Additional stimulus presentations
Running Head: Additional stimulus presentations

Why additional presentations help identify a stimulus

Duncan Guest
University of Warwick

Christopher Kent
University of Bristol

James S. Adelman
University of Warwick

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Additional stimulus presentations
Abstract
Nosofsky (1983) reported that additional stimulus presentations within a trial increase
discriminability in absolute identification, suggesting that each presentation creates an
independent stimulus representation, but it remains unclear whether exposure durationor the formation of independent representations improves discrimination in suchconditions. Experiment 1 replicated Nosofsky’s result. Experiments 2 (masking the
ISI between two presentations) and 3 (manipulating stimulus duration withoutchanging number of presentations or overall trial duration) ruled out an explanation interms of extended opportunities for stimulus sampling, from either a sensory buffer
during additional ISIs or increased stimulus exposure, respectively. Experiment 4(comparing two and three presentations, other factors controlled) provided some
limited additional support for Nosofsky’s original claim that additional stimulus
presentations can create either independent or duplicate representations. Experiments
5 and 6 (both manipulating ISI) demonstrated that a key factor in the additional
stimulus presentation effect is the overall trial duration. We discuss the results inrelation to models of absolute identification, their relative emphasis on stimulus
sampling versus response selection, and the mechanisms by which duplicate
representations could be created.

Keywords: Absolute identification; stimulus sampling; perceptual cognition;mathematical models.

2Additional stimulus presentations
Why additional presentations help identify a stimulus

In absolute identification participants must identify the rank position of a randomly
selected stimulus drawn (with replacement) from a set of stimuli that vary (typicallyin equal psychophysical increments) along a single psychological dimension, such as
pitch or length (see Stewart, G.D.A. Brown, & Chater, 2005 for a review). Once a
response is given, feedback (the correct response) is usually given. The most
perplexing aspect of absolute identification is its overall difficulty, considering thesimplicity of the task. Participants perform surprisingly poorly when as few as six
stimuli (and response options, Lacouture, Li, & Marley, 1998) are used (e.g., Miller,
1956) and typically improve only very slightly with practice (e.g., Lacouture, et al.,
1998; Nosofsky & Shiffrin, 1994; but see Rouder, Morey, Cowan, & Pfaltz, 2004).
Moreover, when information transmitted is measured, a dimension-specific upper
limit is obeyed with increases in the number of stimuli. This severe performance limit
is found no matter what stimulus modality or single psychological dimension is used,suggesting a modality independent limitation in the cognitive system (see S. D.
Brown, Marley, Donkin, & Heathcote, 2008, and Stewart et al., 2005, for a review of
the typical findings). The simplicity of the task, combined with the severe
performance limit, has intrigued theorist for a long time (e.g., Wever & Zener, 1928)
with considerable interest recently (e.g., S. D. Brown et al., 2008; Kent & Lamberts,
2005; Lacouture & Marley, 2004; Mathews & Stewart, 2009; Stewart et al. 2005;
Petrov & Anderson, 2005).
Current theories of absolute identification differ in the emphasis they place on
the mechanisms underlying performance. In particular, the Extended Generalized
Context Model, (EGCM; Kent & Lamberts, 2005) emphasizes the perceptual3Additional stimulus presentations
processing stage of identification. According to the model, over time, perceptual
information is repeatedly sampled and accumulated to build a representation of thestimulus. In categorization, the sampled elements correspond to separable dimensions(Lamberts, 1998), but in the application to absolute identification, each dimension iscomposed of multiple elements contributing to discriminability. This gradual buildup of information means that the perceptual representation (and its relation to otherrepresentation in memory) changes over time from a relatively ambiguous
representation to a distinct representation of the stimulus. In the model, aprobabilistic response is made once a probabilistic threshold on available perceptual
information is reached.
The centrality of the perceptual sampling process in the EGCM differentiates
it from other models of absolute identification. In the EGCM, the time course of theperceptual sampling process links the identification response and the time it takes tomake the response. In contrast, other models such as the Relative Judgment Model(RJM; Mathews & Stewart, 2009; Stewart et al., 2005) and the Selective Attention,
Mapping, and Ballistic Accumulator model (SAMBA; S. D. Brown et al., 2008) place
more emphasis on the response selection stage of identification. Both these models
assume a process of ballistic accumulation of evidence for each response (S. D.
Brown & Heathcote, 2005). Each accumulator’s activation (and accumulation rate) isdetermined by the competition amongst accumulators and the response strength forthat accumulator. However, the RJM and SAMBA differ in the type of input that is
fed to the accumulators. In SAMBA, the response strengths are determined by theoutput of a mapping process that maps the estimate of the stimulus magnitude onto
the response accumulators. In RJM, the response strengths are determined by a
spread of activation arising from recent feedback on the difference between the4Additional stimulus presentations
current and the last (or last-but-one) stimulus. In either model, an identification
response is selected when one of the accumulators reaches a given threshold. Thus in
SAMBA and the RJM, perceptual processes play a relatively minor role incomparison with the EGCM.
Evidence for the importance of perceptual processes in absolute identification
comes from Nosoksky’s (1983) experiments using multiple within-trial stimulus
presentations. Presenting additional presentations during a trial tests the ability to
extract and integrate perceptual information over time. Current models do notcurrently have mechanisms that allow them to make predictions about the impact ofadditional stimulus presentations, making this an important area for further research.
Nosofsky required participants to respond either after all stimulus presentations when
there were one, two, three or four stimulus presentations in a trial (Experiment 1) orafter every presentation when each trial consisted of four stimulus presentations(Experiment 2). Nosofsky reported increased discriminiability with increased stimulus
presentations across both experiments, concluding that each presentation creates an
independent representation, and these representations are then averaged to give a lessnoisy overall stimulus representation. However, there are alternative interpretations of
the multiple presentation effect, which are not ruled out by Nosofsky’s experiments.
One explanation for the increased discriminability with increased stimulus
presentations is that, rather than the actual additional presentation(s), the related
increase in stimulus exposure time improved performance. This explanation isconsistent with the findings of Ward (1991) and Hsieh and Saberi (2007) that
demonstrated increasing exposure duration increases accuracy in an absolute
identification task. However, Nosofsky (1983) suggested that pilot work had shownthat stimulus repetition had a greater effect on performance than increasing exposure5Additional stimulus presentations
time in absolute identification. Thus, it remains unclear whether exposure duration or
the formation of independent representations within an absolute identification trial
was responsible for the improved discrimination with additional presentations
described by Nosofsky (1983).
As well as the overall increase in stimulus duration, in the design used by
Nosofsky (1983), stimulus sampling could also have taken place during the interstimulus intervals (ISIs), the number of which increased with every additionalpresentation. It is possible that a short-term sensory buffer could be sampled during
each ISI unless the ISI is masked (e.g., Loftus, Duncan, & Gehrig, 1992; Loftus &McLean, 1999; Massaro, 1972a). Moreover, other, non-perceptual, processes may
occur during the ISI and throughout the trial, suggesting that overall trial length
should also be a concern.
The experiments presented here address the concerns with the method used by
Nosofsky (1983) and are designed to determine whether the effect of additionalpresentations is caused by the increased opportunity for stimulus sampling, because
total stimulus exposure duration is increased, because of the introduction of anadditional ISI, and/or because total processing time is increased. As well as extending
the findings of Nosofsky (1983) we investigate the nature of the processes underlying
stimulus sampling and the flexibility of the cognitive system to integrate perceptual
information from additional discrete stimulus presentations in absolute identification.
We also investigate response times (RTs) in an attempt to gain a more complete
understanding of the nature of the component processes underlying absolute
identification and provide a robust set of data to constrain future models.
The cause of the additional presentation effect will have important
implications for how models of absolute identification implement a stimulus sampling6

Additional stimulus presentations
mechanism. If the additional presentation effect were caused by increasing exposure
duration, this would suggest that information can be effectively accumulated into asingle representation across successive presentations of the same stimulus in an
absolute identification task. If the additional presentation effect is not caused byincreasing stimulus exposure, this would suggest that perceptual information fromeach additional stimulus presentation is represented independently and perhaps
integrated at a later stage by a mechanism that averages over perceptual
representations (e.g., Nosoksky, 1983, Schwarz & Kühn, 2008).

Overview of Experiments 1 to 4

Experiments 1 to 4 examined possible perceptually-based processes underlying theincrease in discriminability with additional stimulus presentations within a trial in
Nosofsky’s (1983) absolute identification experiments. For each experiment, we used
two (N = 6) sets of stimuli presented in different modalities: tones varying infrequency (experiments suffixed with ‘a’) and distance between two dots
(experiments suffixed with ‘b’). A different group of participants were used for eachstimulus modality. All experiments involved two within-subject conditions (thatvaried between experiment) randomly intermixed1; we now describe those conditions
In Experiment 1, a stimulus was presented once or twice, whereas in Experiments 2-4
a stimulus was always presented at least twice. In Experiments 2-4, the time between
the first onset and the offset of the last stimulus was controlled and a pre-mask waspresented before the first presentation and a post mask was presented after the offsetof the final stimulus presentation.

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Additional stimulus presentations
Experiment 1 attempted to replicate Nosofsky’s (1983) finding that additional
stimulus presentations within a trial increased discrimination. The crucial
manipulation in Nosofsky’s experiments and our Experiment 1 was the number oftimes a stimulus was presented, see Figure 1a. In Nosofsky’s Experiment 1, stimuli
were presented one to four times, but the greatest gain in discriminability wasobserved between one presentation and two presentations, and so we used one andtwo presentations in Experiment 1.
Experiment 2 examined whether the benefit in discrimination for two stimulus
presentations compared to one stimulus presentation was, at least in part, due toadditional stimulus sampling from a short-term sensory buffer during the ISI (e.g.,
Massaro, 1972a, b; Sperling, 1959). On each trial of Experiment 2, the stimulus waspresented twice with either a mask presented between stimulus presentations, serving
to prevent additional sensory buffer sampling (Loftus & McClean, 1999; Sperling,1963), or no mask, see Figure 1b.
In Experiment 3, the overall exposure duration of the stimulus was
manipulated to examine whether the additional stimulus sampling time afforded by
the additional presentation was responsible for the improved discriminability. On
each trial, a stimulus was presented twice, either for a total of 500 ms or for a total of
250 ms. Importantly, the time from the start of the trial to the offset of the final
stimulus was held constant, see Figure 1c.
In Experiment 4, the number of additional stimulus presentations during a
trial, either two or three, was manipulated. Crucially, unlike Nosofsky’s (1983)
experiments, total stimulus exposure time was held constant along with the time fromthe start of the trial to the final stimulus offset. The ISI when two stimuli were8

Additional stimulus presentations
presented was twice that of each ISI when three stimuli were presented, equating total
non-stimulus time, see Figure 1d.

