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Equivalence class formation in accuracy or speed conditions: immediate emergence, adduction, and retention.

Conditional discrimination training in a matching-to-sample format can generate trained relations between arbitrary pairs of stimuli. Then, if certain pairs are interconnected, it is possible to test whether the stimuli are members of equivalence classes. To belong to equivalence classes, the stimuli must show the properties of reflexivity, symmetry, and transitivity. Reflexivity refers to an identity relation of a stimulus to an identical stimulus--if AB is trained, then AA and BB emerge. Symmetry refers to a relation that shows the interchangeability of two stimuli--if AB is trained, then BA emerges. Transitivity is a relation that emerges between separate stimuli that have been trained with a common stimulus--if AB and AC are trained, then BC and CB emerge (e.g., Sidman and Tailby 1982).

Fields and Verhave (1987) described the structure of equivalence classes. Stimuli belonging to a class can be categorized as either nodes or singles, depending on their relation to other stimuli. A node is a stimulus that is related to at least two other stimuli through training, whereas a single is a stimulus that is related to one other stimulus or a node through training. For example, when AC emerges from AB and BC training, A and C are singles, and B is a node. The number of nodes, which separate class members, has been shown to influence both accuracy and reaction time (RT)--or speed of responding--in selection tasks. Thus, a higher nodal number reduces accuracy and increases RTs in the selection of comparison stimuli in tests for emergent relations (Arntzen et al. 2010a, b; Arntzen and Hansen 2011; Arntzen and Holth 2000b; Bentall et al. 1999; Fields et al. 1995; Wang et al. 2011); however, one study (Spencer and Chase 1996) reported a reduction in response speed but not accuracy from a higher number of nodes.

RT (or response speed) has long been considered an important measure in stimulus equivalence research, as it may indicate how equivalence classes form (Holth and Amtzen 2000; Spencer and Chase 1996), being sensitive to variables involved in both the establishment of equivalence classes and their structural composition, such as stimulus relatedness and nodal number. In addition, small-scale differences in RTs may provide an indication of the substitutability of members within a class, which accuracy measures do not capture (Fields et al. 1995).

A number of other studies have shown that RTs differ depending on the trial type. In general, equivalence trials are associated with the slowest RTs (Amtzen et al. 2010a, b; Amtzen and Lian 2010; Bentall et al. 1999; Eilifsen and Amtzen 2009; Holth and Amtzen 2000; Imam 2001, 2006; Spencer and Chase 1996). Some studies have reported slower RTs in symmetry trials than in baseline trials (e.g., Holth and Amtzen 2000; Spencer and Chase 1996). Furthermore, one study showed that RTs in equivalence trials reach the level of RTs in symmetry trials with continued testing (Amtzen and Lian 2010), and when an LH arrangement was used for responses to comparison and/or sample stimuli, no increase from the baseline trials to the test trials for derived relations was reported (e.g., Amtzen and Haugland 2012; Tomanari et al. 2006). For example, Imam (2001, Experiment 2) used a single-subject design for two participants exposed to an equal number of trials in a condition of either accuracy followed by speed or speed followed by accuracy. Three 5-member and three 7-member classes were trained with an LS training structure. The results showed that trial types in testing accounted for 12 % to 15 % of the variance in response speed, with the fastest responses for the baseline trials, followed by the transitivity and equivalence trials, with and without a speed contingency in place. When picture stimuli are used as nodes, a difference between relational types arises, but to a lesser degree than when abstract stimuli are used (Amtzen and Lian 2010). Abstract stimuli are associated with longer RTs in tests for transitivity and equivalence (Amtzen et al. 2010a, b; Bentall et al. 1993) or in equivalence trials only (Amtzen and Lian 2010). While nameable stimuli have been repeatedly shown to facilitate stimulus equivalence formation (Amtzen 2004; Amtzen and Lian 2010; Amtzen et al. 2014; Amtzen and Nikolaisen 2011; Bentall et al. 1993; Fields et al. 2012; Holth and Amtzen 1998a), one study has shown that meaningful nonsense-syllable stimuli hinder stimulus equivalence formation to a greater extent than meaningless syllables (Lyddy et al. 2000).

