable when the difference in information criteria (simple
model - complex model) was >0. Additionally, we compared the two
models in a likelihood ratio test. This likelihood ratio test is based on a χ2
distribution, where thedegrees of freedom aredetermined by the difference
in the number of parameters between the two models. A statistically sig-
nificant likelihood ratio test indicates that the fit of the complex model is
better. Comparisons between the two models were conducted on the
participant level, and we report the percentage of caseswhere the complex
model was preferred over the simple model. The full outputs of the drift
diffusion analyses and plots of the results are reported in the Supple-
mentary Note 9.
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 4

Reporting summary
Further information on research design is available in the Nature Portfolio
Reporting Summary linked to this article.
Results
Experiment 1
To evaluate the effect of reward on hits, we ran the following generalized
linear mixed model with a logit link function: hit (0 or 1) ~ reward +(
reward | participant) +(1 | image) (see Supplementary Table 11; we report
the effect of adding an interaction with exposure duration in Supplementary
Table 48). There was a statistically significant increase in hits the higher the
reward was, β= 0.11, SE = 0.02, z(25600) = 5.59, p<0.001 (see Fig. 2a).
Consequently, the hit rate for the highest reward level (M= 0.64, SD =0.15)
was significantly higher than for the lowest reward level (M= 0.60, SD =
0.14), t(199) = 5.00, p< 0.001, d
z
= 0.35, 95% CI [0.21, 0.50]. We
explored the effect of reward, confidence and their potential interaction in
the following generalized linear mixed model with a logit link function: hit (0
or 1) ~ reward *confidence +(reward +confidence || participant) +
(confidence |image) (see Supplementary Table 12). There was no statisti-
cally significant effect of reward on hits, β= 0.05, SE = 0.03, z(25600) = 1.67,
p= 0.096, but a statistically significant increase in hits as confidence
increased β= 0.45, SE = 0.07, z(25600) = 6.36, p< 0.001. Additionally, there
was a statistically significant interaction between reward and confidence,
β=0.06, SE = 0.02, z(25600) = 2.70, p= 0.007. To follow up on the
interaction, we ran the following generalized linear mixed model with a logit
link function: hit (0 or 1) ~ reward +(1 | participant) +(1 | image), sepa-
rately for each confidence level. Reward had no statistically significant effect
on hits for the lowest confidence level (“guess”), β= 0.05, SE = 0.03,
z(8827) = 1.77, p= 0.076 (see Supplementary Table 13). However, when
participants were “sure”, there was a statistically significant increase in hits
the higher the reward, β= 0.09, SE = 0.03, z(8657) = 2.85, p=0.004 (see
Supplementary Table 14), or “very sure”,β=0.19,SE = 0.04, z(8116) = 4.86,
p< 0.001 (see Supplementary Table 15).
Since lures do not have a true reward, we evaluated the influence of the
expected reward on false alarms. That is, for trials where participants said
that an image was “old”, we ran the following generalized linear mixed
model with a logit link function: false alarm (0 or 1) ~ expected reward *
confidence +(expected reward || participant) +(1 | image) (see Supple-
mentary Table 16). There was a statistically significant decrease in false
alarms relative to hits as confidence increased, β=−0.49, SE = 0.04,
z(25711) = −13.81, p< 0.001. There was no statistically significant main
effect of expected reward on false alarms, β=0.01, SE = 0.03,
z(25711) = 0.31, p= 0.755, but a statistically significant interaction between
expected reward and confidence, β=−0.10, SE =0.03, z(25711) = −3.73,
p< 0.001 (see Fig. 2b and c). We further investigated this interaction by
fitting the following generalized linear mixed model with a logit link func-
tion for each confidence level separately: false alarm (0 or 1) ~ expected
reward +(1 | participant). For the lowest confidence level (“guess”), there
Fig. 2 | Hits and false alarms in experiment 1. a Hit
rate for each reward level in experiment 1, based on
N= 200 participants. The hit rate significantly
increased as the reward increased. In the beeswarm
plot, orange dots represent the hit rate per reward
level for each participant. Light grey lines connect
the dots belonging to the same participant. The line
plot shows the mean hit rate for each reward level.
Black error bars show the within-subject standard
error, as implemented in the R package Rmisc50,51.
The p-value for the reward effect in the mixed model
from the main text is reported. Asterisks represent
significance at α¼.05. bNumber of absolute hits
and false alarms per confidence level and reward
level for trials where participants said a picture was
old. The number of trials on the y-axis represents the
sum across all N= 200 participants (bars are
stacked). cThe absolute difference in the number of
hits and false alarms (summed across all N= 200
participants) for each expected reward level and
confidence level. We found that only when con-
fidence is high, false alarms relative to hits were
reduced the higher the expected reward was. p-
values for the effect of expected reward in three
generalized linear mixed models (outcome: false
alarm (1) or not (0)) per confidence level are
reported (see main text). Asterisks represent sig-
nificance at α¼.05.
0.00
0.25
0.50
0.75
1.00
50 750 1450 2150
reward
hit rate
p0.001*
0.55
0.60
0.65
0.70
50 750 1450 2150
reward
a
guess sure very sure
50 2150 50 2150 50 2150
0
1000
2000
3000
expected reward
n trials
response
false alarm hit
b
p 0.089
p 0.753
p 0.001*
0
500
1000
1500
50 750 1450 2150
expected reward
n hits − n false alarms
confidence
guess sure very sure
c
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Communications Psychology | (2024) 2:31 5

was no statistically significant effect of expected reward on false alarms,
β¼0:05, SE ¼0:03, z9356ðÞ¼1:70, p¼:089 (see Supplementary
Table 17). Likewise, there was no statistically significant effect of expected
reward on false alarms for the medium confidence level (“sure”),
β¼0:01, SE ¼0:03, z9328ðÞ¼0:31, p¼:753 (see Supplementary
Table 18). However, for the highest confidence level (“very sure”), there was
a statistically significant reduction in false alarms relative to hits as reward
expectations increased, β¼0:15, SE ¼0:04 , t7027ðÞ¼3:27, p¼:001
(see Supplementary Table 19). We furthermore investigated the distribution
of the number of trials per expected reward level. For false alarms, partici-
pants did not expect each reward level equally often, χ23ðÞ¼1002:01,
p<:001 (see Supplementary Fig. 1).
We evaluated the effect of reward, confidence and their interaction on
the reward participants expected to receive in the following linear mixed
model run on hit trials only: expected reward ~ reward *confidence +(
confidence *reward || participant) (see Supplementary Table 20). We found
no statistically significant association between the amount of reward asso-
ciated with the target and how much reward participants expected to receive
when they identified the target as old, β¼8:01, SE ¼11:36,
t1108:19ðÞ¼0:71, p¼:480, but there was a statistically significant effect
of confidence: Participants expected higher rewards the higher their con-
fidence was, β¼241:64, SE ¼13:60, t703:98ðÞ¼17:70, p<:001. Cru-
cially, the higher participants’confidence, the higher the relationship
between the true reward and the reward participants expected to receive,
β¼45:37, SE ¼8:64, t1249:44ðÞ¼5:25, p<:001 (see Fig. 3a). Following
up on the interaction, we evaluated the effect of true rewards on expected
rewards individually for the different confidence levels with the following
linear mixed model run on hit trials only: expected reward ~ reward +(
reward || participant). For high-confidencehitswefoundastatistically
significant association between true reward and expected reward β¼90:97,
SE ¼12:32, t340:10ðÞ¼7:39, p<:001 (see Supplementary Table 23). This
was not the case for any of the other confidence levels (all p> 0.661; see
Supplementary Tables 21 and 22). We investigated the effect of confidence
on reward expectations for false alarm trials with the following linear mixed
model: expected reward ~ confidence +(confidence || participant)
(see Supplementary Table 24). Participants likewise expected to receive a
higher reward with increasing confidence β¼272:60, SE ¼12:70,
t207:23ðÞ¼21:46, p<:001 (Fig. 3b).
We next explored whether more accurate reward expectations were
related to a larger effect of true reward on the hit rate. To this end, we
correlated the per-participant slopes for the reward effect from the hit ~
reward model with the % of correct reward expectations for hits per parti-
cipant. This quantifies the relationship between the proportion of accurate
reward expectations (binary classification) and how strongly the hit rate is
influenced by the true reward. For participants whose reward expectations
were more accurate, the hit rate was more strongly influenced by the true
Fig. 3 | Reward expectations in experiment 1.
aExpected reward per level of true reward and
confidence for hits, based on N= 200 participants.
We found no statistically significant main effect of
true reward on reward expectations, but the higher
participants’confidence, the higher their reward
expectations (main effect of confidence: p<:001).
The relationship between true reward and expected
reward varied by confidence (rewa rd x confidence
interaction: p<:001): When participants were con-
fident, the true reward associated with a target pre-
dicted reward expectations. In the beeswarm plot,
coloured dots (jittered randomly along the x-axis)
represent the mean expected reward per true reward
category for each individual participant. The line
plot shows the group means. Black error bars show
the within-subject standard error, as implemented
in the R package Rmisc50,51.P-values for the reward
effect in three mixed models per confidence level are
reported (see main text). Asterisks represent sig-
nificance at α¼.05. bExpected reward per level of
confidence for false alarms, based on N= 200 par-
ticipants. The higher participants’confidence, the
higher the reward they expect for false alarms.