General Method
Participants. 112 (74 female) participants took part, with 28 participants per
experiment (14 per modality). Participants were mostly students from the Universityof Warwick paid £6 (approximately $9) per hour. Participants were excluded if theiraccuracy was less than 25% correct, resulting in exclusion of four participants: one
participant from each of Experiments 1b, 2a, 3a, and 3b. In addition, one participant
was excluded from Experiment 2b because they used response ‘6’ on less than 1% of
the trials.
Apparatus and Stimuli. Pentium 4 computers were used for stimulus
presentation and response registration. In the auditory task, participants sat 100 cm
from the center of a 17-inch Cathode Ray Tube (CRT) monitor used to display
instructions and other visual cues. Auditory stimuli were presented binaurally
through Plantronics Audio 90 Headphones via a SigmaTel soundcard. In the visualtask, a GeForce 7800 GTX graphics card was connected to a 17-inch CRT monitor
with a resolution of 1,280 x 1,024 pixels with a refresh rate of 75 Hz2. Participants sat
160 cm from the center of the monitor in a dimly lit room. In both tasks, responses
were made via the number keys on a standard keyboard. Response mappings werecounterbalanced across participants. For half the participants response ‘1’ referred tothe smallest stimulus magnitude and response ‘6’ referred to the largest stimulus
magnitude. For the other half of the participants the mapping was reversed.
In the auditory task, the stimuli consisted of six tones varying in frequency
from 752.64 Hz to 1,326.41 Hz, with a 12% difference in frequency between

9Additional stimulus presentations
successive stimuli. In Experiment 1a, the tones were presented with a 50 ms linearlyramped onset and offset. In the no-masking condition of Experiment 2a, the firststimulus presentation in the trial had a 50 ms linearly ramped offset and the second
stimulus presentation in the trial had a 50 ms linearly ramped onset (the abrupt onset
or offset of a transmitted audio signal causes spectral splatter, producing an audible‘popping’ sound that can be eliminated by ramping). In all other experiments, pre,post, and ISI masks (chosen randomly from a set of 10 samples of white noise)
avoided the need to ramp the onset and offset of the tones..
In the visual task, six stimuli were created by displaying two white squares (2x 2 pixels) separated by one of six horizontal distances on a black background.
Distances ranged from 75 pixels (0.64° visual angle) to 132 pixels (1.18° visual
angle), with a 12% difference in distance between successive stimuli. We gradually
increased or decreased the luminance of the dots for the first or last 50 ms to matchthe equivalent auditory ramping in Experiment 1 and the no-mask condition ofExperiment 2. In all other experiments and conditions pre, post, and ISI masks wereused and stimulus luminance remained constant. Fifty masks were created byrandomly allocating each screen pixel one of three luminance levels (black, grey,
white). During each masking period, a randomly selected mask was presented oneach screen refresh creating the appearance of dynamic white noise.
Procedure. For either modality, each trial started with a small white fixation
cross at the center of the screen for 300 ms, followed by a 500 ms blank interval. The
stimulus was then presented a variable number of times for a variable duration,
depending on the design of the experiment (e.g., in Experiment 1 the stimulus waspresented for 250 ms either once or twice). After the final stimulus presentation a
response prompt, consisting of three question marks, was displayed at the center of10Additional stimulus presentations
the screen. Participants were requested to respond as quickly and as accurately as
possible upon the onset of the response prompt.
Premature responses, made before the response prompt, were not registered
and were excluded from the analysis. After a premature response, a message wasdisplayed reminding the participant to respond only after the response prompt.
Feedback (the correct response) was displayed at the center of the screen for 800 ms(1,300 ms after a premature response). There was an inter-trial interval of 600 ms
starting from the offset of response feedback.
In each experiment, participants were first presented with each stimulus and its
corresponding response label in ascending order of response. The first 20 trials ofeach experiment were treated as practice and discarded from the analysis. As well as
excluding premature responses, trials with RTs (measured as the time from onset ofthe response prompt to key press) longer than 6,000 ms were excluded. For eachexperiment we calculated a repeated measurements 5 (stimulus) x 2 (condition)
ANOVA on d’i i+1 values and a repeated measurements 6 (stimulus pair) x 2(condition) ANOVA on correct RT3.

When a Mauchly test indicated sphericity was

violated, we applied the Greenhouse Geisser correction to the ANOVA.

Experiment 1
Experiment 1 was designed to replicate the finding from Nosofsky (1983) that
additional stimulus presentations within a trial increased discriminability. In
Experiment 1, stimuli were presented either once or twice per trial. Each stimulus
presentation lasted 250 ms. In the two presentations condition there was a 2,000 ms
unfilled ISI (see Figure 1a). No masking was used in Experiment 1, but otherwise thedesign followed the general method. There were 75 repetitions of each of the cells in

11Additional stimulus presentations
the 6 (stimulus) x 2 (number of presentations) design. Participants were allowed ashort break every 100 trials.

Results

Excluded trials constituted 3.8% and 2.2% of the total number of non-practice trials inExperiments 1a and 1b, respectively.
Figure 2 (top panels) shows the d’i,i+1 scores (see Footnote 3 for an
explanation of d’i,i+1) for the one presentation and two presentations conditions inExperiment 1a (auditory stimuli, left panel) and Experiment 1b (visual stimuli, rightpanel). Typical bow effects were observed in the d’i,i+1 scores resulting in a main
effect of stimulus on discriminability in Experiment 1a, F(4, 52) = 8.67, p = .001,
MSE = 0.481, η P2 = .4, and Experiment 1b, F(4, 48) = 15.10, p < .001, MSE = 0.086,

η P2 = .56 (although in Experiment 1b d’5,6 was lower than d’4,5). There was a main
effect of condition with higher d’i,i+1 scores in the two presentations condition
compared to the one presentation condition in both Experiment 1a, F(1, 13) = 6.96, p= .02, MSE = 0.094, η P2 = .35, and Experiment 1b, F(1, 12) = 11.68, p = .005, MSE =0.078, η P2 = .49. There was no interaction between stimulus and number ofpresentations in either Experiment 1a, F(4, 52) = 0.83, or Experiment 1b, F(4, 48) =0.90.
Figure 2 (bottom panels) shows the mean correct RT for each stimulus in the
one-presentation and two-presentations conditions of Experiment 1a (auditory stimuli,
left panel) and Experiment 1b (visual stimuli, right panel). The typical bow effectwas evident, with faster RTs for stimuli towards the end of the range and slower for
stimuli towards the middle of the range, resulting in a main effect of stimulus on RT
in Experiment 1a, F(5, 65) = 11.83, p < .001, MSE =46492.126, η P2 = .48, and12Additional stimulus presentations
Experiment 1b, F(5, 60) =18.74, p < .001, MSE =64873.072, η P2 = .61. In both tasks,
the bow effect was more prominent in the two-presentation condition, resulting in asignificant interaction between stimulus and number of presentations in Experiment
1a, F(5, 65) = 2.63, p = .046, MSE =18958.701, η P2 = .17, and Experiment 1b, F(5,60) =3.48, p < .008, MSE =9142.786, η P2 = .23. Response times were faster in the
two-presentations condition than in the one-presentation condition for Experiment 1a,
F(1, 13) = 148.30, p <.001, MSE = 282053.223, η P2 = .92, and Experiment 1b, F(1,12) = 147.69, p < .001, MSE = 85254.905, η P2 = 93.

Summary
The results from Experiment 1a and 1b support Nosofsky’s (1983) finding that
discrimination in absolute identification improves as the number of stimulus
presentations per trial increases. In Experiment 1, discrimination was better for trials
on which a stimulus was presented twice per trial in comparison to trials on which a
stimulus was presented only once. The multiple presentation effect was therefore
replicated in two different absolute identification tasks; tone pitch identification andvisual distance identification, and extended to include RTs. Faster RTs were observedin the two-presentation condition compared to the one-presentation condition,
consistent with previous findings showing that accurate absolute identification
responses are associated with faster RTs (e.g. Kent & Lamberts, 2005; Lacouture,1997; Lacouture et al., 1998; Lacouture & Marley, 2004; although see Lacouture’s,
1997, unequal spacing condition for an exception). However, the magnitude of thedifference in RTs between conditions was unusually large (781 ms). It is likely that asignificant proportion of this difference was caused by response preparation and13Additional stimulus presentations
uncertainty regarding the onset of the response signal. As the one-presentation andtwo-presentation conditions were randomly inter-mixed, it is likely that participants
had a higher degree of uncertainty regarding when the response prompt would appear
in the one-presentation condition (i.e., whether the response prompt would follow
stimulus offset, or whether a second stimulus would be presented). This uncertainty
in the one-presentation condition could have led to slower RTs than in the twopresentation condition (where participants were certain a response prompt would
follow the second presentation). Moreover, in the two-presentation condition
participants would have had time to prepare their response during the ISI, enabling
faster responding upon the onset of the response cue. Although these two factors
undoubtedly contributed to faster responding in the two presentation condition, given
the size of the RT difference it seems likely that the faster responding in the twopresentation condition also reflects a benefit provided by the additional presentation(this is supported by proceeding experiments).
Although discrimination was greater in Experiment 1 when the stimuli were
presented twice per trial, compared to when stimuli were presented once, presenting
an additional stimulus also introduced an ISI and increased the total stimulus exposure
duration. Experiments 2, 3, and 4 were designed to assess whether these confounding
variables were responsible for the additional presentation effect.