Another important finding is that RTs become slower from the last baseline trials to the initial test trials for derived relations (Arntzen 2004; Amtzen et al. 2010a, b; Amtzen and Holth 1997, 2000a; Amtzen and Lian 2010; Holth and Arntzen 1998a, 1998b; Hove 2003; Imam 2001, 2006; Spencer and Chase 1996; Wulfert and Hayes 1988) and become faster with repeated testing (Amtzen 2004; Holth and Amtzen 1998a, 2000). These differences in RTs are more pronounced when all the stimuli are abstract than when one meaningful stimulus is used as a class member (Amtzen and Lian 2010; Amtzen and Nikolaisen 2011; Holth and Amtzen 1998a). One explanation for the differences in RTs between baseline trials during training and trials for derived relations during testing is that a mediating naming response or some other precurrent problem-solving behavior expends extra time in the test trials. This might be particularly likely with an LS training protocol, where a participant has experience with only one correct comparison for each sample during training and is exposed to a novel stimulus arrangement during testing (Holth and Amtzen 2000).

In addition, a more general question is whether slower or faster RTs in the last baseline trials can predict the formation of stimulus equivalence classes. Some studies have reported that RTs to comparison stimuli in baseline trials have limited predictive validity for the establishment of equivalence classes (e.g., Amtzen and Holth 1997). However, Holth and Amtzen (2000) found that RTs to comparison stimuli were related to both symmetric responding and certain response patterns. In Experiment 1, they trained 10 participants to form potentially three 3-member classes with an LS training structure. The main findings were that the three of four participants who had the fastest RTs to comparison stimuli were more likely to have responded correctly on symmetry trials and to have consistent response patterns on tests for equivalence. On average, consistent rather than nonsystematic responding was associated with lower RTs.

Spencer and Chase (1996) showed that participants can have near-perfect accuracy in tests for emergent relations but that response latency or speed continues to vary as a function of other variables. Using an LS structure, they trained three groups of participants in matching six sets (A, B, C, D, E, and G) of potentially 3-member classes--a total of 18 relations. The three groups--an instructed group, a queried group, and a standard group--were matched on speed based on a nonsignificant average difference between the groups in training. Speed was defined as the InvRT from the presentation of a sample to the selection of a comparison stimulus. Although no differences in InvRT or accuracy were found between the groups during testing, a two-way ANOVA showed that, on average, the variance in response speed for participants responding in accord with equivalence could be accounted for by a difference between baseline trials and equivalence trials (58 %) and a difference between baseline trials and transitivity trials plus equivalence trials (36.5 %). In addition, symmetry trials were faster than transitivity trials, while equivalence trials were slowest, on average, accounting for 31 % of the variance in response speed. In all trial types, the response speed was lower, on average, as a function of the nodal number: 14 % for symmetry, 17 % for transitivity, and 18 % for equivalence. This result was suggested to indicate an unequal relatedness of class members. The conversion of RT to InvRT, as used in this study, stabilizes the variance in response speed by reducing the distance between greater RT differences and increasing the distance between small RT differences (Baron 1985), although other authors have argued for the use of RT (Whelan 2008). We argue that in this experiment, InvRT facilitates visual analyses of data where detecting systematic small-scale differences is important.

A speed contingency can hinder various types of precurrent behavior, either overt or covert behavior, as faster responding can limit the time available to engage in such behavior. For example, in Holth and Amtzen (2000, Experiment 3), 10 participants were trained with an OTM training structure (AB/AC relations) to establish potentially three 3-member classes. A 2-s LH was imposed on the comparison stimuli during the final part of the training, and the participants were required to complete 24 randomly intermixed AB and AC trials in succession. If the participant did not reach the criterion, the sequence was repeated until the criterion was reached; otherwise, the session was terminated after 65 min. Two tests for derived relations followed the training, the first of which used the same LH as in training and the second of which imposed no time restrictions. Under these conditions, only five participants reached the MTS training criteria, and none of them responded according to stimulus equivalence in the initial test (with an LH imposed). However, one participant responded in accord with stimulus equivalence in the second test, and two more participants responded in accord with stimulus equivalence in the second part of the second test. Regardless of whether precurrent behavior, such as naming, is induced or hindered, the manipulation of environmental variables such as an LH is important in itself: It adds to the understanding of which conditions are more or less likely to lead to the formation of equivalence classes (Tomanari et al. 2006). For example, a comparison of speed and accuracy conditions may be important for future instructional technology with a foundation in basic research.