Coloured dots show the expected reward for each
confidence level. cThe correlation between the
reward effect on the hit rate (in the model hit ~
reward +(reward | participant) +(reward | image))
and the percentage of correct reward expectations.
The more correct reward expectations are, the
stronger the effect of true reward on hit rate. dThe
correlation between the reward effect on the hit rate
(in the model hit ~ reward +(reward | partici-
pant) +(reward | image)) and the reward effect on
expected reward (in the model expected reward ~
(reward | participant)). The more accurate the
relationship between true reward and expected
reward, the stronger the relationship between
reward and hit rate. Pearson correlations each based
on N= 200 participants are reported. Asterisks
represent significance at α¼0.05.
Hits
confidence guess sure very sure
0
500
1000
1500
2000
50 750 1450 2150
reward
expected reward
p 0.661
p 0.145
p0.001*
750
1050
1350
1650
50 750 14502150
reward
a
0
500
1000
1500
2000
1100
reward
expected reward
False Alarms
b
R= 0.24, p< 0.001
0.0
0.2
0.4
0.6
0.0 0.1 0.2
hit ~ reward
% correct expected reward
c
R= 0.26, p< 0.001
−100
0
100
200
300
0.0 0.1 0.2
hit ~ reward
expected reward ~ reward
d
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Communications Psychology | (2024) 2:31 6

reward, r198ðÞ¼:24, p<:001 (Fig. 3c).Additionally,wecalculatedthe
correlation with the per-participant slopes for the reward effect from the hit
~ reward model with the per-participant slopes for the reward effect from an
expected reward ~ reward model (expected reward ~ reward +(reward|
participant) for hits. Other than the previous analysis, this analysis does not
only focus on correct reward expectations, but acknowledges that a parti-
cipant expecting 1450 when the true reward is 2150 is closer to the truth than
a participant expecting 50 gems. Participants whose reward expectations
were more strongly influenced by the true reward showed a larger influence
of reward on the hit rate, r198ðÞ¼:26, p<:001 (see Fig. 3d).
To investigate whether exposure duration influences hit rate, we ran
the following generalized linear mixed model with a logit link function: hit
(0~ or 1) ~ duration +(duration || participant) +(1 | image) (see Supple-
mentary Table 25). The longer an image was presented during the learning
phase, the more likely it was that participants made a hit in a given target
trial, β¼0:18, SE ¼0:04, z25600ðÞ¼4:72, p<:001. Consequently, the hit
rate for the longest exposure duration of 2500 ms (M¼0:63, SD ¼0:15)
was significantly higher than for the shortest exposure duration of 1500 ms
(M¼0:59, SD ¼0:14), t199ðÞ¼4:21, p<:001, dz¼0:30, 95%CI
[0:16, 0:44].
In an exploratory alternative analysis, we investigated whether the
expected reward had an effect on whether participants made a hit or a false
alarm. That is, we ran a drift diffusion model on all trials where participants
responded that a picture was “old”(i.e., where data about reward expecta-
tions was available), with the possible outcomes “hit”(upper boundary) or
“false alarm”(lower boundary). For the complex model, we let boundary
separation, starting point, drift rate, and non-decision time vary by expected
reward level (50, 750, 1450 or 2150 gems). After excluding participants with
<10 trials per condition, the model was run on n= 161 participants.
According to the BIC, the complex model was preferred in 100.00% of cases.
According to the AIC, the complex model was preferred in 100.00% of cases.
According to the number of statistically significant likelihood ratio tests, the
complex model provided a better fit in 49.69% of cases.
To estimate the effect of reward on boundary separation α,werana
linear mixed model of the form alpha ~ expected reward +(expected
reward | participant) (see Supplementary Table 51). There was no statisti-
cally significant effect of reward on boundary separation, β¼0:02,
SE ¼0:03, t160:00ðÞ¼0:72, p¼:472 (see Supplementary Fig. 5a). That
is, there was no statistically significant difference in boundary separation
between the highest expected reward level (M¼2:04, SD ¼0:89) and the
lowest expected reward level (M¼2:06, SD ¼0:39), t160ðÞ¼0:28,
p¼:777, dz¼0:02, 95%CI [0:18, 0:13]. To estimate the effect of
reward on the starting point β, we ran a linear mixed model of the form beta
~ expected reward +(expected reward | participant) (see Supplementary
Table 52). The association between the expected reward and the starting
point was not statistically significant, β¼0:00, SE ¼0:01,
t160:00ðÞ¼0:65, p¼:513 (see Supplementary Fig. 5b). That is, there
was no statistically significant difference between the starting point for the
highest expected reward level (M¼0:52, SD ¼0:12) and the starting point
for the lowest expected reward level (M¼0:53, SD ¼0:11),
t160ðÞ¼0:75, p¼:455, dz¼0:06, 95%CI [0:21, 0:10 ]. However, a
linear mixed model of the form delta ~ expected reward +(expected reward
| participant) (see Supplementary Table 53) revealed that the drift rate
increased as the expected reward increased, β¼0:17, SE ¼0:02,
t160:00ðÞ¼8:27, p<:001 (see Supplementary Fig. 5c). That is, the drift rate
for the highest expected reward level (M¼0:45, SD ¼0:48) was sig-
nificantly higher than the drift rate for the lowest expected reward level
(M¼0:11, SD ¼0:35), t160ðÞ¼7:52, p<:001, dz¼0:59, 95%CI [0:42,
0:76]. A linear mixed model of the form tau ~ expected reward +(expected
reward | participant) (see Supplementary Table 54) showed a trend towards
a decreasing non-decision time as the reward increased, β¼0:02,
SE ¼0:01, t160:00ðÞ¼1:88, p¼:062 (see Supplementary Fig. 5d). That
is, the non-decision time for the highest expected reward level (M¼1:04,
SD ¼0:24) was significantly lower than for the lowest expected reward level
(M¼1:08, SD ¼0:27), t160ðÞ¼2:00, p¼:048, dz¼0:16, 95%CI
[0:31, 0:00]. In general, participants median reaction time (in seconds)
was shorter when they expected a high (M¼1:76, SD ¼0:39) versus low
reward (M¼1:94, SD ¼0:52), t160ðÞ¼7:50, p<:001, dz¼0:59,
95%CI [0:76, 0:42].
Experiment 2
To evaluate the effect of reward on hits in the congruent group, we ran the
following generalized linear mixed model with a logit link function: hit (0 or
1) ~ reward +(reward | participan t) +(reward | image) (see Supplementary
Table 26; we report the effect of adding an interaction with exposure
duration in Supplementary Table 49). There was a statistically significant
increase in hits the higher the reward was, β¼0:13, SE ¼0:03,
z13184ðÞ¼4:94, p<:001 (see Fig. 4a). Consequently, the hit rate for the
highest reward level (M¼0:63, SD ¼0:12) was significantly higher than
for the lowest reward level (M¼0:56, SD ¼0:13), t102ðÞ¼5:25, p<:001,
dz¼0:52, 95%CI [0:31, 0:72]. Even though this effect of reward on hits is
nominally larger than in experiment 1, a comparison between the two
experiments (hit (0 or 1) ~ reward *experiment +(reward +experiment ||
participant) +(1 | image); see Supplementary Table 27), did not show a
statistically significant reward xexperiment interaction, β¼0:04,
SE ¼0:03, z38912ðÞ¼1:33, p¼:182.
We analyzed the effect of true and shown reward on hits in the
incongruent group, with the following generalized linear mixed model with
a logit link function: hit (0 or 1) ~ true reward +shown reward +(shown
reward | participant) +(1 | image) (see Supplementary Table 28). The
higher the shown reward was the more hits participants achieved, β¼0:15,
SE ¼0:04, z13056ðÞ¼4:05, p<:001 (see Fig. 4c),butthetruerewardhad
no statistically significant effect, β¼0:02, SE ¼0:02, z13056ðÞ¼0:96,
p¼:337 (see Fig. 4b). That is, the hit rate for the highest shown reward level
(2150 gems) (M¼0:62, SD ¼0:17) was higher than for the lowest shown
reward level (50 gems) (M¼0:56, SD ¼0:16), t101ðÞ¼3:80, p<:001,
dz¼0:38, 95%CI [0:17, 0:58]. However, there was no statistically sig-
nificant difference between the hit rate for the highest true reward level
(M¼0:60, SD ¼0:13) and the lowest true reward level (M¼0:60),
SD ¼0:15, t101ðÞ¼0:08, p¼:936, dz¼0:01, 95%CI [0:19, 0:20].
Even though the effect of reward on hits was nominally larger in the con-
gruent group than the effect of shownrewardonhitsintheincongruent
group, a comparison between the two groups (hit (0 or 1) ~ shown reward *
group +(shown reward +group | participant) +(1 | image); see Supple-
mentary Table 29) did not show a statistically significant reward xexperi-
ment interaction, β¼0:01, SE ¼0:04, z26240ðÞ¼0:13, p¼:895.