Experiment 2
Experiment 2 examined whether superior performance in the two-presentation
condition in Experiment 1 was due to additional sampling from a short-term sensory
buffer during the ISI. In Experiment 2, stimuli were always presented twice per trial.
In the unmasked condition, the ISI was unfilled, and in the masked condition, the ISI

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Additional stimulus presentations
was filled with white noise. The mask was used to prevent possible sampling from asensory representation. If a short-term sensory buffer can be sampled during the ISI
and used to aid discriminability, then performance should be worse when the ISI ismasked compared to when the ISI is unmasked (e.g., Loftus, Duncan, & Gehrig,
1992; Loftus & McClean, 1999; Sperling, 1963).
The method for Experiment 2 was similar to the general method, with thefollowing exceptions. There was an ISI of 2,000 ms that was either masked orunmasked. When the ISI was masked, the stimuli were not linearly ramped at
stimulus onset or offset (in Experiment 2a, a white noise mask was added to the tone
to create a continuous sound, preventing spectral splatter). However, when the ISI
was unmasked the final 50 ms of the first stimulus was ramped linearly frommaximum amplitude (brightness) to silence (black) and the first 50 ms of the second
stimulus was ramped linearly from silence (black) to maximum amplitude(brightness). Pre and post masks of 250 ms were used so that no linear ramping was
required at the start of the first stimulus presentation or at the end of the second
stimulus presentation. The response prompt was presented upon the offset of the post
mask. There were 70 repetitions of each of the cells in the 6 (stimulus) x 2 (masking)design. Participants were allowed a short break every 105 trials.

Results

Excluded trials constituted 2.4% and 2.4% of the total number of non-practice trials inExperiments 2a and 2b, respectively.
Figure 3 (top panels) shows the d’i,i+1 scores (see Footnote 3) for each for themasked and unmasked conditions in Experiment 2a (auditory task, left panel) andExperiment 2b (visual task, right panel). There were bow effects in the d’i,i+1 scores,

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Additional stimulus presentations
resulting in a main effect of stimulus on discriminability in both Experiment 2a, F(4,48) = 12.06, p < .001, MSE = 0.846, η P2 = .50, and Experiment 2b, F(4, 48) = 17.98, p< .001, MSE = 0.111, η P2 = .60. There was no main effect of masking and no
stimulus-masking interaction for d’i,i+1 in Experiment 2a or 2b (all p > .4).
Figure 3 (bottom panels) shows the mean correct RT for each stimulus for themasked and unmasked conditions in Experiment 2a (auditory task, left panel) andExperiment 2b (visual task, right panel). Typical bow effects were observed. The
main effect of stimulus on RT approached significance in Experiment 2a, F(5, 60) =2.64, p = .084, MSE = 55094.477, η P2 = .18, and was significant in Experiment 2b,
F(5, 60) = 7.53, p = .001, MSE =21761.38, η P2 = .39. There was no main effect ofmasking and no stimulus-masking interaction for RTs in Experiment 2a or 2b (all ps >.1).

Summary
Experiments 2a and 2b demonstrated that presenting a mask during the ISI had
little effect on discrimination or RT in two absolute identification tasks. A mask waspresented in the ISI to prevent additional sampling from a short-term sensory buffer.
Assuming that masking did prevent (or at least reduce) additional sampling, the lackof impairment in the masked condition, relative to the unmasked condition, suggeststhat any additional sampling from a sensory buffer during the ISI had little influenceon performance. It is therefore unlikely that the opportunity for additional samplingin the two-presentation condition, relative to the one-presentation condition ofExperiment 1, resulted in higher discriminability. Although care must be taken
drawing conclusions from a null result, masking effects tend to be robust (e.g.,
Breitmeyer & Öğmen, 2006) and it is therefore surprising that masking had no effect16Additional stimulus presentations
on performance in Experiment 2. The design of Experiment 2 produced typical bow
effects and performance levels were similar to the other experiments in this series.
The results suggest that sampling from a sensory buffer provided at most limited
benefit, possibly because enough stimulus information had already been sampled withwhich to reach asymptotic performance.

Experiment 3

In Experiment 1, the overall stimulus exposure time in the two-presentation condition
was twice as long as the overall stimulus exposure time in the one-presentation
condition (500 ms versus 250 ms). It is possible that this additional exposure time
resulted in improved performance in the two-presentation condition, rather than thefact that there were two stimulus presentations per se. Experiment 3 examined
whether increasing the exposure duration of a stimulus (over a minimum time forstimulus detection) improves absolute identification performance. In Experiment 3,
stimuli were presented twice on each trial but the total exposure duration of a stimulus
was manipulated, whilst the time from stimulus onset to stimulus offset was held
constant by increasing the ISI in the shorter exposure time condition (2,250 ms)
compared to the longer exposure time condition (2,000 ms; see Figure 1c). Stimulus
presentations were 250 ms and 125 ms in the long exposure-duration and shortexposure duration conditions, respectively. In all other respects the method was
identical to that detailed in the general method. There were 70 repetitions of each of
the cells in the 6 (stimulus) x 2 (exposure duration) design. Participants were alloweda short break every 105 trials.

17Additional stimulus presentations
Results

Excluded trials constituted 4.4% and 8.0% of the non-practice trials in Experiment 3a
and 3b, respectively.
Figure 4 (top panels) shows d’i,i+1 (see Footnote 3) for the long and short
exposure conditions in Experiment 3a (auditory task, left panel) and Experiment 3b(visual task, right panel). Bow effects were observed in the d’i,i+1 scores, resulting ina main effect of stimulus on discriminability in Experiment 3a, F(4, 48) = 10.77, p <.001, MSE = 0.643, η P2 = .47, and Experiment 3b, F(4, 48) = 6.45, p < .001, MSE =0.127, η P2 = .35. In Experiment 3b, discrimination of stimuli at the lower end of therange was highest in the long exposure condition, whereas discrimination of stimuli at
the higher end of the range was lowest in the long exposure condition, resulting in aninteraction between stimulus and exposure duration, F(4, 48) = 2.88, p = .032, MSE =0.061, η P2 = .19. There was no interaction between stimulus and exposure duration inExperiment 3a, F(4, 48) = 1.27 and no main effect of exposure duration on d’i,i+1 ineither Experiment 3a, F(1, 12) = 0.04, or Experiment 3b, F(1, 12) = 0.66.
Figure 4 (bottom panels) shows the mean correct RT for each stimulus in thelong and short exposure conditions of Experiment 3a (auditory task, left panel) andExperiment 3b (visual task, right panel). There were bow effects in RTs resulting in amain effect of stimulus on RT for Experiment 3a F(5, 60) = 4.67, p = .01, MSE =59980.998, η P2 = .28, and Experiment 3b, F(5, 60) = 5.33, p = .023, MSE =
137674.670, η P2 = .30. There was no main effect of exposure duration and no
stimulus by exposure duration interaction for RTs in Experiment 3a or 3b (all ps > .1).

Summary18

Additional stimulus presentations
In Experiment 3, the total stimulus exposure duration in the long exposureduration condition was twice that of the short exposure-duration condition.
Nevertheless, both Experiment 3a and 3b demonstrated that doubling stimulus
exposure time had no observable effect on discrimination, or RT. These results
contrast with those in Experiment 1, where overall exposure duration in the (superior
performance) two-presentation condition was twice that of the one-presentation
condition. As overall exposure duration in the short and long exposure-duration
conditions of Experiment 3 was matched with exposure duration in the onepresentation and two-presentation conditions of Experiment 1, respectively, thisindicates that factors other than stimulus exposure duration caused the improved
performance observed in the two-presentation condition of Experiment 1.
The absence of an exposure duration effect suggests that the shorter exposure
duration (2 x 125 = 250 ms) was sufficiently long to be able to perceptually process astimulus to asymptotic accuracy. Thus, providing additional time for stimulus
sampling did not benefit performance in Experiment 3. This finding is consistent withother absolute identification studies in which exposure duration is manipulated andparticipants tend to respond at asymptotic accuracy relatively rapidly. Previous
studies typically show that full information is accumulated after about 135 ms to 405
ms for tone intensity information (e.g. Ward, 1991), and under 100 ms for tone
frequency (Hsieh & Saberi, 2007; although Hsieh & Saberi, 2007, show that some
information about tone frequency is accumulated between 100 ms and 1,000 ms).
The results of Experiment 2 are also consistent with the claim that full stimulus
processing occurred very rapidly. Sampling from a sensory buffer would only bebeneficial if full stimulus sampling had not already been completed, and hence the19Additional stimulus presentations
masking of the ISI would not be expected to worsen performance relative to anunmasked ISI unless there was still information to accumulate during the ISI.
The results of Experiments 2 and 3 indicate that increased duration of stimulus
sampling is not responsible for the advantage of the additional stimulus presentation
observed in Experiment 1. Alongside previous research (e.g., Hsieh & Saberi, 2007;
Ward, 1991), Experiments 2 and 3 indicate that stimulus sampling in absolute
identification is relatively rapid. The apparent rapidity of stimulus sampling suggeststhat stimulus sampling processes do not constitute the majority of the RTs in absolute
identification which are relatively long compared to other cognitive tasks (e.g., Kent
& Lamberts, 2005; Lacouture, 1997). Rather, it appears that other, non-perceptual,
processes play a greater role in determining absolute identification RTs. However,the precise time course of the different component processes in absolute identification
cannot be estimated from either Experiments 2 and 3, or from previous research
indicating rapid perceptual processing, because RTs were delayed until a response
prompt (Experiments 2 and 3) or were not measured (e.g. Hsieh & Saberi, 2007;
Ward, 1991). This is a more general question than that of the influence of additional
stimulus presentations.
Experiment 4

Experiment 4 examined Nososfsky’s (1983) original claim that discrimination is
improved when a stimulus is presented more times during a trial because the ultimate
representation used to judge identity is an average of the independent representations
yielded on each presentation. If this claim is true, then it is the number of stimulus
presentations (over and above the minimum amount of time necessary to encode thestimulus, Schwarz & Kühn, 2008) that is responsible for the increase in20

Additional stimulus presentations
discriminability between the one-presentation and two-presentation conditions ofExperiment 1. In Nosofsky’s experiments, the manipulation of the number ofstimulus presentations was confounded with total exposure duration and trial length.
In Experiment 4, we manipulated the number of stimulus presentations, whilst
controlling the total stimulus exposure duration and the time from stimulus onset tooffset of the final stimulus. Stimuli were either, 250 ms in duration and presented
twice during a trial with a 4,000 ms ISI, or were 167 ms long and presented threetimes during a trial with two 2,000 ms ISIs (see Figure 1d). In all other respects, themethod was identical to that detailed in the general method. There were 50
repetitions of each of the cells in the 6 (stimulus) x 2 (number of presentations)design. Participants were allowed a short break every 75 trials.