Imam (2001) provided data from two participants showing that a speed contingency reduces response accuracy in transitivity and equivalence trials compared with baseline trials. However, with an accuracy contingency, the participants maintained high accuracy in the same trials. A similar trade-off between speed and accuracy was reported in systematic replications with four participants who were trained on potentially 7member classes and who performed three different training and testing sequences. In this study, however, the majority of the errors occurred when the participants were unable to respond within a given time limit (Imam 2006). Although many researchers have introduced a speed contingency with a fixed LH, the gradual introduction of an LH on sample or comparison stimuli in an MTS task has also been attempted recently. Using an OTM training structure, Tomanari et al. (2006) gradually titrated an LH on sample and comparison stimuli in an MTS task in which participants established potentially 4-member classes. The five participants progressed through diminishing LHs until a 95 % accuracy criterion was reached with an LH of 0.4 s to 0.5 s on samples and 1.2 s on comparisons. Three of the five participants then responded in accord with equivalence. The participants' RTs were equal in training and test trials, but for all the participants, response speed tended to be marginally slower on average (a 0.2-0.3-s difference) when responding to comparisons in symmetry and equivalence trials compared with baseline trials. Marginal but consistently higher RTs were also reported for equivalence versus symmetry trials. Amtzen and Haugland (2012) conducted a systematic replication of this study; however, a computer titrated the LH on comparison stimuli, and they used 3-member classes instead of 4-member classes and shorter MTS training sessions. Only one of the five participants responded in accord with equivalence under a 2.5-s LH, and no RT differences related to trial type were found.

Sidman (1992) suggested that the immediacy of equivalence formation may be a measure that is sensitive to whether experimental or uncontrollable variables are responsible for positive test outcomes. However, the degree of immediate emergence of equivalence may be a function of experimenter-controlled variables, such as training conditions and testing protocols (e.g., Fields and Garruto 2009), or previously consistent MTS responding (Holth and Amtzen 1998a). Furthermore, the stability of equivalence classes may be another factor to consider. For example, in a study by Saunders et al. (1988), three of four participants achieved above 90 % accuracy on tests for baseline and emergent relations after up to 206 days without training, and Rehfeldt and Hayes (2000) obtained similar results after 3 months without training. Moreover, symmetric relations were more likely to be retained after 2 to 3 months than equivalence relations, but symmetric relations were retained by all participants who had intact equivalence relations (as cited in Dymond and Rehfeldt 2001, p. 10).

In general, as equivalence classes are less likely to be established with a speed contingency (Arntzen and Haugland 2012; Holth and Amtzen 2000; Imam 2001, 2006; Tomanari et al. 2006), particularly with an LS structure (Holth and Amtzen 2000; Imam 2001, 2006), a speed condition seems to limit stimulus equivalence formation. In addition, given the high number of trials required to reach an accuracy criterion (Amtzen and Haugland 2012; Imam 2001; Tomanari et al. 2006), a speed condition seems to have a greater effect on stimulus equivalence formation than an accuracy condition in a conditional discrimination procedure. The present study aimed to further investigate whether speed or accuracy conditions have differential effects on participants' likelihood of responding in accord with stimulus equivalence by matching speed and accuracy participants with respect to the number of training trials. This study also included only a few test trials to assess whether speed or accuracy influences the immediate emergence of equivalence, which may simultaneously reduce the probability that the effects carrying over from one testing condition to another. A second research question was whether speed and accuracy conditions would generate different probabilities of adduction from the emergent relations. To address this research question, a test was administered to demonstrate the recombination of the emergent relations into novel performances. A third question was whether differences in the stability of the emergent relations and adduction would arise; for this purpose, a retention test was administered following 2 weeks without practice. A fourth purpose was to yoke speed and accuracy participants during one phase of the baseline trials in order to allow for a closer examination of the influence of speed and accuracy conditions on the acquisition of baseline relations. An additional research question was whether the typically reported response speed or RT differences between trial types, or between training and test trials, would appear with either speed or accuracy conditions.