In an exploratory analysis, we investigated whether the influence of the
shownrewardonparticipants’decisions was associated with their overall
memory performance. First, we extracted the by-participant slope for the
shown reward effect from a mixed model of the form response (old or new)
~ shown reward +(shown reward | participant) +(shown reward | image ).
We then correlated the (absolute) slope with participants’overall memory
strength in the task (d’). Participants whose old/new decisions were more
strongly influenced by the shown reward (i.e., the more the slope differed
from 0) performed worse in the Motivated Learning Task, r100ðÞ¼:31,
p¼:002 (see Fig. 4d). Upon visual inspection, it seemed like only a few data
points belonging to participants with steeper slopes were driving the cor-
relation. However, when removing those outliers (all participants with a
slope ≥:3), the correlation remained statistically significant, r89ðÞ¼:23,
p¼:030.Theshownrewardmightinfluence target trials differently,
because for targets, shown reward information can potentially be in conflict
with the true reward information. This is why we repeated the previous
exploratory analysis for target trials. We extracted the by-participant slope
for the shown reward effect from a mixed model of the form hit (0 or 1) ~
shown reward +(shown reward | participant) +(1 | image). We then
correlated the (absolute) slope with participants’overall memory strength in
the task (d’). Participants whose hits were more strongly influenced by the
shown reward (i.e., the more the slope differed from 0) performed worse in
the Motivated Learning Task, r100ðÞ¼:29, p¼:003 (see Fig. 4e). Upon
visual inspection, it seemed like only a few data points belonging to
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Communications Psychology | (2024) 2:31 7

participants with steeper slopes were driving the correlation. However,
when removing those outliers (all participants with a slope ≥:5), the cor-
relation remained statistically significant, r95ðÞ¼:20, p¼:047.
We analyzed the false alarms as a function of shown reward and group
in the following generalized linear mixed model with a logit link function:
false alarm (0 or 1) ~ reward *group +(reward | participant) +(reward ||
image), run on lure trials only (see Supplementary Table 30). The higher the
shown reward was, the more false alarms participants made, β¼0:13,
SE ¼0:03, z26240ðÞ¼4:92, p<:001. There was no statistically significant
difference in the number of false alarms between the two groups, β¼0:14,
SE ¼0:10, z26240ðÞ¼1:43, p¼:153, but a statistically significant
interaction between shown reward and group, β¼0:14, SE ¼0:05,
z26240ðÞ¼2:76, p¼:006 (see Fig. 5). We followed up on the inte raction
with separate models per group (false alarm (0 or 1) ~ reward +(reward |
participant) +(1 | image)). In both the congruent group, β¼0:07,
SE ¼0:03, z13184ðÞ¼2:15, p¼:031 (see Supplementary Table 31), and
the incongruent group, β¼0:20, SE ¼0:04, z13056
ðÞ
¼4:61, p<:001 (see
Supplementary Table 32), the higher the reward for lures, the more false
alarms participants made. However, this relationship was stronger for the
incongruent group. There was no statistically significant difference in the
false alarm rate for the lowest reward level (50 gems) between the incon-
gruent group (M¼0:31, SD ¼0:13), and the congruent group,
0.00
0.25
0.50
0.75
1.00
50 750 1450 2150
reward
hit rate
congruent
a
0.00
0.25
0.50
0.75
1.00
50 750 1450 2150
true reward
incongruent true
b
0.00
0.25
0.50
0.75
1.00
50 750 1450 2150
shown reward
incongruent shown
c
p0.001*
0.55
0.60
0.65
0.70
50 750 1450 2150
reward
hit rate
p 0.337
0.55
0.60
0.65
0.70
50 750 1450 2150
true reward
p0.001*
0.55
0.60
0.65
0.70
50 750 1450 2150
shown reward
R=0.31, p=0.002
0.0
0.5
1.0
1.5
0.00 0.25 0.50 0.75 1.00 1.25
decision ~ shown reward
overall d'
d
R=0.29, p= 0.003
0.0
0.5
1.0
1.5
0.0 0.3 0.6 0.9
hit ~ shown reward
overall d'
e
Fig. 4 | Hit rate in experiment 2. a Hit rate per reward level for the congruent group
(where true and shown reward were identical) based on n= 103 participants. Par-
ticipants’hit rate was higher the higher the reward was. bHit rate per level of true
reward for the incongruent group based on n= 102 participants. There was no
statistically significant association between true reward and hit rate. cHit rate per
level of shown reward for the incongruent group based on n= 102 participants.
Participants’hit rate was higher the higher the shown reward was. For each panel the
beeswarm plot shows orange dots for each individual participant. Light grey lines
connect the dependent data points. The lineplot plot of each panel shows the mean
hit rate per reward level. Black error bars show the within-subjec t standard error, as
implemented in the R package Rmisc50,51.P-values are reported for reward effect in
the mixed models reported in text, with asterisks representing significance at α¼
0.05. dThe correlation between the shown reward effect on the old/new decision (in
the model decision ~ shown reward +(shown reward | participant) +(shown
reward | image)) and overall memory strength in the Motivated Learning Task. The
analysis is based on the incongruent group (based on n= 102 participants). The
stronger the influence of shown reward on participants’decisions, the worse their
memory strength. The correlation remained statistically significant when removing
participants with steep slopes (slope ≥:3). eThe correlation between the shown
reward effect on hits (in the model hit ~ reward +(reward | participant) +(1 |
image)) and overall memory strength in the Motivated Learning Task. The analysis
is based on the incongruent group (based on n= 102 participants). The stronger the
influence of shown reward on whether participants made a hit or not, the worse their
memory strength. The correlation remained statistically significant when removing
participants with steep slopes (slope ≥:5). Pearson correlations are reported.
Asterisks represent significance at α¼.05.
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Communications Psychology | (2024) 2:31 8

(M¼0:32, SD ¼0:12), t202:39ðÞ¼1:07, p¼:288, d¼0:15, 95%
CI [0:42, 0:13]. But for the highest reward level (2150 gems), the false
alarm rate was significantly higher for the incongruent group (M¼0:40,
SD ¼0:16), than for the congruent group, (M¼0:34, SD ¼0:12),
t189:55ðÞ¼2:97, p¼:003, d¼0:42, 95%CI [0:14, 0:69].
Descriptively, the false alarm rate drops between the 3rd (1450 gems;
M¼0:37, SD ¼0:12) and highest (2150 gems; M¼0:34, SD ¼0:12)
reward level, but exploring this difference,wefoundthatitwasnotstatis-
tically significant, t203:45ðÞ¼1:40, p¼:163, d¼0:19, 95%CI
[0:47, 0:08].
For the congruent group, we preregistered an effect of reward on
memory strength, measured as d’. We tested this hypothesis using the
following linear mixed model: d’~reward+(reward || participant). We
found that there was a statistically significant increase in d’the higher the
reward was, β¼0:06, SE ¼0:02, t140:67ðÞ¼2:54, p¼:012 (see Fig. 6a
and Supplementary Table 33). Accordingly, d’for the highest reward level
(2150 gems) (M¼0:79, SD ¼0:51) was significantly higher than for the
lowest reward level (50 gems) (M¼0:66, SD ¼0:43), t102ðÞ¼2:85,
p¼:005, dz¼0:28, 95%CI [0:08, 0 :48]. ROC analyses corroborated these
findings (see Supplementary Fig. 2). Upon visual inspection (see Fig. 6a), it
appeared that the effect of reward on d’seemed to be mainly driven by the
highest reward level, while there seemed to be no difference between the
lower levels. We followed this up with an additional exploratory linear
mixed model of the form d’~reward+(1 | participant), where reward was
not treated as a linear, but a categorical predictor (because more parameters
must be estimated for a categorical predictor, the model structure had to be
simplified in order to reach convergence). The lowest reward level was used
as reference category. Indeed, only for the highest reward level there was a
statistically significant difference from the first level β¼0:13, SE ¼0:05,
t306:00ðÞ¼2:90, p¼:004, but not for the two medium reward categories
(all p>:669; see Supplementary Table 34).
For the incongruent group, a meaningful d’could only be calculated for
the shown reward. We preregistered that there would be no statistically
significant effect of shown reward on d’. In line with this, a linear mixed
model (d’~ shown reward +(shown reward | participant); see Supple-
mentary Table 35) did not show a statistically significant effect of shown
reward on d’,β¼0:04, SE ¼0:02, t101:00ðÞ¼
1:61, p¼:110
(Fig. 6b). Accordingly, there was no statistically significant difference in d’
between the highest shown reward level (2150 gems) (M¼0:61,
SD ¼0:54) and the lowest shown reward level (50 gems) (M¼0:71,
SD ¼0:50), t101ðÞ¼1:72, p¼:088, dz¼0:17, 95%CI
[0:37, 0:03].