Results

Excluded trials constituted 0.6% and 2.56% of the non-practice trials in Experiments
4a and 4b respectively.
Figure 5 (top panels) shows the d’i,i+1 scores (see Footnote 3) for the threepresentations and the two presentations conditions in Experiment 4a (auditory task,
left panel) and Experiment 4b (visual task, right panel). Bow effects were observed in
the d’i,i+1 scores, resulting in a main effect of stimulus on discriminability for bothExperiment 4a, F (4, 52) = 12.72, p < .001, MSE = 0.232, η P2 = .50, and Experiment4b, F(4, 52) = 8.03, p < .001, MSE = 0.116, η P2 = .38. Whilst there was no differencein the d’i i+1 scores between the three-presentations and two-presentation conditions inExperiment 4a, F(1, 13) = 0.05, in Experiment 4b the d’i i+1 scores were higher in thethree-presentation compared to the two-presentation condition, F(1, 13) = 6.94, p =.021, MSE = 0.047, η P2 = .35. There was no interaction between stimulus and number

21

Additional stimulus presentationsof presentations for d’i,i+1 in Experiment 4a, F(4, 52) = 0.83, or Experiment 4b, F(4,52) = 1.71.
Figure 5 (bottom panels) shows the mean correct RT for each stimulus for thethree presentations and two presentations conditions in Experiment 4a (auditory task,
left panel) and Experiment 4b (visual task, right panel). There were bow effects in
RTs resulting in a main effect of stimulus on RT for Experiment 4a, F(5, 65) = 3.42, p= .03, MSE =37631.284, η P2 = .21, and Experiment 4b, F(5, 65) = 6.26, p <.001, MSE= 16134.810, η P2 = .33. Response times in the three-presentation condition weresignificantly faster than those in the two-presentation condition in both Experiment
4a, F(1, 13) = 13.95, p = .002, MSE =57534.319, η P2 = .62, and Experiment 4b, F(1,13) = 14.26, p = .002, MSE = 43719. 353, η P2 = .52. There was no interaction
between stimulus and number of stimulus presentations for RTs in either Experiment
4a, F(5, 65) = 1.21, or Experiment 4b, F(5, 65) = .40.

Summary
Manipulating the number of stimulus presentations whilst controlling stimulus
exposure duration and the time between stimulus onset and stimulus offset had asignificant effect on RTs, with faster responses when there were three presentations
per trial, compared to two presentations per trial. This result replicates the RT effectobserved in Experiment 1 and suggests that participants found the three-presentation
condition easier than the two-presentation condition. However, the RT effect inExperiment 4 was smaller in magnitude than the RT effect found in Experiment 1,
with a mean difference of 781 ms in Experiment 1 and 134 ms in Experiment 4. It is
possible that the reduction in the RT difference was due to the diminishing impact ofadditional stimulus presentations on performance (cf. Nosofsky, 1983). A more likely
22Additional stimulus presentations
explanation is that, factors that contributed to the RT effect in Experiment 1 were lessimportant in determining RT in Experiment 4. For example, in Experiment 1,
uncertainty about when the response signal would onset would have been much lessin the two-presentation condition, leading to faster responding. In Experiment 4
however, the long 4,000 ms ISI should have been an adequate indicator that there
were to be only two stimulus presentations and not three, and so uncertainty overwhen the response cue would be presented should have had less of an effect on RT.
Similarly, in Experiment 1 the ISI between the two stimulus presentations would haveenabled additional response preparation in comparison to the one presentation
condition. However in Experiment 4 the 4,750 ms from stimulus onset to onset of the
response cue should have given ample time to prepare to respond. Thus, it seems
unlikely that the RT effect observed in Experiment 4 was determined by either
response preparation or uncertainty about when the response signal would onset.
Rather it suggests some added benefit provided by the additional stimulus
presentation.
The pattern of results for discrimination was less clear than that for RTs in
Experiment 4. In Experiment 4b, discrimination was greater in the three presentations
condition compared to the two presentations condition, providing some evidence tosupport Nosofsky’s (1983) claim that additional stimulus presentations increase
discrimination in absolute identification. However, in Experiment 4b discrimination
was not uniformly superior in the three-presentation condition compared to the twopresentation condition across all stimulus positions. Moreover, manipulating thenumber of presentations had no effect on discrimination in Experiment 4a, suggestingthat the addition of independent samples does not always occur.

23

Additional stimulus presentations
It is not clear why there were different effects of additional stimulus
presentations between the two modalities in Experiment 4. In Nosofsky’s (1983)
experiments, the greatest benefit in discrimination was gained from one to two
stimulus presentations, with a diminishing benefit for additional stimulus
presentations. Thus, a reduced effect of an additional stimulus presentation would be
expected between the two-presentation and three-presentation conditions inExperiment 4. It is possible that the increased difficulty of the visual task
(Experiment 4b) compared to the auditory task (Experiment 4a), which is evident
across all experiments, meant that the additional stimulus presentation provided alimited benefit in the visual task only. For example, if stimulus representations wereless noisy in the auditory task compared to the visual task, and if additional stimulus
presentations serve to reduce perceptual noise (Nosofsky, 1983) then the effect of thethird stimulus presentation would be reduced in the auditory task compared to thevisual task. Another possibility is that the 167 ms auditory stimulus was too brief inthe three presentations condition to provide an additional benefit. When time is held
constant, multiple presentations only appear to provide a benefit above single
presentation after a minimum time has elapsed (total presentation duration andnumber of presentations interact, supporting an independent representation for eachpresentation, with a peaked hazard function for sampling probability [i.e., initially
increasing but then decreasing probability of identification, such as the inverse
Gaussian or lognormal distribution] see Schwarz & Kühn, 2008, for a discussion4).
However, previous studies suggest that the majority of sampling is completed by 50
ms for auditory stimuli (Hsieh & Saberi, 2007; Ward, 1991).
The result may also reflect the visual modality's greater susceptibility to
extraneous failures such as eye blinks, eye or head movements, and lapses of24Additional stimulus presentations
attention. A further possibility is that the result arises from the summation of
independent samples when the instantaneous probability of perceiving the information
first rises, then falls (i.e., the psychophysical hazard is peaked). This could- dependingon the exact shape of the peak- have the consequence that an overall advantage forthree stimuli over two stimuli is observed only when the total stimulus duration islong, but not when it is short (as in Schwarz & Kühn's, 2008, experiments andanalysis). Moreover, it could be the case that a duration is “long” for the visual stimuli
in Experiment 4b but “short” for the auditory stimuli of Experiment 4a. However,this account can be ruled out. For performance in the 3 x 167 ms condition ofExperiment 4a to be equivalent to that in the 2 x 250 ms condition, the chances ofidentification (or integrated hazard) in the final 167 ms presentation must be
equivalent to that in the two 167-250 ms periods of the 250 ms presentations. But (aswe are assuming independence) we know the first 167 ms yields a non-zeroprobability of identification, because the 2 x 250 ms presentations show no advantage
over 2 x 125 ms presentations (Experiment 3a), ruling out the whole 125-250 ms
period for identification (similar to previous experiments e.g., Hsieh & Saberi, 2007;
Ward, 1991).
The findings from Experiments 2-4 suggest that the improvement in absolute
identification performance with additional stimulus presentations during a trial is notdue to an increased opportunity for stimulus sampling. Presenting a mask in the ISI toprevent sampling of a sensory buffer had no effect on performance (Experiment 2)
and neither did increasing total exposure duration (Experiment 3). Stimulus sampling
influences arising specifically from the presentation of discrete stimuli (Experiment 4)
also only had a very weak effect that was limited (in discriminability) to the visual25

Additional stimulus presentations
stimuli. Such a meager magnitude effect of the additional third presentation suggests
the influence of another process.
In Experiment 1 and Nosofsky’s (1983) experiments, the time from stimulus
onset to final stimulus offset was not controlled, but in our Experiments 2-4 wecontrolled the time from stimulus onset to final stimulus offset. However, it ispossible that the time from stimulus onset to final stimulus offset may influence
absolute identification performance, especially given the negligible effect ofadditional stimulus sampling, and the implication that response selection processes
are perhaps critical to performance. Experiment 5 therefore examined whether timefrom stimulus onset to stimulus offset influenced absolute identification performance.

Experiment 5
In Experiment 5, the time from initial stimulus onset to final stimulus offset was
manipulated. Stimuli were presented twice on each trial and the length of the ISI was
manipulated (2,000 ms versus 50 ms). In addition, the post mask and response
prompt were presented simultaneously upon stimulus offset in both ISI duration
conditions. Stimuli were pre-masked, post-masked and masks were presented during
the ISI (see Figure 6). Note that stimuli were presented twice per trial so thatparticipants were motivated to fully utilize the time between stimulus repetitions (andhence allow response selection processes to be at least near completion in the long ISI
condition). There were 75 repetitions of each of the cells in the 6 (stimulus) x 2 (ISI
duration) design. Participants were allowed a short break every 100 trials.

Participants. 28 (17 female) participants took part.

26

Additional stimulus presentations
Apparatus, stimuli, design, and procedure. These were identical to that in the general
methods section with the following exceptions. Stimuli were always presented twice
per trial and the length of the ISI was manipulated (short, 50 ms, or long, 2,000 ms).
In order to minimize time from offset of the first stimulus presentation to onset of the
response cue, the response cue was presented simultaneously upon offset of the final
stimulus. This meant that the post masks in the visual task (Experiment 5b) had to bemodified. In Experiment 5b, a set of 50 post masks were created using the techniquedescribed in the general method, with the exception that there was a 150 x 100 pixel
black rectangle 340 pixels above the horizontal center and at the vertical center of thescreen containing the ‘???’ response cue.