Method

Participants

Participants were run in two rounds. In Round 1, eleven participants were recruited from a college campus. They ranged in age from 22 to 30 years. The six participants (1) who completed all the experimental phases ranged in age from 22 to 29 years ([M.sub.age]=25). Of those, three were men, and three were women.

In Round 2, fifteen participants were recruited through personal contacts. They ranged in age from 22 to 34 years. The six participants (2) who completed all the experimental phases ranged in age from 22 to 29 years ([M.sub.age] = 23, 5). Of those, five were men, and one was a woman.

For illustration purposes, the numbers for the participants are renumbered. For all pairs, the speed participant has a participant number ending as an even number, and the accuracy participant has a participant number ending as an odd number.

Setting

The experiment took place in the Laboratory of Complex Human Behavior Studies at Oslo and Akershus University College. The participants were seated in booths approximately 1.75 x 5 m in diameter, in front of a 45 x 90 cm table. The participants faced a wall or a window with drawn curtains. The booths were situated in two different housing locations affiliated with the laboratory, one approximately 25 [m.sup.2] in size and the other approximately 20 [m.sup.2].

Instruments

A custom-made program, Matching to Sample (second edition), was used to run the experiment. The program was run on a Hewlett Packard HP Compaq Nc 6320 PC with Windows 7 Professional 32-bit operating system. The screen of the laptop was 15", with a 16:9 aspect ratio and 1400x 1050 resolution. A Magic Touch KTMT-1500-USB touch screen was mounted onto the screen. A Magic Touch v.2.21 for Windows 7 driver was used to run the touch screen.

Stimuli

For the pretraining phase, three numbers and three nonsense syllables, approximately 2 x 3 cm in size, were used as stimuli (see Fig. 1). Six abstract 2.5 x 2.5 cm stimuli and three numbers were used in the remaining phases (see Fig. 2).

Experimental Design

A matched design was used for this experiment, with the accuracy condition partially yoked to the speed condition with respect to the number of responses. Therefore, the first two participants were assigned to a speed contingency. The subsequent participants were then matched to one speed participant and assigned to an accuracy contingency, only if one participant was within [+ or -]12 trials of the criterion in the pretraining phase. If the next participant could not be matched to a speed participant, this participant also completed a speed condition. Subsequent participants were successively matched based on the trial number needed to complete the pretraining phase. Three participants who could be matched to one of the speed participants were then entered into the experiment at various stages and were assigned to an accuracy condition.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

General Procedure

All participants read an information sheet that explained the broad goals of the research conducted at the laboratory, although the purpose of the experiment was not mentioned, and stimulus equivalence was neither defined nor explained. In addition, their rights as research participants were explained, and they were informed that they could withdraw from participation at any time. Each participant then read and signed an informed consent form. Each session lasted approximately 1.5 to 3.5 hrs for the participants in Round 1 and approximately 1.5 to 9 hrs for the participants in Round 2. The sessions started with instructions that were separate for each condition of the experiment, as described below. When the participants finished reading the instructions, they pressed a square marked "Begin" on the bottom of the touch screen to start the experiment. A trial started with the presentation of a single sample stimulus in the center of the screen. Touching the sample stimulus made it disappear, and three comparison stimuli then appear simultaneously, with a 0-s delay. The program determined the positioning of the comparison stimuli randomly from trial to trial. The comparison stimuli appeared in a circular layout, 10 mm from the sample stimulus. Choosing one of the comparison stimuli lead to a 500-ms programmed consequence in which "good," "excellent," and so forth was the displayed, followed correct class-consistent responses. By contrast, choosing an incorrect comparison stimulus was followed by the display of "wrong." No consequences resulted from any other type of response. The bottom of the screen presented a count of the correct responses. Reaction time was recorded based on the interval between touching the sample stimulus and selecting a comparison stimulus, which was transformed into the inverse reaction time. The intertrial interval (ITI) was set to 1,000 ms in all phases; at the end of the feedback interval, the screen remained black. No consequences resulted from touching the screen during the ITI or presentation of the feedback. Participants completed Phases 1, 2, and 3, which were different for the speed and accuracy participants, whereas Phases 4 and 5 were identical for both groups. Phases 1 through 4 were completed in one session, whereas Phase 5 was completed 2 weeks later. The experiment proceeded through a simultaneous protocol, in which all relations were first trained (Phases 1-3) and in which probe trials were presented in a mixed order in separate test blocks (Phases 4 and 5).

