Psychon Bull Rev (2018) 25:1123–1128 DOI 10.3758/s13423-017-1342-4 BRIEF REPORT The contribution of stimulus frequency and recency to set-size effects 1,2 Félice van ‘t Wout Published online: 5 December 2017 The Author(s) 2017. This article is an open access publication Abstract Hick’s law describes the increase in choice reaction (Hick, 1952;Hyman, 1953), approximately linearly with the time (RT) with the number of stimulus-response (S-R) map- logarithm of the number of alternatives. This may be seen as pings. However, in choice RT experiments, set-size is typical- an example of the more general finding that the difficulty of ly confounded with stimulus recency and frequency: With a memory retrieval increases with the number of competing smaller set-size, each stimulus occurs on average more fre- items in memory. Other examples of such a Bset-size effect^ quently and more recently than with a larger set-size. To de- include the Bfan effect^ (Anderson, 1974) and the decrease in termine to what extent stimulus recency and frequency con- free recall performance with list length (Murdock, 1962). tribute to the set-size effect, stimulus set-size was manipulated However, one feature of such paradigms is that increasing independently of stimulus recency and frequency, by keeping set-size usually results in each item being tested less frequent- recency and frequency constant for a subset of the stimuli. ly and hence less recently. As recency and frequency are likely Although this substantially reduced the set-size effect (by ap- to influence retrieval time (Anderson, 1976), it is possible that proximately two-thirds for these stimuli), it did not eliminate set-size effects reflect (at least in part) effects of stimulus re- it. Thus, the time required to retrieve an S-R mapping from cency and frequency. The purpose of this experiment was to memory is (at least in part) determined by the number of examine the contribution of stimulus recency and frequency to alternatives. In contrast, a recent task switching study (Van ‘t the set-size effect found in choice RT experiments. Wout et al. in Journal of Experimental Psychology: Learning, This experiment was motivated in part by a recent task- Memory & Cognition., 41, 363–376, 2015) using the same switching study, which investigated whether the effect of the manipulation found that the time required to retrieve a task- number of competing items on retrieval time also applies to set from memory is not influenced by the number of alterna- the number of tasks among which a participant must switch tives per se. Hence, this experiment further supports a distinc- (Van ‘t Wout, Lavric & Monsell, 2015). In this study partici- tion between two levels of representation in task-set control: pants were required to switch among three or five tasks. The level of task-sets, and the level of S-R mappings. Overall, the five-task condition yielded longer RTs and switch costs, especially with no time to prepare for the upcoming trial. For two of the tasks, the frequency (and hence, recency) . . Keywords Hick’slaw Memory retrieval Set-size effect with which they were encountered was matched between the five-task and the three-task condition. For those tasks, the According to Hick’s law, reaction time (RT) increases as a number of tasks among which participants had to switch in a function of the number of stimulus-response (S-R) mappings block of trials did not influence performance. Hence the effect of number of tasks on the other tasks was not in fact attribut- able to a greater difficulty in task-set activation when more * Félice van ‘t Wout email@example.com tasks were in play. Van ‘tWout et al.’s(2015) finding that task-set retrieval is University of Exeter, Exeter, UK not influenced by the number of alternatives is in contrast with the common observation that memory retrieval increases Present address: School of Experimental Psychology, University of Bristol, Bristol BS8 1TH, England with the number of alternatives. There are two possible 1124 Psychon Bull Rev (2018) 25:1123–1128 explanations: 1) the process of retrieving a task-set in a task- inconclusive: Whereas some have argued that set-size effects cueing environment is somehow Bspecial^ and differs from might disappear with vast amounts of practice (Teichner & other kinds of memory retrieval in this respect; or 2) set-size Krebs, 1974), others have found that a substantial set-size effects observed for other kinds of memory retrieval actually effect remains even after extensive practice (for example, both might also result from the confound with the recency and/or Hale, 1968, and Hyman, 1953, reported sizeable set-size ef- frequency of retrieval, not from set-size per se. The experi- fects after 5000 and 15000 trials, respectively). ment reported here tested the latter explanation for the set-size In summary, it appears at least possible that the set-size effect found in choice RT experiments (Hick, 1952;Hyman, effects found in choice RT experiments are (in part) the result 1953). of the frequency and recency with which the specific S-R In a typical set-size experiment, participants are required to retrieval has been exercised. To assess this possibility, this execute a varying number of arbitrary S-R associations in experiment manipulated S-R frequency, recency, and set-size different blocks. Hick’s law describes the increase in RT with in a choice RT experiment much as van’t Wout et al. (2015) the number of S-R mappings. According to Schneider and did for tasks. To achieve this, participants were required to Anderson’s(2011) memory-based model of Hick’slaw, one classify a set of 4 stimuli with 4 responses in some blocks, source of this set-size effect is associative interference during and a set of 6 stimuli with 6 responses in others. Two different retrieval. The idea that Hick’s law can be explained in terms of sets of stimuli were used: a set of colours, and a set of shapes, basic memory effects is supported by studies that have shown so that half of the participants classified 4 colours, and 6 that set-size effects are not found when the need to retrieve shapes, and vice versa for the other half of participants. For arbitrary S-R associations is eliminated. Examples of such 2 of those stimuli (which we will refer to as Bprobe^ stimuli), studies include experiments involving saccades to a target recency and frequency were matched between the 4 S-R and location (Kveraga, Boucher & Hughes, 2002), aimed arm the 6 S-R conditions. If the set-size effect really results from a movements (Wright, Marino, Belovsky & Chubb, 2007), confound between set-size and recency or frequency, then a and the naming of very familiar stimuli, such as letters set-size effect should be found for the nonprobe stimuli but not (Morin, Konick, Troxell & McPherson, 1965). In contrast, for the probe stimuli for which recency and frequency did not others have found evidence of set-size effects even when differ between the 4 and 6 S-R conditions. memory load was constant across set-size conditions (anti- saccades in Kveraga, Boucher & Hughes, 2002;Brown, Steyvers & Wagenmakers, 2009), arguing against a purely Method memory-based model of Hick’slaw. Another factor known to influence set-size effects is the Participants frequency of immediate response repetitions on successive trials. As Kornblum (1968) noted, there is an inverse correla- Twenty-four participants (aged between 18 and 45 years, M = tion between the number of S-R mappings and the probability 21.6, 22 females and 2 males) took part in this experiment. All of an immediate S-R repeat. Because RTs are typically faster provided informed consent prior to participating, and the ex- for an S-R repeat than for an S-R switch (Bertelson, 1961), periment was approved by the University of Exeter School of decreasing the number of S-R mappings inflates the propor- Psychology Ethics Committee. Participants were paid be- tion of fast(er) responses in the RT distribution. Kornblum tween £5.40 and £7.00, depending on the speed and accuracy (1968) tested this prediction by varying the number of S-R of their performance. repetitions independent of set-size and found that RTs in- creased as a function of set-size only when the probability of Design and procedure an S-R repetition was high. However, less appears to be known about the effect of To manipulate the number of S-R mappings within subjects stimulus recency beyond immediate response repetitions on between the two halves of the experiment, whilst avoiding any Hick’s law. Although Hyman (1953) did find a positive cor- impact of previous exposure to the same stimuli on perfor- relation between RT and stimulus frequency (Experiment 2) mance in the second half, 2 sets of 6 stimuli were used: a set and recency (Experiment 3) in his original paper, the interac- of 6 colours (green, red, light blue, purple, yellow, and dark tion between these variables was not further investigated. In blue), and a set of 6 shapes (circle, cross, drop, square, star, other words, Hyman’s findings did not tell us whether, if re- and triangle). Responses were made using (4 or all) the X, C, cency and frequency were matched, the set-size effect would V, B, N, and M keys on a computer key board, pressed with disappear. The experiment reported was aimed at investigating the ring, middle, and index fingers of the left and right hands. whether this was indeed the case. This experiment additional- Half the participants completed the shape task with 4 S-R ly investigated the effect of practice on set-size effects, as mappings and the colour task with 6 S-R mappings, and vice previous research into theroleofpracticehasbeen versa for the other half of participants. In this way, the Psychon Bull Rev (2018) 25:1123–1128 1125 Fig. 1 Trial matrix displaying the frequency of all transition types in the 6 S-R condition (left) and the 4 S-R condition (right), with the probe transitions highlighted in bold experiment was split into two parts (a 6 S-R and a 4 S-R part), Results and the order of parts (and tasks) was balanced between participants. Very long (>2,000 ms) and short (<200 ms) reaction times Each part was split up into 9 blocks of 48 trials each, plus 1 (RTs), trials following an error and warm-up trials were ex- warm-up trial. For 2 of the S-R mappings (the Bprobe^ map- cluded from the data set (0.5% of the correct responses). pings), recency and frequency were matched between the 4 S- Furthermore, immediate response repetitions were excluded R and 6 S-R conditions. This was achieved by yoking one from analysis (Kornblum, 1968) except for the analysis of participant (P ) with another participant (P ). First, a 6 S-R the effect of recency. As a result, the probe task trials analysed 1 2 sequence (for participant P ) was created, in which the probe were either AB or BA transitions (16.67% of all trials). transitions (AA, BB, AB, and BA) occurred 4 times as often Because both of these trial types involved a hand switch, hand as all the other (nonprobe) transitions (Fig. 1). In order to repeats were excluded from the analysis of the nonprobe trials. create the 4 S-R sequence (for participant P ), all Es and Fs were replaced with Cs and Ds, respectively. In this manner, in Set-size effects the 4 S-R sequence, all 4 probe transitions (and the CC, DD, CD, and DC nonprobe transitions) occurred twice as often as Set-size effects for probe and nonprobe stimuli are shown in the other nonprobe transitions. So, stimulus recency was Fig. 2 (left). A 2 (4 S-R or 6 S-R) x 2 (probe or nonprobe) matched for probe stimuli between (yoked) subjects, and fre- repeated measures ANOVAwas run on the mean correct RT data quency also was matched within subjects. to compare set-size effects for probe trials (following probe trials) The order of number of S-R mappings (in the two halves of and nonprobe trials (following nonprobe trials). Overall, this anal- the session) and the order of stimulus set used for each half ysis revealed a significant set-size effect of 101 ± 17 ms, F(1,23) was manipulated between subjects. Furthermore, in the 4 S-R = 36.94, p < 0.001, η = 0.616. A significant two-way interaction condition each participant was assigned one of three response demonstrated that the set-size effect was much larger for the sets, consisting of two responses of the left and right hands: 1) nonprobe stimuli (150 ± 20 ms) than for the probe stimuli (52 ± ring and middle finger; 2) middle and index finger; and 3) 22 ms), F(1,23) = 13.48, p = 0.001, η = 0.370. RTs also were index and ring finger. This was done so that between subjects, shorter for probe stimuli (622 ± 16 ms) than for nonprobe stimuli each response was made equally often in the 4 and 6 S-R (686 ± 16 ms), F(1,23) = 19.65, p < 0.001, η = 0.461. Additional condition. ANOVAs revealed that the set-size effect was significant both for Prior to the start of each of the 4 S-R and 6 S-R parts, probe stimuli, F(1,23) = 5.56, p = 0.027, η =0.195, and for participants completed 1 practice block of 48 trials (plus 1 nonprobe stimuli, F(1,23) = 53.74, p <0.001, η = 0.700. warm-up trial). In both the practice and the experimental ses- Hence, although matching for recency and frequency reduced sions, the trial sequence was as follows: a 500-ms blank inter- the set-size effect considerably (by 65%), a significant set-size val between trials, followed by a 500-ms fixation dot, after effect still remained for probe stimuli, suggesting that the effect which the stimulus appeared. The stimulus remained on the cannot be entirely attributed to stimulus recency or frequency. screen until a response was made. On incorrect trials, an error message remained on the screen for 1,000 ms until the trial Plus or minus symbol (±) indicates the SEM difference. sequence resumed. The 4 S-R and 6 S-R parts both consisted 2 This analysis was restricted to probe-probe and nonprobe-nonprobe se- of 9 blocks of 48 trials (plus 1 warm-up trial) each, and the quences in case performance also was influenced by the recency/frequency of the immediately preceding trial. Without restrictions on the preceding trial parts were separated by a 5-minute break. At the end of each type, the set-size effect was still much larger for the nonprobe stimuli (142 ± block, participants were presented with a score that was based 2 20 ms, F(1,23) = 48.31, p < 0.001, η = 0.677) than for the probe stimuli (67 ± 2 2 on the speed and accuracy of their responses. When 20 ms, F(1,23) = 10.91, p = 0.003, η = 0.322), F(1,23) = 8.19, p = 0.009, η = p p 0.263, although this difference is somewhat smaller (the effect for nonprobe participants improved on this score, a bonus point (£0.10 exceeds that for probe stimuli by a factor of 2 rather than 3). This suggests each) was awarded. In total, the session lasted approximately frequency/recency of the preceding trial may matter; hence the main analysis 50 minutes. was restricted to probe-probe and nonprobe-nonprobe sequences. 