To investigate the effect of reward on decision-making (criterion C), we
ran the following linear mixed model: criterion ~ reward +(reward | par-
ticipant), in the congruent group (see Supplementary Table 36). The higher
the reward was, the more lenient criterion was (i.e., participants were more
likely to categorize a picture as old for higher rewards), β¼0:06,
SE ¼0:01, t101:99ðÞ¼4:84, p<:001 (see Fig. 6c). Criterion for the lowest
reward level (M¼0:16, SD ¼0:29) was more strict than for the highest
reward level (M¼0:04), SD ¼0:26, t102ðÞ¼4:56, p<:001,
dz¼0:45, 95%CI [0:65, 0:25]. For the incongruent group, a
meaningful criterion could only be calculated for the shown reward. We
preregistered that there might be an effect of shown reward on criterion. In a
linear mixed model (criterion ~ shown reward +(shown reward | partici-
pant); see Supplementary Table 37), we found that the criterion became
more lenient the higher the shown reward was β¼0:11, SE ¼0:02,
t101:00ðÞ¼5:19, p<:001 (see Fig. 6d). Criterion for the lowest reward
level (M¼0:20, SD ¼0:35) was more strict than for the highest reward
level (M¼0:03, SD ¼0:42), t101ðÞ¼5:24, p<:001, dz¼0:52,
95%CI [0:72, 0:31].
We explored whether confidence affected hits, potentially interacting
with reward, in the following generalized linear mixed model with a logit link
function for the congruent group: hit (0 or 1) ~ reward *confidence +(
reward +confidence | participant) +(confidence | image) (see Supple-
mentary Table 38). The higher their confidence,themorehitsparticipants
made, β¼0:55, SE ¼0:10, z13184ðÞ¼5:66, p<:001. However, there was
no statistically significant effect of reward on hits, β¼0:08, SE ¼0:04,
z13184ðÞ¼1:69, p¼:090 (although the p-value suggests a trend in the
same direction as without adding confidence), and no statistically significant
interaction between reward and confidence, β¼0:05, SE ¼0:04,
z13184ðÞ¼1:32, p¼:187. For the incongruent group, we explored the
influence of true reward and confidence on hits in the following generalized
linear mixed model with a logit link function: hit (0 or 1) ~ true reward *
confidence +(confidence || participant) +(1 | image) (see Supplementary
Table 39). With increasing confidence, hits increased, β¼0:58, SE ¼0:09,
z13056ðÞ¼6:53, p<:001, but there was no statistically significant effect of
true reward on hits, β¼0:05, SE ¼0:04, z13056ðÞ¼1:22, p¼:221, nor a
statistically significant interaction between true reward and confidence,
Fig. 5 | False alarm rate in experiment 2. False
alarm rate is shown per level of shown reward for
each group (congruent: n= 103 participan ts;
incongruent: n= 102 participants). In both groups,
the false alarm rate increased as the shown reward
increased (main effect: p<:001). However, this rela-
tionship was stronger in the incongruent group
(interaction effect: p¼:006). In the beeswarm plots,
blue dots show the false alarm rate per participant,
with light grey lines connecting the dependent data
points. The line plots panels show the mean false
alarm rate per shown reward level. Black error bars
show the within-subject standard error, as imple-
mented in the R package Rmisc50,51.P-values for the
effect of reward in a mixed model per group each are
reported (see main text). Asterisks represent sig-
nificance at α¼.05.
0.0
0.2
0.4
0.6
0.8
1.0
50 750 1450 2150
shown reward
false alarm rate
congruent
0.0
0.2
0.4
0.6
0.8
1.0
50 750 1450 2150
shown reward
incongruent
p 0.031*
0.30
0.35
0.40
50 750 1450 2150
shown reward
false alarm rate
p0.001*
0.30
0.35
0.40
50 750 1450 2150
shown reward
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 9

β¼0:02, SE ¼0:03, z13056ðÞ¼0:57, p¼:572. We further investi-
gated the influence of shown reward and confidenceonhitsintheincon-
gruent group with the following generalized linear mixed model with a logit
link function: hit (0 or 1) ~ shown reward *confidence +(shown
reward +confidence | participant) +(confidence || image) (see Supple-
mentary Table 40). The higher the shown reward, the more hits participants
made, β¼0:19, SE ¼0:05, z13056ðÞ¼3:69, p<:001, and the higher their
confidence, the more hits participants made, β¼0:61, SE ¼0:10,
z13056ðÞ¼5:99, p<:001. However, there was no statistically significant
interaction between shown reward and confidence, β¼0:05, SE ¼0:04,
z13056ðÞ¼1:37, p¼:170.
We explored whether confidence and reward affected false alarms in the
congruent group using the following generalized linear mixed model with a
logit link function: false alarm (0 or 1) ~ shown reward *confidence +(
shown reward | participant) +(1 | image) (see Supplementary Table 41).
With increasing confidence, false alarms decreased, β¼0:31, SE ¼0:05,
z13184ðÞ¼5:75, p<:001, but there was no statistically significant effect of
shown reward on false alarms, β¼0:05, SE ¼0:05, z13184ðÞ¼1:04,
p¼:300, nor a statistically significant interaction between shown reward
and confidence, β¼0:03, SE ¼0:04, z13184ðÞ¼0:71, p¼:480. For the
incongruent group, we investigated whether confidence and reward affected
false alarms using the following generalized linear mixed model with a logit
link function: false alarm (0 or 1) ~ shown reward *confidence +(shown
reward +confidence | participant) +(1 | image) (see Supplementary
Table 42). The higher the shown reward, the more false alarms participants
made, β¼0:20, SE ¼0:06, z13056ðÞ¼3:51, p<:001, and the higher their
confidence, the less false alarms participants made, β¼0:53, SE ¼0:10,
z13056ðÞ¼5:52, p<:001. However, there was no statistically significant
interaction between shown reward and confidence, β¼0:01, SE ¼0:04,
z13056ðÞ¼0:26, p¼:794.
By introducing rewards that are orthogonal to the true reward, we
might have decreased participants’confidence in their memory. By violating
their reward expectations, participants might not have relied on their
memory anymore, but only on the reward information that was presented.
In an exploratory analysis, we compared confidence for targets and lures
between the two groups in the following model: confidence ~ group *image
type +(image type | participant) (see Supplementary Table 43). We found
confidence to be higher for targets than for lures, β¼0:10, SE ¼0:01,
t203:01ðÞ¼9:37, p<:001. However, there was no statistically significant
difference in confidence between the two groups, β¼0:05, SE ¼0:05,
t203:00ðÞ¼0:91, p¼:365, and no statistically significant group x image
type interaction, β¼0:01, SE ¼0:02, t203:01ðÞ¼0:66, p¼:510.
To investigate whether exposure duration influences hit rate, we ran
the following generalized linear mixed model with a logit link function for
thecongruentgroup:hit(0or1)~duration+(duration | participant) +(1
|| image) (see Supplementary Table 44). The longer an image was presented
during the learning phase, the more likely it became that participants in the
congruent group made a hit in a given target trial, β¼0:14, SE ¼0:05,
z13184ðÞ¼2:50, p¼:012. Consequently, in the congruent group, the hit
rate for the longest exposure duration of 2500 ms (M¼0:62, SD ¼0:11)
was significantly higher than for the shortest exposure duration of 1500 ms
(M¼0:60, SD ¼0:12), t102ðÞ¼2:36, p¼:020, dz¼0:23, 95%CI
congruent
−0.5
0.5
1.5
2.5
3.5
50 750 1450 2150
reward
d'
p 0.012*
0.55
0.75
0.95
50 2150
reward
aincongruent
−0.5
0.5
1.5
2.5
3.5
50 750 1450 2150
shown
reward
d'
p 0.11
0.55
0.75
0.95
50 2150
shown
reward
b
congruent
−0.9
−0.3
0.3
0.9
1.5
50 750 1450 2150
reward
criterion
p0.001*
−0.1
0.0
0.1
0.2
0.3
50 2150
reward
cincongruent
−0.9
−0.3
0.3
0.9
1.5
50 750 1450 2150
shown
reward
criterion
p0.001*
−0.1
0.0
0.1
0.2
0.3
50 2150
shown
reward
d
Fig. 6 | Memory strength and decision criterion in experiment 2. a Memory
strength d’per level of reward for the congruent group. Memory strength increased
with increasing reward. bMemory strength d’per level of shown reward for the
incongruent group. The effect of shown reward on memory strength was not sta-
tistically significant. Note that participants with an overall memory performance of
d’≤0 were excluded from data analysis. However, participants may still show a
performance of d’≤0 when d’is calculated for each reward level. cDecision criterion
C per level of reward for the congruent group. The higher the reward, the more
lenient the decision criterion was. dDecision criterion C per level of shown reward
for the incongruent group. The higher the shown reward, the more lenient the
decision criterion was. In the beeswarm plots of each panel, coloured dots represent
data per participant, with light grey lines connecting the dependent data points. In
the line plots of each panel, coloured dots show group means. Black error bars show
the within-subject standard error, as implemented in the R package Rmisc50,51. For
the congruent group, n= 103 participants are shown, for the incongruent group,
n= 102 participants are shown. P-values for the reward effect in separate models for
memory strength and decision criterion per group are reported (see main text).