Training

Pretraining This condition was identical for all participants. First, they were presented with the following instructions:

A stimulus will appear in the middle of the screen. Choose it by pressing on the screen. Two other stimuli will appear. Choose one of these by pressing on the screen in the same manner. If you choose the stimulus we have defined as correct, words such as "very good," "excellent," and so on will appear on the screen. If you press the wrong stimulus, the word "wrong" will appear on the screen. At the bottom of the screen, the number of correct responses you have made will be counted. Please do your best to get everything right. Good luck! Press Start to begin the experiment.

Potentially two 3-member classes of nonsense syllable stimuli (see Fig. 1) were then trained with an MTO training structure with blocks containing 36 trials to generate the following conditional discriminations: A1C1, A2C2, B1C1, and B2C2. Trials were arranged on a concurrent basis so that multiple classes were trained simultaneously, and the trial types were not introduced in a particular order. The training finished after the participants had reached a 100 % accuracy criterion within a single block. An additional 36-trial training block was added after the accuracy criterion was achieved, after which the pretraining phase ended.

Phase 1. This condition was different for the speed and accuracy participants. The speed participants were presented with the following instructions:
   A stimulus will appear in the middle of the screen.
   Choose it by pressing on the screen. Three other stimuli
   will appear. Choose one of these by pressing on the
   screen in the same manner. If you choose the stimulus
   we have defined as correct, words such as "very good,"
   "excellent," and so on will appear on the screen. If you
   press the wrong stimulus, the word "wrong" will appear
   on the screen. At the bottom of the screen, the number of
   correct responses you have made will be counted. Try to
   respond as quickly and correctly as you can. Good luck!
   Press Start to begin the experiment.


Potentially, three 3-member classes were then trained with an LS training structure. The following conditional discriminations were trained: A1B1, A2B2, A3B3, B1C1, B2C2, and B3C3. Trial types were again introduced in a simultaneous protocol with trials presented on a concurrent basis. Each training block consisted of 18 trials, divided into three 6-trial titration blocks. A sample stimulus was presented with a fixed 1,000-ms LH. A descending titrated LH on comparison stimuli occurred in 100-ms steps. The initial value of the titration was based on the average reaction time of the last five trials in the pretraining phase, with 1,000 ms added. Progress through the titration blocks was based on a 100 % accuracy criterion in six consecutive trials. Achieving the accuracy criterion reduced the LH by one step. If the participants responded incorrectly to the comparison stimuli or if they did not respond within the LH, the same text--incorrect--occurred, and a new trial began. Incorrect or correct responses that occurred after the LH ended were recorded separately as misses. The titration continued until the participants reached the accuracy criterion with a 1,000-ms LH. They were then given an extra block of 18 trials with the lowest LH value. Reaching a 94 % accuracy criterion with the lowest LH in a single block ended this phase; a 5-min break was granted before the next phase started.

The accuracy participants began the same phase with the same instructions as the speed participants, except the sentence "Try to respond as quickly and correctly as you can" was replaced with "Try to respond as correctly as you can." Each accuracy participant was yoked to a different individual speed participant: The former was given the same number of trials that the latter had required to reach the accuracy criterion. These trials appeared in one block, without an LH on sample and comparison stimuli. All the other experimental parameters were identical, so the accuracy participants had to reach the same criterion.

Phase 2. The speed participants were presented with the same instructions, stimuli, and training protocol as in the previous phase but without titration, and the sample and comparison stimuli were presented with a fixed 1,000-ms LH. Each training block had 18 trials and an accuracy criterion of 94 %. Reaching the criterion in one training block started the next phase. Furthermore, the accuracy participants were presented with the same instructions as in Phase 1 and were then exposed to a new block of 18 trials without an LH on sample or comparison stimuli and without yoking. All the other experimental parameters were identical to those for the speed participants.

Phase 3. This phase introduced blocks of 18 trials, in which the probability of programmed consequences was reduced to 75 %, 25 %, and then 0 %, if 94 % accuracy was reached in individual blocks. If the 94 % accuracy criterion was not reached, a previous fading block was introduced. Reaching an accuracy criterion with a 0 % probability of programmed consequences (i.e., extinction) immediately started the next phase. The speed participants completed this phase with a 1,000-ms LH, and the accuracy participants, without an LH.