Results
Excluded trials constituted 2.1% and 1.6% of the non-practice trial in Experiments 5aand 5b, respectively.
Figure 7 (top row) shows the d’i,i+1 scores (see Footnote 3) for each pair ofadjacent stimuli for short and long ISI conditions for Experiment 5a (auditory task,
left panel) and Experiment 5b (visual task, right panel). There were bow effects,
resulting in a main effect of stimulus on discriminability in both Experiment 5a, F(4,52) = 22.46, p < .001, MSE = 0.739, η P2 = .63, and Experiment 5b, F(4, 52) = 17.71, p< .001, MSE = .133, η P2 = .58 (although in Experiment 5b d’4,5 was greater than d’5,6).
There was a main effect of ISI duration on discriminability with higher d’i,i+1 scoresfor the long ISI condition compared to the short ISI condition in both Experiment 5a,
F(1, 13) = 9.60, p = .008, MSE = 0.155, η P2 = .43, and in Experiment 5b, F(1, 13) =11.04, p = .005, MSE= 0.091, η P2 = .46. However, in Experiment 5a d’5,6 was greaterin the short presentation-interval condition compared to the long interval condition,
27

Additional stimulus presentations
resulting in an interaction between stimulus and ISI duration, F(4, 52) = 4.67, p =.003, MSE = 0.086, η P2 = .26. There was no interaction between stimulus and ISI
duration in Experiment 5b, F(4, 52) = 1.00.
Figure 7 (bottom row) shows the mean RT for each stimulus in the short andlong ISI conditions for Experiment 5a (auditory task, left panel) and Experiment 5b(visual task, right panel). Bow effects in RTs were evident, however the main effectof stimulus on RT only approached significance in Experiment 5a, F(5, 65) = 2.94, p= .070, MSE =15386.015, η P2 = .18. The main effect of stimulus on RT was
significant in Experiment 5b, F(5, 65) = 10.66, p < .001, MSE =28350.132, η P2 =..45.
Response times were faster for the long ISI condition compared to the short ISI
condition in Experiment 5a, F(1, 13) = 67.19, p < .001, MSE = 61107.156, η P2 = .84,
and Experiment 5b, F(1, 13) = 39.79, p < .001, MSE =146249.437, η P2 = .75.
There was no interaction between stimulus and ISI duration in Experiment 5a, F(5,65) = 1.98, or Experiment 5b F(5, 65) = 1.26.

Summary
Manipulating ISI duration did affect discrimination and RT in bothExperiment 5a and 5b. Discrimination was better and RTs faster in the long ISI
condition compared to the short ISI condition. The effect of manipulating the ISI
duration on all indicators of task difficulty provides considerable evidence thatabsolute identification performance can be improved by increasing the time fromonset of the first stimulus to offset of the second stimulus, at least with the stimuli andrange of durations used in these experiments. The findings from Experiment 5,
suggest that in Experiment 1 and Nosofsky’s (1983) experiments, the improvement in

28

Additional stimulus presentations
performance observed between presenting a stimulus once or twice, may have been
partly caused by the associated increase in time from onset of the first stimulus tooffset of the final stimulus.
An alternative interpretation is that increasing ISI made it more likely that therepeated stimulus presentations were represented independently. If discrimination is
improved by averaging the independent representations formed from each stimulus
repetition, increasing the likelihood that stimuli are independently represented should
aid performance. Indeed, Nosofsky (1983) reported that in pilot studies an ISI of 2 s
was optimal in ensuring stimulus presentations were represented independently. In
Nosofsky’s interpretation, more separated repetitions cause more precise
representations than a mere increase in duration because separation in time leads tounrelated (rather than related) samples of noise. However, for such an interpretation
to hold for Experiment 5 one would have to posit a source of psychophysical noise inpitch perception that is impervious to presentation of a mask of high intensity and awhite spectrum of frequencies, and a corresponding source of psychophysical noise invisual distance perception that is impervious to presentation of a mask of highintensity and a white spectrum of spatial and temporal frequencies. Moreover,
Experiment 4 showed that, when trial length and stimulus duration are controlled,additional presentations are of limited benefit, improving discrimination in the visual
distance task only. The results of Experiment 5 therefore appear more consistent with
the idea that increasing the ISI allows more time to complete non-perceptual
processes such as those involved in decision making and response selection andtherefore more in line with models proposing an accumulator process in response
selection (e.g., S.D. Brown et al., 2008; Lacouture & Marley, 2004; Mathews &Stewart, 2009; Nosofsky, 1997) than models emphasizing the perceptual processing29Additional stimulus presentations
stage (Kent & Lamberts, 2005). Allowing more time for a response in an accumulator
process can reduce the impact of variation in starting position and accumulation rateby increasing the threshold for response production, decreasing the number of trials
on which an incorrect accumulator wins.
Nevertheless, in order to determine whether it is the increase in total trial
length that is critical rather than the amount of temporal separation between stimulus
repetitions, Experiment 6 included two conditions in which a stimulus was presented
once and the response cue was either presented at stimulus offset or after a delay.
However, presenting stimuli only once per trial is problematic because there is little
incentive to use any additional time after stimulus offset. This was why there werealways two stimulus presentations in Experiment 5. To address this issue both trial
length (short or long) and number of presentations (one or two) were manipulated inExperiment 6 (see Figure 8). By intermixing trials from each of these conditions, an
incentive is provided to utilize the time between offset of the first stimulus and theonset of the response cue because there is a chance that the stimulus will be presented
a second time.
In a change from previous experiments, Experiment 6 used an individual
participants design with each participant undergoing extensive testing. Nosofsky(1983) used an individual subjects design and it is useful to examine the effects oftrial length and number of presentations at the level of the individual subject.
Participants completed the auditory absolute identification task only.

Participants. Five participants (two female) took part in the study, the three authors(Participants 1-3) and two naïve participants (Participants 4-5).

30Additional stimulus presentations
Apparatus, stimuli, design, and procedure. These were identical to those described in
the general method section with the following exceptions. The design was a 2 (trial
length short or long) x 2 (one or two stimulus presentations) x 6 (stimulus) design.
Each stimulus presentation lasted 125 ms. The response cue was presented either 250
ms (short condition) or 2,125 ms (long condition) after the offset of the first stimulus.
If stimuli were presented twice per trial the second stimulus was presented either 125
ms (short condition) or 2,000 ms after offset of the first stimulus. In all cases white
noise was presented for 250 ms following onset of the response cue (see Figure 8).
Participants completed eight one hour sessions. There were 25 repetitions of each of
the cells in the design within each session. At the start of each session participants
were first presented with each stimulus and its corresponding response label inascending order of response. Trials with RTs (measured as the time from onset of the
response prompt to key press) longer than 2,000 ms were excluded.

Results

Excluded trials constituted 1.5%, 0.31%, 2.54%, 3.58% and 0.47% of the total
number of non-practice trials for Participants 1-5, respectively.
Figure 9 shows the d’i,i+1 scores (see Footnote 3) for each condition for eachParticipant as well as d’i,i+1 scores averaged across participants. First, data wereanalyzed at the individual subjects level by splitting data from each session into three
200 trial blocks (yielding 24 blocks in total) and calculating d’i,i+1 scores for eachcondition within each block6. For each participant a 2 (trial length) x 2 (number ofpresentations) x 5 (stimulus pair) repeated measures ANOVA was conducted on thesed’i,i+1 scores with the scores from each block treated as an independent observation.
The results of this analysis are shown in Table 1. All participants showed typical bow

31Additional stimulus presentations
effects resulting in a significant main effect of stimulus for each participant.
Discrimination was significantly better when trial length was long for all participants
except Participant 3. Although discrimination for all participants was slightly betterin trials with two stimulus presentations compared with trials with one stimulus
presentation, this difference was significant for Participant 5 only (all other ps > .39).
Although only Participant 4 showed an interaction between number ofpresentations and trial length (with worse discrimination for the two presentations
condition for short trials, but the reverse pattern for longer trials) separate analyses
were conducted on trials from the one-presentation condition and trials from the twopresentation condition. We felt this necessary as a good indicator of the importanceof trial length is whether it affects discrimination even when a stimulus is presented
once. A 2 (trial length) x 5 (stimulus pair) repeated measures ANOVA was
conducted on d’i,i+1 scores from the one-presentation condition only. For the four
participants who displayed a main effect of trial length in the omnibus ANOVA, themain effect of trial length was significant (one tailed) for Participant 2, 4 and 5 (p =.095, p = .064 and p = .079, respectively). The same analyses on d’i,i+1 scores fromthe two-presentation condition yielded main effects of trial length for Participants 1,
2, 4 and 5 (p = .006, p = .005, p < .001 and p < .008 respectively). Thus despite a
non-significant interaction between trial length and number of stimulus presentations,for four participants, trial length did show a tendency to have a greater effect on
discrimination when stimuli were presented twice per trial.
Supposing that an analysis of probability correct that would not require us toaverage over trials might be more powerful, we also conducted probit regressions oneach participant's data. Accuracy was predicted from (centered) dummy-coded trial
length, (centered) number of presentations, and their interaction; and session (dummy-32

Additional stimulus presentations
coded, 8 levels), stimulus (dummy-coded, 6 levels) and (signed) difference to laststimulus (dummy-coded, 11 levels) were entered as covariates. An advantage forlonger trials was significant for four of the five participants (Wald zs = 3.400, 3.817,
1.228, 4.084, 3.631, for Participants 1-5 respectively). The main effect of number ofpresentations approached significance for only one participant (zs = 0.355, 0.742,
0.339, 1.118, 1.753), and the interaction was not significant (zs = 0.988, 1.401, 0.138,
0.670, 0.525). We further examined the simple effects in analogous analyses. When
there was a single presentation, the advantage for longer trials was significant for twoparticipants and approached significance for two more (zs = 1.806, 1.767, 0.779,
2.460, 2.290). When there were two presentations, the effect of trial length wassignificant for four participants (zs = 3.102, 3.501, 0.980, 3.299, 2.763). The effect ofnumber of trials reached significance neither when trial length was short (zs = 0.514,
0.470, 0.154, 0.352, 0.891) nor when it was long (zs = 0.972, 1.489, 0.372, 1.477,
1.563).
Figure 10 shows average correct RTs for each condition for each participant aswell as RTs averaged across participants. Average correct response times were
calculated for each 200 trial block for each participant. For each participant a 2 (trial
length) x 2 (number of presentations) x 6 (stimulus pair) repeated measures ANOVA
was conducted on these RTs with RTs from each block treated as independent
observations. Bows in RT were observed for all participants, leading to a significant
main effect of stimulus pair for each participant. For all participants, RTs were much
longer when trial length was short and the main effect of trial length was significant
for each participant. Number of presentations had little effect on RT, with Participant
2 only showing significantly faster responding in the two-presentation condition
compared to the one-presentation condition. Several significant interactions were33

Additional stimulus presentations
observed. Participant 1 showed a significant interaction between trial length andnumber of stimulus presentation, with faster responding in the two-presentation
condition when trial length was short, but the reverse when trial length was long. In
addition, Participants 4 and 5 showed a significant interaction between trial length andstimulus, with bows more evident in the one-presentation condition.