Asterisks represent significance at α¼.05.
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 10

[0:04, 0:43]. For the incongruent group, we fit a generalized linear mixed
model with a logit link function of the same structure as for the congruent
group. The longer an image was presented during the learning phase, the
more likely it became that participants in the incongruent group made a hit
in a given target trial, β¼0:15, SE ¼0:06, z13056ðÞ¼2:56, p¼:010 (see
Supplementary 45). Consequently, in the incongruent group, the hit rate for
the longest exposure duration of 2500 ms (M¼0:60, SD ¼0:16) was
significantly higher than for the shortest exposure duration of 1500 ms
(M¼0:57, SD ¼0:14), t101ðÞ¼2:60, p¼:011, dz¼0:26, 95%CI
[0:06, 0:45].
In an exploratory alternative analysis of the congruent group of
experiment 2, we investigated whether the reward had an effect on whether
participants responded “old”or “new”. That is, we ran a drift diffusion
model on all trials with the outcome variable “old”(lower boundary) or
“new”(upper boundary). For the complex model, we let boundary
separation, starting point, drift rate, and non-decision time vary by reward
level (50, 750, 1450 or 2150 gems). Since no participants had to be excluded
due to a lack of trials, the model was run on all n= 103 participants. When
using the difference in BIC as criterion, the complex model was preferred in
100.00% of cases. When using the difference in AIC as criterion, the com-
plex model was preferred in 100.00% of cases. According to the number of
statistically significant likelihood ratio tests between the two models, the
complex model provided a better fit in 45.63% of cases.
To estimate the effect of reward on boundary separation α,werana
linear mixed model of the form alpha ~ reward +(reward | participant) (see
Supplementary Table 55). There was no statistically significant effect of
reward on boundary separation, β¼0:00, SE ¼0:01, t102:00ðÞ¼0:45,
p¼:656 (see Supplementary Fig. 6a). That is, there was no statistically
significant difference between boundary separation for the highest reward
level (M¼2:06, SD ¼0:36) and the lowest reward level (M¼2:05,
SD ¼0:35), t102ðÞ¼0:51, p¼:608, dz¼0:05, 95 %CI [0:14, 0:24]. To
estimate the effect of reward on the starting point β, we ran a linear mixed
model of the form beta ~ reward +(reward | participant) (see Supple-
mentary Table 56). The starting point decreased as the reward increased,
β¼0:01, SE ¼0:00, t102:00ðÞ¼3:14, p¼:002 (see Supplementary
Fig. 6b). That is, the starting point for the highest reward level (M¼0:48,
SD ¼0:08) was significantly lower (closer to “old”) than the starting point
for the lowest reward level (M¼0:51, SD ¼0:08), t102ðÞ¼3:24,
p¼:002, dz¼0:32, 95%CI [0:52, 0:12]. A linear mixed model of
the form delta ~ reward +(reward | participant) (see Supplementary
Table 57) revealed a trend towards a decreasing drift rate as the reward
increased, β¼0:02, SE ¼0:01, t102:00ðÞ¼1:85, p¼:068 (see Sup-
plementary Fig. 6c). However, there was no statistically significant difference
between the drift rate for the highest reward level (M¼0:06, SD ¼0:23)
and the lowest reward level (M¼0:10, SD ¼0:23), t102ðÞ¼1:63,
p¼:106, dz¼0:16, 95%CI [0:35, 0:03]. A linear mixed model of the
form tau ~ reward +(1 | participant) (see Supplementary Table 58) indi-
cated a significant increase of the non-decision time as the reward increased,
β¼0:02, SE ¼0:00, t308:00ðÞ¼3:47, p<:001 (see Supplementary
Fig. 6d). That is, the non-decision time for the highest reward level
(M¼1:03, SD ¼0:18) was higher than for the lowest reward level
(M¼0:99, SD ¼0:19), t102ðÞ¼3:67, p<:001, dz¼0:36, 95%CI [0:16,
0:56]. In the congruent group of experiment 2, participants’median reaction
times (in seconds) were slower when they made a decision for a high
(M¼1:90, SD ¼0:47) vs. a low reward (M¼1:84, SD ¼0:39),
t102ðÞ¼2:48, p¼:015, dz¼0:24, 95%CI [0:05, 0:44].
For the incongruent group, we likewise ran an exploratory alternative
analysis and investigated whether the shown reward had an effect on
whether participants responded “old”or “new”. That is, we ran a drift
diffusion model on all trials with the outcome variable “old”(lower
boundary) or “new”(upper boundary). For the complex model, we let
boundary separation, starting point, drift rate, and non-decision time vary
by reward level (50, 750, 1450 or 2150 gems). Since no participants had to be
excluded due to a lack of trials, the model was run on all n= 102 participants.
When using the difference in BIC as criterion, the complex model was
preferred in 100.00% of cases. When using the difference in AIC as criterion,
the complex model was preferred in 100.00% of cases. According to the
number of statistically significant likelihood ratio tests between the two
models, the complex model provided a better fit in 60.78% of cases.
To estimate the effect of reward on boundary separation α,werana
linear mixed model of the form alpha ~ reward +(1 | participant) (see
Supplementary Table 59). There was no statistically significant effect of
reward on boundary separation, β¼0:01, SE ¼0:01, t305:00ðÞ¼1:54,
p¼:124 (see Supplementary Fig. 7a). That is, there was no statistically
significant difference between boundary separation for the highest reward
level (M¼2:12, SD ¼0:35) and the lowest reward level (M¼2:09,
SD ¼0:34), t101ðÞ¼1:71, p¼:090, dz¼0:17, 95 %CI [0:03, 0:36]. To
estimate the effect of reward on the starting point β, we ran a linear mixed
model of the form beta ~ reward +(reward | participant) (see Supple-
mentary Table 60). The starting point decreased as the reward increased,
β¼0:02, SE ¼0:00, t101:00ðÞ¼3:87, p<:001 (see Supplementary
Fig. 7b). That is, the starting point for the highest reward level (M¼0:48,
SD ¼0:09) was significantly lower (closer to “old”) than the starting point
for the lowest reward level (M¼0:52, SD ¼0:08), t101ðÞ¼3:76,
p<:001, dz¼0:37, 95%CI [0:57, 0:17]. A linear mixed model of the
form delta ~ reward +(reward | participant) (see Supplementary Table 61)
revealed that the drift rate decreased as the reward increased, β¼0:04,
SE ¼0:01, t100:99ðÞ¼3:54, p<:001 (see Supplementary Fig. 7c). That is,
the drift rate for the highest reward level (M¼0:01, SD ¼0:26) was sig-
nificantly lower than the drift rate for the lowest reward level (M¼0:11,
SD ¼0:24), t101ðÞ¼3:71, p<:001, dz¼0:37, 95%CI [0:57,
0:17]. A linear mixed model of the form tau ~ reward +(reward | par-
ticipant) (see Supplementary Table 62) revealed that the non-decision time
increased as the reward increased, β¼0:02, SE ¼0:01, t101:00ðÞ¼3:13,
p¼:002 (see Supplementary Fig. 7d). That is, the non-decision time for the
highest reward level (M¼1:01, SD ¼0:26) was significantly higher than
for the lowest reward level (M¼0:98, SD ¼0:26), t101ðÞ¼2:82,
p¼:006, dz¼0:28, 95%CI [0:08, 0:48]. In the incongruent group of
experiment 2, participants’median reaction times (in seconds) were slower
when they made a decision for a high (M¼1:90, SD ¼0:49) vs. a low
reward (M¼1:84, SD ¼0:46), t101ðÞ¼3:45, p<:001, dz¼0:34, 95 %CI
[0:14, 0:54].
Experiment 3
The hit rate for the high reward level (M¼0:64, SD ¼0:14) was sig-
nificantly higher than for the low reward level (M¼0:62, SD ¼0:14),
t186ðÞ¼3:26, p¼:001, dz¼0:24, 95%CI [0:09, 0:38] (see Fig. 7a).
The false alarm rate for the high reward level (M¼0:34, SD ¼0:14)
was significantly higher than for the low reward level (M¼0:32,
SD ¼0:14), t186ðÞ¼2:65, p¼:009, dz¼0:19, 95%CI [0:05,
0:34] (Fig. 7b).
We preregistered a one-sided t-test to evaluate our hypothesis that
memory strength (d’)wouldbehigherforhighthanforlowrewards.
However, there was no statistically significant difference in d’between the
high (M¼0:86, SD ¼0:58) and low reward (M¼0:85, SD ¼0:61) in a
preregistered, one-sided t-test, t186ðÞ¼0:42, p¼:337, dz¼0:03, 95%CI
[0:09, Inf ](seeFig.7c). ROC analyses corroborated the findings from the
d’analyses (see Supplementary Fig. 2). We preregistered that the confidence
interval for the effect of reward on memory strength in experiment 3 would
lie entirely above the effect size estimate in experiment 2 (congruent group),
which was not the case. However, memory strength was significantly higher
in experiment 3 (M¼0:84, SD ¼0:57) than in experiment 2 (M¼0:67,
SD ¼0:38), t322:01ðÞ¼3:43, p<:001, d¼0:35, 95%CI [0:15, 0:55].