Testing

Phase 4. This condition was identical for all participants and consisted of one block of 36 mixed-test trials presented in a random order without any time restrictions. One exception was Accuracy Participant 6, who completed 54 test trials in the initial test because of a programming error; his first 36 test trials were used for the analysis. First, the participants were presented with the following instructions:
   A stimulus will appear in the middle of the screen. Choose
   it by pressing on the screen. Three other stimuli will
   appear. Choose one of these by pressing on the screen in
   the same manner. Try to get as many correct as possible.
   Good luck! Press Start to begin the experiment.


The 36 test trials included 12 baseline trials, 12 symmetry trials, 6 transitivity trials, and 6 equivalence trials. The trial types involved in tests for symmetry were B1A1, B2A2, B3A3, C1B1, C2B2, and C3B3; for transitivity, A1C1, A2C2, and A3C3; and for equivalence, CIAI, C2A2, and C3A3. Test types were mixed in a randomly determined order, and each relational type was tested twice. Each test had a an accuracy criterion of maximum one error for each relation, and no programmed consequences occurred for any test trial. Following the completion of the last test trial, the participants received a message on the screen that the experiment had ended. Seated in the same booth, the experimenter then administered an adduction test with the following verbal instructions: "Please calculate the following addition problems." Similar to the test used in Bucklin et al. (2000), the adduction test consisted of an A4 piece of paper showing all possible relational types of symmetry, transitivity, and equivalence, totaling 15 relations set up as summation tasks (see Fig. 3).

[FIGURE 3 OMITTED]

Phase 5. This phase was a retention test administered 2 to 3 weeks after Phase 4. The participants received the same instructions and completed an identical test, including the adduction test, as in Phase 4.

Phase 6. This phase was a retention test administered 6 weeks after Phase 4. The participants received the same instructions and completed an identical test, including the adduction test, as in Phase 4.

Results

Pretraining

The participants completed the pretraining in a number of trials ranging from 60 to 144 trials. All participants were matched based on a [+ or -]12 trial difference in reaching the 100 % accuracy criterion. The first pair, P9056 and P9057, completed the pretraining in 72 and 60 trials, respectively; the second pair, P9058 and P9059, in 48 and 60 trials, respectively; and, the third pair, P9060 and P9061, in 144 and 132 trials, respectively. The fourth pair (P9072 and P9075) completed the pretraining in 108 and 120 trials, respectively; the fifth pair (P9076 and P9083) completed the pretraining in 72 and 72 trials, respectively; and the sixth pair (P9074 and P9085) completed the pretraining in 96 and 108 trials, respectively.

Training Trials

The average RT for the speed participants in the last five trials of their pretraining plus 1,000 ms yielded initial LH values of 4,955; 3,927; 1,771; 2,068; 2,474; and 2,012 ms for P9056, P9058, P9060, P9072, P9076, and P9074, respectively, from the beginning of the titration. As shown in Tables 1 and 2, the speed participants required 390; 432; 492; 2,712; 1,200; and 1,008 trials to complete the titration in Phase 1. Matched accuracy participants were then yoked to complete the same trial number in this phase. In this phase, the number of correct responses in Pair 1 was 317 for P9056 versus 356 for P9057; in Pair 2, 283 for P9058 versus 414 for P9059; in Pair 3,319 for P9060 versus 461 for P9061; in Pair 4, 1,880 for P9072 versus 2,469 for P9075; in Pair 5, 796 for P9076 versus 1,182 for P9083; and in Pair 6,625 for P9074 versus 967 for P9085. Thus, in Phase 1, all the accuracy participants had a higher number of correct responses than their matched counterparts.