Summary
Increasing trial length improved discrimination and reduced RT for the majority ofparticipants in Experiment 6. Moreover, increasing trial length improved
performance both in trials where there was one stimulus presentation and in trials
where there were two stimulus presentations. This supports the conclusion from
Experiment 5 that discrimination is influenced by trial length and that the difference
in discrimination between the one- and two-presentation conditions in Experiment 1
may be due to trial length and not number of presentations. Indeed, when trial length
was controlled in Experiment 6, increasing the number of stimulus presentations
improved discrimination for only one participant. This improvement may have been
due to the additional presentation, the extra stimulus time provided by the additionalpresentation or a combination of both. Regardless, it indicates that the benefit fromadditional presentations is very limited.
One potential explanation for the weak effect of the additional stimulus
presentation is that the use of masking in Experiment 6 prevented stimulus
integration. Without stimulus integration an additional stimulus presentation would
not lead to improved performance. However, several findings run counter to thisargument. In Experiment 2, manipulating the presence of a mask had no influence on
any performance indicators. If masking did prevent stimulus integration then34

Additional stimulus presentations
performance in the unmasked condition should have been superior to the masked
condition. Second, an additional stimulus presentation did improve discrimination for
one participant in Experiment 6, indicating that masking did not interfere withstimulus integration (at least not in an all-or-none manner).
Although a significant interaction between number of presentations and trial
length was evident for only one participant, there was some evidence that the effect of
trial length was more prominent when stimuli were presented twice. This isconsistent with the idea that two stimulus presentations are more likely to be
represented independently when separated by a longer ISI (Nosofsky, 1983; although
see arguments against this in the Summary of Experiment 5). Alternatively, a long
ISI may be useful in that it provides time for non-perceptual processes (e.g., response
selection) to complete following the presentation of the first stimulus. A response
derived from the first stimulus presentation could be treated as an estimate that is thenused to modify the response selection process before the second stimulus presentation.
For example, the involvement of accumulators for stimuli that are far away from theinitial stimulus estimate might be inhibited or even drop out of the competition,
producing faster and more accurate responses when the second stimulus is presented(cf. Nosofsky, 1997). Whilst either of these alternatives is feasible, the evidence for
an interaction between trial length and number of presentations was relatively weak.
A simpler explanation is that on a proportion of trials participants were notconcentrating at the beginning of the trial, and so made more errors when stimuli were
presented in quick succession. The central finding from Experiment 6 is therefore
that absolute identification discrimination can be improved by increasing trial length.

General Discussion

35Additional stimulus presentations

Current models of absolute identification allocate different levels ofimportance to the perceptual processes involved in completing the task. Following
models of other cognitive processes (e.g., Cohen & Nosofsky, 2003; Lamberts, 2000;
Loftus & McLean, 1999), the EGCM (Kent & Lamberts, 2005) places central
importance on the stimulus sampling process. In the EGCM, stimulus sampling links
accuracy and RT, with more accurate responding when more information has been
accumulated. In comparison, other models of absolute identification give little
importance to stimulus sampling and focus more on the dynamics of the response
selection process (S.D. Brown et al., 2008; Nosofsky, 1997; Matthews & Stewart,2009).
In the series of experiments presented here we used a repeated stimulus
presentation methodology developed by Nosofsky (1983) to examine the importanceof stimulus sampling in absolute identification. Previously, Nosofsky (1983)
demonstrated that discrimination in absolute identification improves with additional
stimulus presentations during a trial. However, presenting a stimulus more times also
increases overall stimulus duration and introduces additional ISIs, both of which canlead to additional opportunities for stimulus sampling, either of the stimulus itself orfrom a short term sensory buffer (e.g., Massaro, 1972a). We therefore examined inExperiments 2, 3, and 4 whether the improvement in discriminability with additional
stimulus presentations was caused by an increased opportunity for stimulus sampling(either directly, or via the sensory buffer).
Experiment 1 replicated the additional stimulus presentation effect observedby Nosofsky (1983) demonstrating that discrimination was better when a stimulus
was presented twice per trial as opposed to once per trial. Moreover, we showed that36

Additional stimulus presentations
this improvement in discrimination did not just occur for the central stimuli(Experiment 1a and 1b demonstrated improvement across the full range of stimuli).
In addition, we also showed that RTs were considerably shorter when stimuli were
presented twice per trial compared with a single stimulus presentation. Response
times appear more sensitive to the additional stimulus manipulation than choiceproportions; we speculate that some of the difference in RTs is due to response
preparation (see below and Summary sections of Experiments 1 and 4).
Experiment 2 demonstrated that the two-presentation benefit in Experiment 1
was not caused by additional sampling from a very short-term sensory buffer during
the ISI, as presenting a mask (which effectively eradicates information in the sensory
buffer) during the ISI did not reduce performance. Manipulating the duration of
stimulus exposure in Experiment 3 also had little effect on performance,
demonstrating that the improvement in discrimination in Experiment 1 for the onepresentation condition relative to the two-presentation condition was not caused byincreased opportunity for stimulus sampling. In Experiment 4, the number of
additional stimulus presentations was manipulated whilst holding the total stimulus
exposure time constant. Increasing the number of repetitions only improved
discrimination for the visual task. The effect of decreased RTs was present for bothtasks, but much smaller than the magnitude of effect observed in Experiment 1.
Although Nosofsky (1983) found reduced advantages for three over two stimulus
presentations, they were still of a sizable magnitude. However, the total exposure andtrial length were not controlled in Nosofsky’s experiments.
The results of Experiments 2, 3, and 4 demonstrated that the additional
stimulus benefit in absolute identification is not created by increased stimulus
sampling per se. Moreover, the evidence for the formation of independent37

Additional stimulus presentations
representations (at the beginning of each presentation) contributing to the effect inExperiment 1 was limited: When the number of presentations was manipulated
independently of other factors in Experiment 4, the effect on discrimination was small
in the visual modality, and absent in the auditory modality. The relatively small
influence of stimulus repetition suggests involvement of other processes incontributing to the advantage of the additional stimulus presentation in Experiment 1.
Experiments 5 and 6, therefore, investigated whether a non-perceptual factor, theoverall trial duration from onset of the first stimulus to onset of the response cue,affected performance. Both Experiments 5 and 6 demonstrated that manipulating
non-perceptual processing time influenced both discrimination and RT.
Discrimination was worse and RTs were slower when the time from onset of the firststimulus to onset of the response cue was shorter, suggesting multiple contributions tothe benefit of the two presentations condition in Experiment 1. In particular,
Experiment 6 ruled out the possibility that increasing non-perceptual processing time
improves performance simply because it increases the likelihood that two stimulus
presentations are represented independently (a possibility in Experiment 5 where
stimuli were always presented twice per trial). In Experiment 6, increasing nonperceptual processing time improved performance even when stimuli were presented
once per trial. Furthermore only one out of five participants who completedExperiment 6 showed better performance when stimuli were presented twice per trial
compared to when they were presented once per trial and the time from offset of thefirst stimulus presentation to onset of the response cue was controlled. Althoughadditional presentations can provide some benefit, increasing the time available fornon-perceptual processes also appears to aid performance.

38

Additional stimulus presentations
Perceptual and non-perceptual processing in absolute identification
The experiments presented here demonstrate that stimulus sampling in
absolute identification can occur relatively quickly, probably in less than 250 ms, asmasking during the ISI did not decrease performance, and increasing exposure
duration beyond 250 ms did not improve performance. Stimulus sampling is likely to
be important in determining performance, but only at relatively short durations (andcertainly less than those we have used). As RTs in absolute identification are
typically quite long (> 1,000 ms), such a short duration for stimulus samplingsuggests that this process alone does not account for the majority of the processing
underlying the time taken to produce a response in absolute identification. The timecourse of non-perceptual processing may therefore constitute a significant proportionof the RT. This finding has important implication for the EGCM (Kent & Lamberts,2005) according to which the time course of stimulus sampling is of central
importance, directly linking accuracy and RT. Whilst other non-perceptual processes
are incorporated into the model in the form of a ‘residual time’ parameter, the timecourse of these non-perceptual components is not detailed, and are assumed constantover different stimuli. Previous estimates of the time course of stimulus sampling
range from approximately 750 ms to 1,240 ms on average (depending on set size; see
the model predictions in Kent & Lamberts, 2005). However, these model estimates
were derived from a standard single stimulus absolute identification task in which
there were no restrictions on either stimulus duration or time to respond. Further
studies manipulating these factors will need to be conducted in order to test whether
the stimulus sampling process modelled by the EGCM is of central importance toperforming the standard absolute identification tasks (Hsich & Saberi, 2007, andWard, 1991, also did not control or report RTs).