Criterion was significantly more lenient for the high (M¼0:04,
SD ¼0:32) than for the low reward level (M¼0:04, SD ¼0:32),
t186ðÞ¼3:84, p<:001, dz¼0:28, 95%CI [0:43, 0:13] (see
Fig. 7d). That is, participants were more willing to identify a picture as old
when the reward was high.
There was no statistically significant difference between the hit rate for
the long duration level (M¼0:63, SD ¼0:13) and the short duration level
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 11

(M¼0:64, SD ¼0:14), t186ðÞ¼1:49, p¼:137, dz¼0:11, 95%CI
[0:25, 0:03].
In an exploratory analysis, we evaluated the influence of confidence
and reward on the hit rate and the false alarm rate. We ran the following
generalized linear mixed model with a logit link function on the target trials:
hit (0 or 1) ~ confidence *reward +(confidence +reward | partici-
pant) +(confidence || image) (see Supplementary Table 46). In this model,
we confirmed that the higher the reward, the more hits participants
achieved, β¼0:11, SE ¼0:05, z23936ðÞ¼2:43, p¼:015. Furthermore,
participants had more hits with increasing confidence, β¼0:92,
SE ¼0:07, z23936ðÞ¼13:12, p<:001. There was no statistically significant
interaction between reward and confidence, β¼0:01, SE ¼0:04,
z23936ðÞ¼
0:24, p¼:810. For lure trials, we ran the following gen-
eralized linear mixed model with a logit link function: false alarm (0 or 1) ~
confidence *reward +(confidence +reward || participant) +(confidence
|| image) (see Supplementary Table 47). For high rewards, participants made
more false alarms, β¼0:10, SE ¼0:05, z23936ðÞ¼2:25, p¼:024.
Likewise, participants made more false alarms with increasing confidence,
β¼0:39, SE ¼0:08, z23936ðÞ¼4:84, p<:001. There was no statisti-
cally significant interaction between reward and confidence, β¼0:03,
SE ¼0:05, z23936ðÞ¼0:63, p¼:527.
In an exploratory alternative analysis, we investigated whether the
reward had an effect on whether participants responded “old”or “new”.
That is, we ran a drift diffusion model on all trials with the outcome variable
“old”(lower boundary) or “new”(upper boundary). For the complex model,
we let boundary separation, starting point, drift rate, and non-decision time
vary by reward level (£ 0.2 or 10). Since no participants had to be excluded
due to a lack of trials, the model was run on all N= 187 participants. When
using the difference in BIC as criterion, the complex model was preferred in
99.47% of cases. When using the difference in AIC as criterion, the complex
model was preferred in 99.47% of cases. According to the number of sta-
tistically significant likelihood ratio tests between the two models, the
complex model provided a better fit in 39.04% of cases.
There was no statistically significant difference between boundary
separation for the high reward level (M¼2:15, SD ¼0:35) and the low
reward level (M¼2:15, SD ¼0:35), t186ðÞ¼0:04, p¼:970,
dz¼0:00, 95%CI [0:15, 0:14] (see Supplementary Fig. 8a). There was no
statistically significant difference between the starting point for the high
reward level (M¼0:51, SD ¼0:07) and the low reward level (M¼0:50,
SD ¼0:06), t186ðÞ¼1:18, p¼:238, dz¼0:09, 95%CI [0:23,
0:06] (see Supplementary Fig. 8b). The drift rate for the high reward level
(M¼0:00, SD ¼0:22) was significantly lower than the drift rate for the
low reward level (M¼0:05, SD ¼0:21), t186ðÞ¼3:05, p¼:003,
dz¼0:22, 95%CI [0:08, 0:37] (see Supplementary Fig. 8c). There was no
statistically significant difference between the non-decision time for the high
reward level (M¼0:83, SD ¼0:33) and the low reward level (M¼0:82,
SD ¼0:31), t186ðÞ¼0:49, p¼:625, dz¼0:04, 95%CI [0:18,
0:11] (see Supplementary Fig. 8d). In experiment 3, there was no statistically
significant difference in median reaction times between high (M¼1:76,
SD ¼0:40) and low reward decisions (M¼1:75, SD ¼0:40),
t186ðÞ¼1:24, p¼:216, dz¼0:09, 95%CI [0:05, 0:23].
Discussion
In three experiments, we investigated whether reward impacts memory
strength at encoding or decision-making strategies at retrieval for reward-
related long-term memory. We replicated the well-documented finding that
reward increases the hit rate. While experiment 1 did not yield an inter-
pretable false alarm rate per reward level, experiments 2 and 3 provided
evidence that reward modulates decision-making strategies at retrieval. In
the congruent group of experiment 2, we found an effect of reward on
memory strength, but in experiment 3, there was no statistically significant
effect of reward on memory strength. Crucially, in experiment 1, we found
that participants displayed explicit knowledge of reward contingencies,
which was related to the effect of reward on hit rate.
In experiment 1, we aimed to disentangle the contribution of memory
strength versus decision-making strategies to this effect. For this,
0.00
0.25
0.50
0.75
1.00
0.2 10
reward
hit rate
p 0.001*
0.55
0.60
0.65
0.70
0.2 10
reward
hit rate
a
0.0
0.2
0.4
0.6
0.8
1.0
0.2 10
reward
false alarm rate
p 0.009*
0.30
0.35
0.40
0.2 10
reward
false alarm rate
b
−0.5
0.5
1.5
2.5
3.5
0.2 10
reward
d'
p 0.337
0.55
0.75
0.95
0.2 10
reward
d'
c
−0.9
−0.3
0.3
0.9
1.5
0.2 10
reward
criterion
p0.001*
−0.1
0.0
0.1
0.2
0.3
0.2 10
reward
criterion
d
Fig. 7 | Memory performance in experiment 3. a Hit rate, bfalse alarm rate,
cmemory strength and ddecision criterion for both reward based on N= 187
particpants. In the beeswarm plot of each panel, coloured dots show individual data
points. Light grey lines connect the dots belonging to the same participant. The line
plots of each panel show the group mean for each reward level. Black error bars show
the within-subject standard error, as implemented in the R package Rmisc50,51.P-
values for separate t-tests for hit rate, false alarm rate, memory strength and decision
criterion are reported (see main text). Asterisks represent significance at α¼.05.
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 12

participants rated their expected reward in order to calculate a false reward
rate per reward level. However, reward expectations were highly biased
towards medium rewards for false alarms. This prevented us from calcu-
lating a meaningful d’, because it is unclear what the appropriate denomi-
nator for the false alarm rate would be. There are two alternatives: One is to
divide the number of false alarms per expected reward level by the number
of total trials per expected reward level (per participant). This is technically
not a false alarm rate, because it pits false alarms against hits. The false alarm
rate is normally calculated as the number of false alarms divided by the
number of all lure trials - but since correct rejections are not associated with
a reward value, this does not work on a reward-level basis. The other issue
with this method is that the information that each false alarm rate per
expected reward level is based on a different number of trials is lost. This
might mask criterion effects, e.g., when participants are less likely to identify
a picture as old when their reward expectations are lower, leading to less
trials for the lowest expected reward category. The other alternative would
be to divide the false alarms per expected reward level by a constant (e.g.,
128, the total number of target trials - dividing by 32 trials, the number of
trials per expected reward if lures were evenly distributed across rewards,
does not work, because some participants would end up with a false alarm
rate > 1). This way, a participant who, e.g., is heavily biased towards
expecting medium reward levels will have a lower false alarm rate when
expecting a high reward, which does not necessarily reflect higher accuracy
or a more conservative response criterion. Lastly, when combining the hit
rate and the false alarm rate into d’, for both methods, the reward-dependent
distribution of targets (uniform) and lures (more medium rewards) would
differ, further complicating the interpretation of d’. These issues would be
fixed if we had information about reward expectations for misses and
especially correct rejections. However, we did not want to frustrate parti-
cipants by asking them for their reward expectations when they just told us
that they think a picture is new - and thus has no associated reward. Because
of these issues, we concluded that the false alarm rate per expected reward
level cannot be used to calculate a meaningful d’.Thus,wemodified the
paradigm again in experiment 2. For interested readers, we report d’ana-
lyses in the Supplementary Materials (both based on a denominator per
expected reward level, and a fixed denominator; see Supplementary Note 6).
In our experiment 2, the influence of reward on false alarms differed
between the congruent and incongruent group. In the congruent group,
higher rewards increased the false alarm rate to a lesser degree than in the
incongruent group –in fact, there was a decrease in false alarms between the
third (1450 gems) and the fourth (2150 gems) reward level. Given that the
reward-related increase in memory strength for the congruent group only
emerged for the highest reward level, it is plausible that it is the reduction in
false alarms for the highest reward level that is contributing to the effect.
That is, both the hit rate and the false alarm rate increase as a function of
reward for lower reward levels, reflected in a more lenient decision criterion.