As shown in Tables 1 and 2, the speed and accuracy participants differed substantially in the number of trials needed to complete Phases 2 and 3, where the LH was fixed for the speed participants. In Pair 1, P9056 completed 162 trials, while P9057 completed 72 trials. In Pair 2, P9058 completed 1,620 trials, while P9059 completed 72 trials. In Pair 3, P9060 completed 492 trials, while P9061 completed 90 trials. In Pair 4, P9072 completed 7398 trials, while P9075 completed 90 trials. In Pair 5, P9076 completed 522 trials, while P9083 completed 90 trials. In Pair 6, P9074 completed 1,746 trials, while P9085 completed 90 trials. A higher number of trials were required for P9058 and P9060 to complete Phases 2 and 3 than to complete Phase 1. A lower number of trials were needed for the accuracy participants to complete Phases 2 and 3 than for speed participants to complete Phases 2 and 3. For P9056, the number of missed responses decreased from Phase 1 to Phase 2, while the other two speed participants had an increased number of missed responses in Phase 2 compared with Phase 1.

The combined number of acquisition trials for Phases 1 through 3 was clearly higher for all the speed participants than for their matched counterparts. The combined number of acquisition trials in Pair 1 was 552 for P9056 and 462 for P9057; in Pair 2,2052 for P9058 and 504 for P9059; in Pair 3, 984 for P9060 and 582 for P9061; in Pair 4,10,110 for P9072 and 2,802 for P9075; in Pair 5,1,722 for P9076 and 1,290 for P9083; and in Pair 6, 2,754 for P9074 and 1,098 for P9085. For Pairs 4, 5, and 6, the difference in the number of acquisition trials between the speed and the accuracy participants was 7,308,432, and 1,656 trials, respectively. The high number of acquisition trials for speed participants P9058 and P9060 is largely attributable to the number of trials needed to complete Phase 3, where the probability of programmed consequences was reduced. For the speed participants, most of the acquisition trials occurred in Phases 1 and 3, with the exception of P9076 for which most trials occurred in Phase 1.

Derived Relations

Table 3 shows the results for the first three pairs for all tests for baseline and emergent relations as well as the adduction test. All participants were exposed to the retention test after exactly 14 days, except P9056, who returned after 28 days, and P9060, who returned after 16 days. During the initial test, P9056 (speed) did not respond in accord with stimulus equivalence, while P9057 (accuracy) responded in accord with stimulus equivalence. Both participants in Pair 1 had 100 % accuracy in adduction test. In the retention test, neither participant in Pair 1 responded according to any of the emergent relations, but they continued to have 100 % accuracy in the adduction test. In Pair 2, both P9058 (speed) and P9059 (accuracy) responded in accord with stimulus equivalence, and both had 100 % accuracy in the adduction test. During the retention test, P9058 continued to respond in accord with stimulus equivalence, while P9059 did not. For both participants, the baseline relations remained intact, and both had 100 % accuracy in the adduction test. In Pair 3, P9060 (speed) did not respond according to any of the emergent relations at the criterion level, but the baseline relations remained intact, and the participant had 100 % accuracy in the adduction test. P9061 (accuracy) responded in accord with stimulus equivalence and had 93 % accuracy in the adduction test. In the retention test, neither P9060 nor P9061 responded in accord with stimulus equivalence, while the baseline relations remained intact. Both participants in Pair 3 continued to show intact baseline relations and to have 100 % accuracy in the adduction test.