39

Additional stimulus presentations
Perhaps the success of the EGCM at accounting for data from a standard
absolute identification experiment (Kent & Lamberts, 2005) relies on the analogous
processes involved in perceptual processing and memory retrieval processing (e.g.,
Kent & Lamberts, 2006a, 2006b, 2008; Lamberts & Kent, 2008). According to such arevised model, the rapid stimulus sampling process would be partnered with a slower
process of sampling representations from memory in the response selection stage.
The current implementation of the EGCM (Kent & Lamberts, 2005) might beapproximating such a process by overestimating the duration of stimulus sampling.
Such a revision would allow the EGCM to be independent of stimulus presentation
duration and still predict RT differences, consistent with the data presented here5. Of
course, such a model would retain the close link between RT and accuracy, which we(e.g., the current Experiment 4; Adelman & Stewart, 2006) and others (Donkin, S. D.
Brown, Heathcote, & Marley, 2009) have demonstrated is not always straightforward.
When total stimulus time was controlled, additional stimulus presentations did
provide some benefit in the distance identification task, supporting Nosofsky’s (1983)
conclusion that an increase in duration is not the same as a stimulus repetition. In
Nosofsky’s interpretation, separated repetitions cause more precise representations
than a mere increase in duration because separation in time leads to unrelated (rather
than related) samples of noise. If this were true, the decrease in separation in timemight account for the effect of reducing interstimulus interval in Experiments 5 and 6.
However, Experiment 6 showed that discrimination can be improved by increasing
the amount of non-perceptual processing time after a single stimulus presentation.
This suggests the effect of increasing the interstimulus interval in Experiments 5 and
6 was mostly due to increased time for non-perceptual processes and not increased
separation. Whilst separation may have played a role, presenting an additional40

Additional stimulus presentations
stimulus during a trial had only a limited effect on performance, and so any effect of
separation would have been relatively small.
The improvement in absolute identification performance as the time before a
response may be made increases indicates the relative importance of non-perceptual
processes in absolute identification. Relevant non-perceptual processes are: retrieval
from memory, decision making, and response selection. In both contemporary andolder models that attribute variation in response time to processes other than stimulus
sampling (including SAMBA, S. D. Brown et al., 2008; the leaky competing
accumulator model, Lacouture & Marley, 2004; the EBRW, Nosofsky, 1997; and theballistic accumulator version of the RJM, Matthews & Stewart, 2009) response
selection is implemented as an accumulation processes with either sampling
variability or variability in starting point (or both). All accumulator-based models canpredict that absolute identification performance improves when response selection
processing time is increased as these sources of variability are surmounted over time(for example by shifting the threshold for selecting a winning accumulator).
Whilst models that detail the time course of response selection processes areable to account for the improved performance when non-perceptual processing time isincreased, none of them currently account for the (albeit rapid) stimulus sampling
process. Only one model currently considers both stimulus sampling and response
selection, the EBRW-PE (Cohen & Nosofsky, 2003) which is a hybrid of both the
EBRW (Nosofsky & Palmeri, 1997) and the EGCM (Lamberts, 2000). So far thismodel has not been applied to absolute identification, although individually bothconstituent models have (Kent & Lamberts, 2005; Nosofsky, 1997), and so the
EBRW-PE could potentially be extended to absolute identification. Such an
extension may also increase the viability of the EBRW as a model of absolute41Additional stimulus presentations
identification, as in its current format, the EBRW explicitly assumes a linear relation
between the variances of the memory representations and the distance from thenearest edge of the stimulus range, essentially forcing the model to produce bow
effects. In the EBRW-PE, the need for this assumption would be decreased as bow
effects in RT could also be determined by the time required for stimulus sampling (asin the EGCM). However, further work will be required to determine whether the
EBRW-PE is a viable model of absolute identification.
Although all the major current models of absolute identification can probably
be modified to allow for the data presented in the experiments here, we have shownthat response selection (including retrieval of memory representations) and not
stimulus sampling, is the crucial limiting process in the majority of absolute
identification studies. Response selection processes are therefore likely to constitutethe majority of the time required to identify a stimulus.

How do additional stimulus presentations affect processing?
Finally, we discuss the specific effects of additional stimulus presentations on
processing of the trial as a whole.
Quite apart from the processing of the stimulus itself, it is likely that the
expectation of a stimulus leads to a different mode of processing. If no further
information is expected (e.g., with a delayed response deadline, but no further
stimulus) then response selection may complete, response preparation may proceedand only execution need be delayed. By contrast, if further information is expected(i.e., in the gap between two stimuli) it would seem sensible to delay the completionof response selection until this information (the further stimulus) has been presented.

42Additional stimulus presentations
Such strategies may be immune to the absence of any actual benefit from theexpected further information. Indeed, such a benefit is not always seen, as when threestimuli are equivalent to two in Experiment 4a. We now go on to address the modesof processing the additional stimulus may receive despite its lack of influence on
discrimination.
The first possibility to consider is that the additional presentation is ignored,
either because of the instruction to participants that each presentation is identical, or
the ability to detect that the additional stimulus is identical, or because theidentification decision has already been made on the basis of the previous
presentation(s). If the additional presentation is ignored, this would explain theabsence of an effect on discrimination in Experiment 4a, but if stimuli are completely
ignored, then the RT difference in Experiment 4a is not explained.
The second possibility is that the additional presentation affects response
criteria only. For example, the response threshold (the amount of accumulated
evidence needed in favor of one response) might be influenced by the number ofstimulus presentations. However, this explanation is somewhat less favorable when it
is considered that Experiments 5 and 6 seemed to indicate that the number ofpresentations was acting as a proxy for extending the amount of non-perceptual
processing time between stimulus onset and response onset (i.e., improvements wereseen in the absence of additional stimulus presentations). More generally, it seems
necessary that there should be a limit on the effectiveness of changing response
criteria; otherwise, there is nothing to prevent a suitably motivated participant
increasing his or her criteria arbitrarily far to obtain perfect accuracy. Critically, thislimit cannot be due to forgetting, as the additional stimulus presentation prevents this.
Overall, it seems that the locus of the limit on information transmission is at an earlier

43Additional stimulus presentations
stage, which is well justified as it seems a limit that depends on the stimulus
dimension should not occur due to decision parameters.
The third possible explanation for the lack of the additional stimulus
presentation affecting accuracy is that each additional presentation starts afresh the
response selection process with new evidence. Thus, essentially the whole process isrepeated with no memory for each stimulus presentation. In principle, starting again
with the second (or third) stimulus presentation would produce no change indiscrimination, but would imply an increase in RT, which is inconsistent with theevidence for all the experiments. One would have to suppose that there is a local
speed-up of response selection processing after each stimulus presentation, in order topredict the decrease in RT with additional stimulus presentations.
A fourth explanation is that the additional stimulus explanation evokes a new
independent representation of the stimulus that is integrated with evidence fromprevious presentations. If the evidence is integrated then the evidence, on the whole,should better support the correct response (Nosofsky, 1983). However, Experiment
4a is clear evidence against such an explanation.
The final possibility we consider, is that the additional presentation produces arepresentation that supports the same (possibly erroneous) response. Such a biased
process would lead to faster responding, with no concurrent increase indiscrimination. In SAMBA, for instance, there is non-psychophysical variability due
to the allocation of limited selective attention resources during the mapping process.
If the allocation of these resources were to move very slowly (much slower than in theparameter sets that have previously been used in prior applications of the model) themagnitude estimation process will have the same error (and hence the same error
would be propagated into the response selection mechanism). The ballistic

44

Additional stimulus presentations
accumulators would receive the same inputs, and added to the existing values, thiswould speed the response selection process, without a concurrent increase indiscrimination. This, however, runs counter to the usual understanding of selective
attention as a resource that is rapidly moved to relevant information. An alternative
version of this possibility is that the attention limit does not lie in the stimulus
representation, but in its allocation to the response. Specifically, if on a particular
trial, the mapping of stimulus to responses is erroneous, the representation of thestimulus can be perfect (and therefore not improved by additional representations or
sampling) but the error in response selection occurs because the mapping between
stimulus and response is incorrect. Within this framework, the RT advantage forlonger trials (Experiments 5 and 6) is due to slow memory sampling, with thepossibility of using poorer quality memory representations reducing over time.

Conclusion
The evidence presented here suggests: a) the presentation of additional stimuli withina trial can have an artefactual effect from the duration of response selection processes;b) that there are situations where the cognitive system is able to obtain and integrate
multiple independent perceptual representations from additional presentations toimprove discrimination; but c) that there are situations where the cognitive system isunable to obtain an independent representation, but the representation is integrated in
the same way to obtain an improvement in latency but not accuracy. This implicates,in either selective attention or memory, a strong influence on performance in absolute
identification that varies slowly, which forms the limit on information transmission.

45

Additional stimulus presentations
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50

Additional stimulus presentations
Author notes

This research was supported by Economic & Social Research Council grants RES000-22-2459 and RES-062-23-0545 and a Great Western Research Fellowship to thesecond author. We are grateful to Neil Stewart for input throughout the design andanalysis of the research, and William Matthews, Koen Lamberts and Derrick Watsonfor helpful discussions.

51

Additional stimulus presentations
Footnotes
1

We used intermixing here to avoid long-term strategy use by participants. That is,

the state of the participant going into a trial was not confounded with the type of thetrial, which would occur in a blocked design.

2

For the visual stimuli this refresh rate meant we actually had exposure times of 253,

173, and 120 ms for the different stimulus presentation times in Experiments 1-6, andthe inter-presentations gaps and masks were rounded up to the nearest multiplier of
13.333 ms.

3Following Luce, Nosofsky, Green, and Smith (1982), d’i i+1 was used as a measureof discriminability between the stimulusi and stimulusi+1 (lower d’i i+1 scores indicate
less discriminability). The following definition of d’i, i+1 is with respect to a stimulus
pair (i, i+1). A response of i + 1 or greater to Stimulus i + 1 is considered a ‘hit’,
whereas a response of i or less is considered a ‘miss’. Similarly a response of i + 1 orgreater to Stimulus i is considered a ‘false alarm’ whereas a response of i or less is a‘correct rejection’ (Nosofsky, 1983b). d’i, i+1 is then calculated in the normal way (seeGreen & Swets, 1966 or Macmillan & Creelman, 2006). The RT analysis was
conducted on both correct and incorrect RT, but in all cases the main effect ofCondition was the same as that for correct RT and so only analysis on correct RT ispresented.

4

The hazard must be decreasing in the tail because accuracy asymptotes before 1.

52Additional stimulus presentations
5

Decreasing or peaked hazard for stimulus sampling would be required to fit

Experiment 4b. This could perhaps be achieved rather trivially by a small probability
that stimulus sampling never proceeds on any given presentation.