However,thereductioninfalsealarmsfor the highest reward level results in
an increased memory strength for the highest reward level. Since the reward
for lures is only presented during the test phase, it is not based on memory,
however, the decrease in false alarms for the highest reward category might
still be a result of memory processes. Participants in the congruent group
could rely on their source memory especially for high reward targets. When
encountering a new picture with a high reward, this might have resulted in a
greater conflict with their source memory, which made them more careful.
Participants in the incongruent group may have been surprised by the
incongruence of their memory for stimulus-reward contingencies, and
unable to use such strategies.
At first glance, it may be disappointing that hit rate reflects an influence
of reward on decision-making strategies during retrieval rather than memory
strength. However, for reward to influence decision-making processes in a
memory test where no reward information is presented, participants need to
remember which reward belongs to which picture, as was the case in our
experiment 1. That is, participants must learn stimulus-reward associations,
which are then used to make a decision at test. Along this line, it was recently
shown that even memory for unchosen rewards can bias decision making33.
Thus, pure measures of memory strength (i.e., d’) do not isolate the processes
underlying the memory-related modulation of performance by reward in the
Motivated Learning Task. Instead, measures of the decision criterion and
ideally, reward association memory, are preferred. However, modifying the
Motivated Learning Task in such a way that these measures can be assessed is
not trivial, and alternative versions of the task proposed so far all come with
drawbacks. This is why we conclude that the standard version of the task,
with the hit rate as outcome measure, might be a valid option in many
scenarios. However, it should not be interpreted as a measure of memory
strength, but rather as a measure of a memory-based criterion.
Our third experiment with only two reward categories and perfect
information about the rewards at recognition is most comparable to prior
work that –as we did in experiment 3 –finds that reward does not influence
memory strength, but only decision criterion. Two interpretations are
possible: There might be an effect of reward on memory strength, but it
could be so small that it cannot be detected reliably with even large sample
sizes as in our study (around N= 100), let alone with “standard”sample sizes
in the field (around N= 30). This would make it very hard to assess these
effects in more resource-heavy neuroscientific experiments. The alternative
explanation is that effects of reward on memory strength only arise under
very specific conditions. For example, the reward-based change in memory
strength in our second experiment was largely driven by the highest reward
level, while the lower reward levels did not differ in the effect on memory
strength. It might be the case that effects of reward on memory strength only
emerge when there are at least more than two reward levels, allowing par-
ticipants to focus on the comparably few trials with a very high reward, as
compared to half of the trials with a high reward in the case of two reward
levels. This potential moderator of reward context should be teste d in future
research.
Reward contingencies are a form of source memory (i.e., participants
remember the reward associated with a stimulus). In support of this
interpretation, we found participants to have more accurate reward
expectations when their confidence was high. We did not ask for remember/
know judgements, to not further burden our participants, and can thus not
distinguish remember-based responses from familiarity-based responses34.
Similar to our findings, Adcock et al.2report that –unlike for high-
confidence responses –there was no statistically significant effect of reward
on low-confidence responses. Likewise, Shigemune et al.4found that
rewards modified item-source associations, but did not affect item memory
alone. Our observation that more accurate memory of stimulus-reward
associations was correlated with a reward-related increase in hit rate pro-
vides further evidence that the effects of reward on hit rate rely on source
memory.
Bowen et al.20 associated categories with different amounts of reward to
give lures an objective value. Their approach provides perfect information of
reward contingencies and removes the need to form stimulus-reward
associations, since participants rely on perfectly learned category-reward
associations. This decouples decision-making during retrieval from mem-
ory processes. We tried to design a paradigm without perfect reward
information that would still yield a false alarm rate per reward level in
experiment 1, but were not successful. In experiment 2 and 3, we presented
rewards during the test phase, providing an objective reward-modulated
false alarm rate. As the paradigm used by Bowen et al.20,thismeansthat
participants had (or believed to have) perfect information about reward
contingencies, so could base decision on cues presented during retrieval
rather than memory for stimulus-reward associations. However, we directly
manipulated the reward information presented to the participants, which
was either accurate (congruent group) or not (incongruent group). The
differences between the congruent and incongruent group provide
empirical evidence that reward information presented during retrieval
influences participants’behaviour. Crucially, our set of studie sdemonst rates
that the reward associations that bias decision making during retrieval are
part of the construct that is of interest to researchers studying long-term
memory for rewards rather than an unfortunate side effect of the
measurement.
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 13

It is possible that providing participants with reward information
during recognition changes the cognitive processes participants use to
complete the task. I.e., when participants are not presented with any reward
information during recognition (experiment 1), they might rely more
strongly on (stimulus-reward) memory. When reward information is
provided during recognition (experiments 2 and 3), participants might shift
their criterion based on the presented reward, and disregard previously
formed (stimulus-reward) memory. While we cannot rule out this expla-
nation entirely, we argue against it: Overall memory performance is
descriptively even better in experiments 2 and 3 than in experiment 1 (see
Supplementary Table 4), and better performance can only be achieved by
improved discrimination between old and new pictures. Furthermore,
reward information presented during recognition is not neutral, but seems
to influence memory performance: For participants in the incongruent
group, memory strength is worse when they are more strongly influenced by
the shown reward. In line with this, response patterns in experiment 2 differ
between the congruent and the incongruent group, especially for false
alarms. This suggests that even when reward information is presented
during recognition, knowledge about stimulus-reward associations is used
to retrieve matching memory traces. If the reward information presented
during recognition would override the participants’memory entirely, there
would be no difference in performance between the congruent and incon-
gruent group. We argue that rather than overriding existing memory traces,
the reward information presented during recognition is used as a memory
cue that guides retrieval. Lastly, it would be maladaptive if participants
disregarded their memory of the pictures in favour of the reward infor-
mation presented during recognition.
Generally, it makes sense that animals form stimulus-reward associa-
tions, rather than only relying on strengthening of the memory trace for the
highly rewarded stimulus. Remembering a stimulus strongly without
information about its reward contingencies prevents the organism from
adapting to changing reward contexts. For example, scrub jays memorize
where they cached their highly preferred food, mealworms, but also
remember the location of less preferred food, peanuts35. Restricting access to
the mealworms until they have gone bad, leads to the birds reliably retrieving
less perishable peanuts. Likewise, participants in the Motivated Learning
Task use stimulus-reward information encoded during learning or provided
at retrieval testing to optimize decision-making during retrieval. This
interpretation aligns with findings that the effects of reward on decision-
making are sensitive to modulations of punishments for incorrect
decisions20, and that rewards influence retrieval strategies36. This account
also connects the present research to research about model-based versus
model-free learning in reinforcement learning tasks37. For model-based
behaviour the participant can use information about expected stimulus-
reward contingencies to adapt the criterion and maximize monetary gain.
Flexible model-based representations enable participants to generalize
knowledge about rewards to new stimuli across different contexts38.Thisis
in line with recent evidence that dopamine signals causal associations
between cue and reward39. Model-based explanations oppose accounts of
more automatic influences of reward on memory, e.g., automatic dopami-
nergic processes during encoding strengthening the subsequently formed
memory trace2. In tasks where participants have a good, explicit repre-
sentation of the task structure (which we ensured with our validation
questions about the reward contingencies), behaviour is mainly model-
based40,41. In contrast, when learning is incidental, prediction errors based on
reward probability influence (automatic) strengthening of the memory
trace42. Future research could relate inter-individual differences in reward-
associated memory performance to model-based versus model-free deci-
sion-making tendencies.
Our experiments reach similar conclusions as the experiments by
Bowen et al.20. However, our study goes beyond them since in contrast to
their work, we are able to examine the effect of associative reward memory
and the item-specific effects of showing rewards at retrieval, which the
authors draw implicit conclusions about without directly investigating
them. Detailing on this, we test participants’source memory for the rewards
in experiment 1, which provided crucial insights into participants’reward
expectations. Like Bowen et al.20, our version of the task in experiments 2 and
3 provided participants with perfect reward information, minimizing the
need for source memory during recognition. What makes our version of the
task different is that we were able to manipulate the congruency of the
reward information presented during the test phase. We believe that our
results complement and go beyond the results of Bowen et al.20.Inaddition,
our large sample allows for a more precise and more robust estimate of effect
sizes. We demonstrate that reward effects on memory can be categorized as
small43, which means that common sample sizes around 30 participants are
not enough to detect them reliably and therefore the work by Bowen et al.20
was likely not powerful enough to find subtle effects on sensitivity and thus
their conclusions based on absence of evidence were premature.
While our conclusions are based on our preregistered mixed model
analyses, it is helpful to look at the data from a different perspective. Our
alternative analysis based on drift diffusion models, which take reaction
times into account, generally confirms our findings that reward influences
participants’performance at retrieval. In experiment 1, we found that
reward expectations do not bias participantsinthedirectionofahitorfalse
alarm (starting point). Note that the starting point cannot be interpreted as
equivalent to a decision criterion in this model, because the outcome was
“hit”/“false alarm”, and not “old”/“new”. That is, we cannot draw any
conclusions about decision criteria with this model. The drift rate increased
as reward expectations increased, which means evidence accumulation was
faster and more accurate when participants expected a higher reward,
potentially due to more noisy memory traces for low rewards. There was a
trend towards a decreasing non-decision time as the reward increased; the
non-decision time was higher for low rewards than for high rewards. That is,
descriptively, participants needed more time for components that are not
part of the decision process (e.g., early stimulus processing, preparing the
motor response) when the reward was very low. Memory processes during
early retrieval of stimuli might also contribute to the non-decision time.