1126 Psychon Bull Rev (2018) 25:1123–1128 Fig. 2 Mean correct RT (top) and % error (bottom) data, for 6 S-R and 4 S-R trials, plotted as a function of probe/nonprobe stimuli (left), and as a function of practice (right) Participants also made slightly more errors in the 6 S-R (5.9 128 ± 22 ms, a reduction of 47 ms or 27%), although the three- ± 0.7%) compared with the 4 S-R condition (5.0 ± 0.7%), way interaction between probe, number, and practice was not although this difference was not significant, F(1,23) = 1.33, significant, F(1,23) = 0.87, p =0.362, η = 0.036.The reduc- p =0.261, η = 0.055. They made significantly fewer errors on tion in set-size effect with practice is interesting, because it probe (4.1 ± 0.6%) than on nonprobe (6.8 ± 0.8%) trials, might suggest that, perhaps with more practice, the set-size F(1,23) = 12.32, p = 0.002, η = 0.349. Although, as for effect could disappear altogether. Indeed, for probe trials, RTs, the set-size effect was larger for nonprobe (1.9 ± 1.2%) when the first part was excluded from the analysis, the set- than for probe stimuli (−0.1 ± 1.0%), the two-way interaction size effect was no longer statistically significant, F(1,23) = 2 2 was not significant, F(1,23) = 1.64, p =0.213, η =0.067. 1.68, p = 0.208, η = 0.068. However, it was nontrivial in p p magnitude (28 ms) and appears asymptotic. Modulation of set-size effect by practice Recency analysis To investigate potential effects of practice on the set-size ef- fect, the data were split up into 3 parts of 144 trials each (first 3 RT and errors also were analysed as a function of lag: the blocks vs. second 3 blocks vs. third 3 blocks. Note that the number of trials since the previous appearance of the present sequential constraints described in the Method section were stimulus. This analysis was restricted to trials with a lag up to applied per block trio, so that each part contained equal 6 (with lag 1 being an immediate S-R repeat). The analysis numbers of all stimuli, transition types, etc.). A 3 (practice) included all probe and all nonprobe trials (there was not x 2 (4 S-R or 6 S-R) x 2 (probe or nonprobe) repeated mea- enough data to restrict this analysis to probe-probe and sures ANOVAwas run on the mean RTand % error data. Only nonprobe-nonprobe sequences). The first thing to notice from significant interactions with the linear component of the effect Fig. 3 is the massive (190 ± 12 ms, F(1,23) = 267.64, p < of practice are reported. 0.001, η = 0.921) increase in RT from lag 1 to lag 2. That Overall, the effect of set-size was significantly reduced is, most of the effect of lag was due to immediate repetitions. with practice (from 137 ± 24 ms in the first part to 78 ± This increase also was significantly larger in the 6 S-R condi- 16 ms in the third part, a reduction of 59 ms or 43%), tion (216 ± 17 ms) than in the 4 S-R condition (164 ± 10 ms), 2 2 F(1,23) = 8.06, p =0.009, η = 0.259. This reduction in set- F(1,23) = 9.77, p =0.005, η =0.298. p p size effect with practice was numerically greater for the probe Of interest is whether RTs continued to increase beyond lag stimuli (from 99 ± 27 ms to 27 ± 21 ms, a reduction of 72 ms 2. In a further analysis, lag 1 trials were excluded from the or 73%) than for the nonprobe stimuli (from 176 ± 30 ms to analysis. Only effects of and interactions with the linear Psychon Bull Rev (2018) 25:1123–1128 1127 Fig. 3 Mean correct RT (left) and % error (right) data for 6 S-R and 4 S-R trials, plotted as a function of lag component of recency will be reported below. There was a small of the frequency effect was overall confounded with stimulus (slope 8 ms) but significant recency effect beyond lag 2, F(1,23) recency, the same analysis was run with the data binned by lag = 9.47, p = 0.005, η = 0.292. This recency effect is only present (restricted to lag positions 2 to 6, hence not including imme- in the 6 S-R condition (slope 14 ± 4 ms, F(1,23) = 10.37, p = diate stimulus repetitions) and then averaging over lag. This 0.004, η = 0.311), and not in the 4 S-R condition, (slope 1 ± estimate of the frequency effect could not be affected by an 2ms, F=0.39, p =0.539, η = 0.017.); the difference between inflated proportion of more recent stimuli for the more fre- conditions in the magnitude of the recency effects beyond lag 2 quent stimuli. The result was similar: RTs remained faster was significant, F(1,23) = 6.81, p =0.016, η =0.229. for the more frequent (681 ± 23 ms) than the less frequent However, this pattern is not replicated in the error data. (744 ± 23 ms) stimuli, F(1,23) = 8.40, p = 0.008, η = Although the error rates increased substantially (by 5.0 ± 0.286. This frequency analysis confirms that frequency influ- 0.6%) from lag 1 to lag 2, F(1,23) = 65.87, p <0.001, η = ences RT independently of set-size. 0.741, this increase was not significantly larger in the 6 S-R (5.1 ± 0.8%) than in the 4 S-R (4.8 ± 0.8%) condition, F(1,23)=.54, p=.819, η =.002. Furthermore, beyond lag 2, Discussion the error lag effect opposed the RT lag effect: participants made fewer errors (slope −0.6 ± 0.2%) with an increase in This experiment was designed to determine the contribution of lag, F(1,23) = 13.63, p =0.001, η =0.372. stimulus recency and frequency to the set-size effect found in Most importantly, the difference in slope between the 6 S-R choice RT tasks. Participants were required to identify six col- and 4 S-R condition demonstrates that unequal proportions of ours and four shapes (or vice versa), in two separate parts of the more recent trials alone cannot explain the occurrence of set- experiment. For two of the stimuli in each part (the Bprobe^ size effects; had this been the case, there should have been no stimuli), frequency and recency of usage were matched between difference whatsoever between the 4 S-R and 6 S-R condi- parts. It was predicted that if the set-size effect merely describes tions once the data are plotted as a function of recency. an effect of recency and/or frequency, not an effect of set-size per se, then no set-size effect should be observed for the probe Frequency analysis stimuli. The results did not confirm this prediction. Although the set-size effect was approximately 3 times larger for nonprobe The large effect of set-size for the nonprobe items, coupled stimuli compared with probe stimuli, a significant overall set- with the absence of a marked recency effects beyond lag 1 size effect of 52 ms remained for probe stimuli. This finding suggests frequency is important. The effect of frequency can suggests that although stimulus frequency and/or recency are a be assessed independently of the number of S-R mappings, source of set-size effects in Buncontrolled^ data sets, they are not because in the 6 S-R condition, probe stimuli were responded the only source. Further analyses showed that immediate stim- to more frequently (108 times each per session) than nonprobe ulus repetitions substantially contribute to set-size effects, as stimuli (54 times each per session; Fig. 1). These more fre- does stimulus frequency. Stimulus recency beyond immediate quent probe stimuli were responded to 96 ± 27 ms faster than repetitions did not appear to have much of an effect. Altogether, the less frequent nonprobe stimuli, F(1,23) = 12.88, p = 0.002, the analyses clearly demonstrated that even when recency and η = 0.359. The same trend was apparent in the errors (7.9 ± frequency of usage are matched, retrieving an S-R mapping 0.9% less frequent stimuli; 4.0 ± 0.7% more frequent stimuli), from among alternatives is influenced by the number of F(1,23) = 16.58, p <0.001, η = 0.419. Because this analysis competitors. p 1128 Psychon Bull Rev (2018) 25:1123–1128 Acknowledgments The work described in this paper was performed as These results are consistent with Schneider and Anderson’s part of a PhD project by Félice van’t Wout under the supervision of (2011) memory-based model of Hick’slaw,inwhicha Stephen Monsell and Aureliu Lavric and supported by a studentship from chunk’s base-level activation reflects frequency and recency the Economic and Social Research Council (UK). of usage. Although other models (such as Brown et al.’s (2009) evidence accumulation model, or Usher, Olami, & Author’s note I would like to thank Stephen Monsell and Aureliu McClelland’s(2002) model, which views the set-size effect Lavric for their helpful comments on draft versions of this manuscript. as a speed accuracy trade-off) also are able to produce set-size effects, it is not obvious how these models could account for Open Access This article is distributed under the terms of the Creative the effects of recency and frequency observed here. Commons Attribution 4.0 International License (http:// As it has previously been demonstrated that practice modu- creativecommons.org/licenses/by/4.0/), which permits unrestricted use, lates set-size effects (Hale, 1968; also see Longstreth, El-Zahar & distribution, and reproduction in any medium, provided you give appro- priate credit to the original author(s) and the source, provide a link to the Alcorn, 1985), the data also were analysed as a function of prac- Creative Commons license, and indicate if changes were made. tice. Consistent with previous findings, this analysis revealed that overall, the set-size effect decreased as a function of practice. For the nonprobe stimuli, the set-size effect decreased by 27% in the References last third of the half-session compared with the first third. For the probe stimuli, however, this reduction was much larger (73%). Anderson, J. R. (1974). 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Published: Dec 5, 2017
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