6Note that, if the proportion false alarms or hits in a cell is either 0 or 1, then d’i,i+1

will tend to infinity. For this reason whenever either proportion was 0 or 1 it was
replaced with .05 and .95 respectively. Given that the maximum number of cells percondition in the 200 trial blocks was 16 this replacement is adequate in that thedifference between 1/20 (the shift used for the replacement of ceiling and floor
proportions) and 1/16 is greater than that of 1/16 and 1/15. Thus d’i,i+1 scores wouldchange more for more extreme responding. Replacing proportions of 0 or 1 by .025
or .975 had little effect on the outcome of the d’i,i+1 analyses. Note that using
replacements with much smaller differences is problematic as d’i,i+1 scores become
very large or very small, increasing the variance in d’i,i+1 scores.

53

Additional stimulus presentations
Table 1.
Participant
1

2

3

4

5

Stimulus

** ^^

** ^^

** ^

** ^^

** ^^

Trial length

** ^^

** ^^

^^

** ^^

** ^^

Number of presentations^

Stimulus x Length*

Stimulus x Number
Length x Number

^^

*
^^

^^

*
*

Stimulus x Length x Number
Note. ANOVA results for d’i,i+1 (*) and RT (^) analysis of individual participant datafrom Experiment 6. Single symbols (* or ^) indicate p<.05 and two symbols (** or^^) indicates p<.01.

54

Additional stimulus presentations
Figure list

Figure 1. A temporal schematic of Experiments 1-3. S = stimulus; M = mask; numbers referto milliseconds; ??? is the response prompt.

Figure 2. Discrimination (top row) and response times (bottom row) for the absolute
identification of tone frequency task (Experiment 1a, left column) and the absolute
identification of line length task (Experiment 1b, right column). Each graph shows
data for the 1-stimulus (○) and 2-stimulus (□) conditions and for each stimulus (orstimulus pair d’i, i+1). d’i, i+1 = discriminability; RT = mean correct response time.
Large symbols represent grand condition means. Errors bars represent within subject
95% confidence intervals.

Figure 3. Discrimination (top row) and response times (bottom row) for the absolute
identification of tone frequency task (Experiment 2a, left column) and the absolute
identification of line length task (Experiment 2b, right column). Each graph shows
data for the masked ISI (○) and unmasked ISI (□) conditions for each stimulus (orstimulus pair d’i, i+1). d’i, i+1 = discriminability; RT = mean correct response time.
Large symbols represent grand condition means. Errors bars represent within subject
95% confidence intervals.

Figure 4. Discrimination (top row) and response times (bottom row) for the absolute
identification of tone frequency task (Experiment 3a, left column) and the absolute
identification of line length task (Experiment 3b, right column). Each graph shows
data for the short exposure (○) and long exposure (□) duration conditions for each55

Additional stimulus presentations
stimulus (or stimulus pair d’i, i+1). d’i, i+1 = discriminability; RT = mean correct
response time. Large symbols represent grand condition means. Errors bars represent
within subject 95% confidence intervals.

Figure 5. Discrimination (top row) and response times (bottom row) for the absolute
identification of tone frequency task (Experiment 4a, left column) and the absolute
identification of line length task (Experiment 4b, right column). Each graph shows
data for the 2-stimulus (○) and 3-stimulus (□) conditions for each stimulus (orstimulus pair d’i, i+1). d’i, i+1 = discriminability; RT = mean correct response time.
Large symbols represent grand condition means. Errors bars represent within subject
95% confidence intervals.

Figure 6. A temporal schematic of Experiment 5. S = stimulus; M = mask; numbers
refer to milliseconds; ??? is the response prompt.

Figure 7. Discrimination (top row) and response times (bottom row) for the absolute
identification of tone frequency task (Experiment 5a, left column) and the absolute
identification of line length task (Experiment 5b, right column). Each graph shows
data for the short ISI (50 ms; ○) and long ISI (2000 ms; □) conditions for eachstimulus (or stimulus pair d’i, i+1). d’i, i+1 = discriminability; RT = mean correct
response time. Large symbols represent grand condition means. Errors bars represent
within subject 95% confidence intervals.

Figure 8. A temporal schematic of Experiment 6. S = stimulus; M = mask; numbers
refer to milliseconds; ??? is the response prompt.

56

Additional stimulus presentations

Figure 9. Discrimination for the absolute identification of tone frequency task
(Experiment 6). Each graph shows data for the conditions crossing short responsedelay (250 ms; ○) and long response delay (2150 ms; □) with one-presentation (+) andtwo-presentation (×) conditions for each adjacent stimulus pair. d’i, i+1 =discriminability. Panels 1-5 show results for Participants 1-5 respectively and panel 6
shows the average results. Large symbols represent grand means for the main effects.
Errors bars represent repeated measures 95% confidence intervals on the basis of trial
blocks (see text). Panel AVG shows averaged data.

Figure 10. Mean correct response times for the absolute identification of tone
frequency task (Experiment 6). Each graph shows data for the conditions crossing
short response delay (250 ms; ○) and long response delay (2150 ms; □) with onepresentation (+) and two-presentation (×) conditions for each stimulus. Panels 1-5
show results for Participants 1-5 respectively and panel 6 shows the average results.
Large symbols represent grand means for the main effects. Errors bars represent
repeated measures 95% confidence intervals on the basis of trial blocks (see text).
Panel AVG shows averaged data.

57a) Experiment 1
1−stimulus
S

???

250

2−stimulus
S

???

S

250

250

2000

b) Experiment 2
Unmasked
M

S

250

250

S

M

2000

250

250

???

Masked
M

S

M

S

M

250

250

2000

250

250

???

c) Experiment 3
Long exposure
M

S

M

S

M

250

250

2000

250

250

???

Short exposure
M

S

M

S

M

250

125

2250

125

250

???

d) Experiment 4
2−stimulus
M

S

M

S

M

250

250

4000

250

250

???

3−stimulus
M

S

M

S

M

S

M

250

167

2000

167

2000

167

250

FIGURE 1

???

0

0

1000

1500

1
2

iii
2000

3,4

3
Stimulus
4,5

4
5
6
1500

2,3

1000

2000
1,2

500

Mean correct response time (ms)500

Mean correct response time (ms)

1.0

1.0

1.5

1.5

2.0

d’

2.0

d’

2.5

2.5

3.0

3.0

i

5,6
ii

1,2

1

2,3

2
3,4

Stimuli

3
Stimulus

FIGURE 2 / EXPT 1
4,5

4
5,6

Stimuli

iv

5
6

0

0

1000

1500

1
2

iii
2000

3,4

3
Stimulus
4,5

4
5
6
1500

2,3

1000

2000
1,2

500

Mean correct response time (ms)500

Mean correct response time (ms)

1.0

1.0

1.5

1.5

2.0

d’

2.0

d’

2.5

2.5

3.0

3.0

i

5,6
ii

1,2

1

2,3

2
3,4

Stimuli

3
Stimulus

FIGURE 3 / EXPT 2
4,5

4
5,6

Stimuli

iv

5
6

0

0

1000

1500

1
2

iii
2000

3,4

3
Stimulus
4,5

4
5
6
1500

2,3

1000

2000
1,2

500

Mean correct response time (ms)500

Mean correct response time (ms)

1.0

1.0

1.5

1.5

2.0

d’

2.0

d’

2.5

2.5

3.0

3.0

i

5,6
ii

1,2

1

2,3

2
3,4

Stimuli

3
Stimulus

FIGURE 4 / EXPT 3
4,5

4
5,6

Stimuli

iv

5
6

0

0

1000

1500

1
2

iii
2000

3,4

3
Stimulus
4,5

4
5
6
1500

2,3

1000

2000
1,2

500

Mean correct response time (ms)500

Mean correct response time (ms)

1.0

1.0

1.5

1.5

2.0

d’

2.0

d’

2.5

2.5

3.0

3.0

i

5,6
ii

1,2

1

2,3

2
3,4

Stimuli

3
Stimulus

FIGURE 5 / EXPT 4
4,5

4
5,6

Stimuliiv

56Experiment 5Long trial
M

S

M

S

250

250

2000

250

M
???
250

Short trial
M

S

M

250

250

50

S

250

M
???
250

FIGURE 6

0

0

1000

1500

1
2

iii
2000

3,4

3
Stimulus
4,5

4
5
6
1500

2,3

1000

2000
1,2

500

Mean correct response time (ms)500

Mean correct response time (ms)

1.0

1.0

1.5

1.5

2.0

d’

2.0

d’

2.5

2.5

3.0

3.0

i

5,6
ii

1,2

1

2,3

2
3,4

Stimuli

34,54

Stimulus

FIGURE 7 / new EXPT 5
5,6

Stimuliiv

56Experiment 6
Long trial, 2 presentations
M

S

M

S

250

125

2000

125

M
???
250

Short trial, 2 presentations
M

S M S

250

125

125

125

M
???
250

Long trial, 1 presentation
M

S

M

250

125

2125

M
???
250

Short trial, 1 presentations
M

S

M

250

125

250

M
???
250

FIGURE 8

2

0.5

1.5

1.0

2.0

d’

1.5

d’

2.5

2.0

3.0

1

1,2

2,3

3,4

4,5

5,6

1,2

2,3

Stimuli

3,4

4,5

5,6

4,5

5,6

4,5

5,6

Stimuli

3

d’
2.0

1.0

2.5

1.5

d’

3.0

2.0

3.5

2.5

4

1,2

2,3

3,4

4,5

5,6

1,2

2,3

Stimuli

3.0

Stimuli

AVG

2.0
1.0

1.0

1.5

1.5

d’

2.0

2.5

2.5

5

d’

3,4

1,2

2,3

3,4
Stimuli

4,5

5,6

1,2

2,3

3,4
Stimuli

FIGURE 9 / EXPT 6 d’

200

200

600

800

1

5

1000

2

2
200

200

600

800

3
4

3

4

Stimulus
1000

3

5

5

6
800

5

600

1000

4

400

Mean correct response time (ms)

400

3

800

1
2

600

1000

Mean correct response time (ms)1

400

Mean correct response time (ms)400

Mean correct response time (ms)

200

200

600

800

400

600

800

Mean correct response time (ms)400

Mean correct response time (ms)
1000

1000

1

6

6

2

1

1

1

2

2

2

3

Stimulus
Stimulus

4

3

Stimulus
Stimulus

AVG

3

4
5
6

4
5
6

4

5

6

Stimulus

FIGURE 10 / EXPT 6 RT