According to the REM (retrieving effectively from memory44) model, each
item in memory is stored as a vector of features. During a recognition
memory test, the probe vector of the test item is compared to the vectors in
memory to determine whether the item is old or new. While the comparison
of the vectors could be regarded as part of the evidence accumulation phase,
earlier phases of the REM model, e.g., compiling an initial set of vectors that
the probe vector is compared to, could affect the non-decision time. Within
this framework, it might be more effortful to generate a set of possible
matches for low-reward items, because their representation in memory is
weaker.
For both the congruent and incongruent group of experiment 2, we
found that the higher the reward, the more participants were biased towards
responding “old”, which corresponds to the effect of reward on the decision
criterion we found in the main analysis. We found a reduced drift rate as the
reward increased (a trend for the congruent group; a significant effect for the
incongruent group). This may seem at odds with the findings of experiment
1, where the drift rate increased for higher rewards. However –in contrast to
experiment 1 –in experiment 2, the reward information was presented
before the test stimulus was revealed. Participants might spend additional
effort on stimuli labelled as high rewards, even if they do not recognize them.
This might make the evidence accumulation for stimuli labelled as high
rewards more noisy, resulting in an increased drift rate. In experiment 1, on
the other hand, participants might quickly skip over stimuli that do not have
a strong representation in memory. A similar explanation could apply to the
non-decision time, which also increased as the reward increased: Partici-
pants might spend more time on processing a stimulus following a high-
reward cue during the test phase, or generating potentially matching vectors
in memory. The findings of the drift diffusion models for experiment 3
follow a different pattern. There was no statistically significant association
between reward and starting point, but the drift rate was significantly lower
for the high reward level. It is intriguing that experiment 3 had a different
pattern of results in both the main analysis and the exploratory alternative
drift diffusion analysis. A speculative explanation could be that processing
https://doi.org/10.1038/s44271-024-00074-9 Article
Communications Psychology | (2024) 2:31 14

two reward levels is different from processing four reward levels. With two
reward categories, there are more stimuli per category –potentially too
many to prioritize the high rewards.
Taken together, these findings suggest that participants spend more
effort when a stimulus is announced as a high-reward item, regardless of
whether its memory representation is strong. In contrast, decisions based on
reward expectations require less effort, because resources are not “wasted”
on stimuli that are only represented weakly in memory. Our results might
further indicate that non-decision processes might be related to memory
sensitivity. Lastly, it should be noted that because they also take reaction
times into account, the parameters of driftdiffusionmodelsdonotdirectly
correspond to signal detection measures such as memory strength and
decision bias. Thus, the drift diffusion models reported here provide com-
plementary information to the analyses in the main manuscript, rather than
challenging their interpretations.
In previous literature investigating the influence of reward on decisions
and reaction times, the phenomenon of “magnitude sensitivity”has been
described: “a choice between equal alternatives of high magnitude is made
faster compared with a choice between equal alte rnatives of low magnitude”,
where “magnitude”means the summed value of the alternatives45.Inour
experiments, we find the opposite pattern: Participants generally make
slower decisions for stimuli preceded by a high reward. The most striking
differences between our paradigm and those reported in the literature and
magnitude sensitivity is that our participants a) do not choose between
multiple alternatives presented on the screen and b) make their decision
based on memory. To our knowledge, there are no studies investigating the
classical magnitude sensitivity effect in memory-based paradigms. Even
though our Motivated Learning Task differs in several aspects from typical
magnitude sensitivity paradigms, our data might provide tentative evidence
that reward magnitude affects memory-based decisions differently.
Limitations
While experiment 1 enabled us to investigate participants’reward expec-
tations and experiments 2 and 3 allowed us to calculate a reward-de pendent
false alarm rate, we were not able to create a paradigm that solved both
problems at the same time. Future research would greatly benefitfromtasks
that do not need to provide their participants with perfect information about
rewards, but still allow researchers to calculate a reward-dependent false
alarm rate. A step in this direction might be an elegant two-step paradigm by
Jang et al.42, who associated reward probabilities with image categories,
which changed over the course of the experiment. This provided them with
a memory-based false alarm rate per reward probability. They found that
reward prediction errors based on reward probability were associated with
memory strength, but did unfortunately not report a measure of criterion.
Furthermore, in experiment 1, reward expectations were only available
for “old”responses, which means that for correct rejections or misses,
information about reward expectations is missing, limiting our analyses. We
decided not to ask participants about the reward they expecte d to receive for
their “new”decisions because that might have confused or frustrated par-
ticipants. After all, when they identify a picture as new, they do not expect
that the picture is associated with a reward.
In experiment 1 and 2, we used four different reward levels to inves-
tigate potential effects of reward in a more fine-grained manner, which
might make our findings less comparable to previous literature, where it is
common to use only two reward levels2,8,20. It is possible that rewards are
processed differently when there are more reward levels. For example, since
there are more images per reward level, participants might have less asso-
ciative memories for each reward level. Less stimuli per reward level might
allow them to prioritize the most salient information (i.e., the highest reward
level). This would explain why results for experiment 3, where we used only
two reward levels, differed from those for the congruent group of experi-
ment 2, even though we cannot attribute the different results between the
two experiments to the difference in reward levels with complete certainty.
Future work should systematically investigate the influence of the number of
reward levels on memory performance. However, another methodological
limitation for paradigms that employ more reward levels is that less infor-
mation (number of trials) per reward level is available, limiting statistical
analyses.
Another limitation of our (and many previous) studies is the com-
parably small amount of money that participants could earn during the task.
However, the striatal response t o rewarding stimuli is not only modulated by
absolute magnitude but also by relative magnitude of rewards46–48.In
addition, our use of gems as rewards instead of money may be criticized.
However, in classical tasks such as the Monetary Incentive Delay task
participants are able to transfer reinforcement properties to novel reward
cues fast27,49. Additionally, we found no relative advantage of using monetary
cues instead of gems in experiment 3.
Conclusion
In conclusion, the highlyrobust effect of rewardon hit rate reflects decision
criteria at retrieval rather than changes in memory strength during
encoding or consolidation. We propose that the decision criterion at
recognition is based on memory for stimulus-reward associations learned
during encoding and consolidated thereafter. However, itwill be important
to develop tasks that can reliably measure memory for stimulus-reward
associations and reward effects on memory strength within one task in the
future.
Data availability
All data (https://doi.org/10.23668/psycharchives.13963) are publicly avail-
able at the PsychArchives of the Leibniz Institute of Psychology (ZPID).
Code availability
All analysis code (https://doi.org/10.23668/psycharchives.13967) is publicly
available at the PsychArchives of the Leibniz Institute of Psychology (ZPID).
All analyses and plots were generated using R (version 4.3.1 (2023-06-16
ucrt)52). Effect sizes were calculated using the R package effectsize (version
0.8.553). (Generalized) linear mixed models were calculated using the R
package lme4 (version 1.1.3429), and p-values for these models were calcu-
lated using the R package lmerTest (version 3.1.354). Drift diffusion models
(DDM) were fit using the wdm() function from the R-package RWiener
(version 1.3.355). Plots were created using the following packages: ggplot2
(version 3.4.356), ggbeeswarm (version 0.7.257), cowplot (version 1.1.158),
ggpubr (version 0.6.059), ggh4x (version 0.2.560), and scales (version 1.2.161).
Received: 2 June 2023; Accepted: 11 March 2024;
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Acknowledgements
This research was supported by an Emmy-Noether-Grant (FE 1617/2-1) to
Gordon B. Feld. Simon Kern was supported by a PhD scholarship by the
Studienstiftung des Deutschen Volkes. The funding sources had no role in the
study design, or in the collection, analysis and interpretation of data, in the
writing of the report, and in the decision to submit the article for publication.
We wouldlike to thank Eduard Ort for hisadvice on the drift diffusion models.
Author contributions
Juliane Nagel: developed the study concept and study design, generated
the study material, performed data collection, performed the data analysis
and interpretation, draftedand revised the manuscript.David Philip Morgan:
developed the study concept and study design, generated the study
material, performed data collection, drafted the manuscript. N. Çağatay
Gürsoy: Provided criticalfeedback on the studydesign, generated thestudy
material.Samuel Sander: performed data analysis and interpretation. Simon
Kern: provided critical feedback on the study design. Gordon B. Feld:
developed the study concept and design, supervised data analysis and
interpretation, revised the manuscript. All authors approved the final version
of the manuscript for submission.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s44271-024-00074-9.
Correspondence and requests for materials should be addressed to
Juliane Nagel or Gordon Benedikt Feld.
Peer review information Communications Psychology thanks Sebastian
Gluth and theother, anonymous,reviewer(s) for their contribution to the peer
review of thiswork. Primary Handling Editor: Marike Schiffer. A peer review
file is available
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