Table 4 presents the results for the last three pairs. All participants were exposed to the retention test after exactly 14 days, except P9072, who returned after 15 days, and P9085, who returned after 16 days. For the second retention test, all participants returned 6 weeks and 2 days after the initial testing, except for P9076 who returned after 6 weeks and 6 days. In Pair 4, P9072 (speed) responded according to transitivity, and the baseline relations remained intact; furthermore, the participant had 100 % accuracy in the adduction test. In the initial testing, P9075 (accuracy) failed to reach the criterion level for symmetry, transitivity, and equivalence and had 20 % accuracy in the adduction test; however, the baseline relations remained intact. In the first retention test, the baseline relations remained intact for P9072, and the participant had 100 % accuracy in the adduction test. P9075 did not reach any of the experimenter-defined criterion levels, and the accuracy in the adduction test remained the same. In the second retention test, P9072 responded according to experimenter-defined equivalence classes and had 100 % accuracy in the adduction test. P9075 did not reach any of the experimenter-defined criterion levels for the derived relations, whereas the accuracy in the adduction test increased to 67 %. In Pair 5, P9076 (speed) failed to reach the criterion level for symmetry, transitivity, and equivalence and had 0 % accuracy in the adduction test. P9083 (accuracy) showed equivalence class formation and had 100 % accuracy in the adduction test. In the retention test, P9076 responded according to symmetry, and the baseline relations remained intact. P9083 did not reach any of the experimenter-defined criterion levels. Both participants had 47 % accuracy in the adduction test. In the second retention test, P9076 responded according to symmetry but failed to reach the criterion level for symmetry, transitivity, and equivalence and had 60 % accuracy in the adduction test. P9083 did not respond according to symmetry, transitivity, or equivalence and had 47 % accuracy in the adduction test. In Pair 6, P9074 (speed) did not respond according to symmetry, transitivity, or equivalence, and the trained relations did not reach criterion level. P9085 (accuracy) responded in accord with stimulus equivalence. Both participants in Pair 6 had 100 % accuracy in the adduction test. In the first retention test, P9074 responded according to transitivity and had 100 % accuracy in the adduction test. P9085 did not respond according to experimenter-defined criterion levels for the derived relations and had 47 % accuracy in the adduction test. In the second retention test, P9074 responded in accord with stimulus equivalence and had 100 % accuracy in the adduction test. P9085 did not respond according to symmetry, transitivity, or equivalence and had 47 % accuracy in the adduction test.

Inversed Reaction Time in Training

Figure 4 presents the average InvRT to comparison stimuli in Phase 1 for Pairs 1-3 and Pairs 4-6, where the accuracy participants were yoked to the speed participants. InvRT values gradually increased in Phase 1 for both the speed and the accuracy participants. Both the speed and the accuracy participants in the first, second, fifth, and sixth pairs had a lower average InvRT in Phase 1 than in the last few blocks of training. However, the InvRT values overlapped considerably for Pairs 1, 2, and 6 throughout Phase 1. For Pairs 3, 4, and 5, the speed participants clearly responded faster than the accuracy participants throughout Phase 1. The terminal InvRT values (last six trials) were always higher for the speed participants than for their matched participants, as well as for all the accuracy participants.

Inversed Reaction Time in Test Trials

Figure 5 shows the InvRT throughout the test trials for Pairs 1-3 and Pairs 4-6, respectively. As shown in Fig. 5, P9056 (speed) had more stable responses than P9057 (accuracy) in the initial test and was faster than P9057 in 24 of the 36 trials. In the retention test, the values overlapped considerably, but P9056 had more stable responses in the first 21 trials and was faster in 20 of the 36 trials than P9057. P9058 (speed) and P9059 (accuracy) showed similar variability in the initial testing, with considerable overlap, but P9059 was faster than P9058 in 17 of the 36 test trials. However, in the retention test, P9058 was faster than P9059 in 27 of the 36 test trials. P9061 (accuracy) responded faster than P9060 in 30 of the 36 test trials during the initial test and in 28 of the 36 trials during the retention test. P9060 (speed) continued to show slightly more variability during the initial testing, while the variability was similar between the participants during Retention 1. P9072 (speed) responded faster than P9075 (accuracy) in the initial testing (39 vs. 54 trials), in Retention 1 (48 vs. 54 trials), and in Retention 2 (42 vs. 54 trials). P9076 (speed) responded faster than P9083 (accuracy) in the initial testing (49 of 54 trials), in Retention 1 (33 of 54 trials), and in Retention 2 (42 vs. 54 trials). P9074 (speed) responded slower than P9085 (accuracy) in the initial testing (16 vs. 54), in Retention 1 (30 vs. 54 trials), and in Retention 2 (37 vs. 54 trials).

[FIGURE 4 OMITTED]

Inversed Reaction Time in the Last Part of Training and Different Parts of Testing

The difference in InvRT values between the last five training trials and the first five test trials was 0.46 and 0.93 for P9056 and P9057, respectively; 0.55 and 0.17 for P9058 and P9059, respectively; and 0.39 and 0.32 for P9060 and P9061, respectively (see Fig. 6, upper panel). The first five retention test trials were slower, on average, than the initial test trials for the participants. The exception was P9058, who was slightly faster in first five retention test trials, while P9057 and P9061 had a marginal slowdown. The upper panel in Fig. 6 shows the average InvRT values for Pairs 4-6. The InvRT for last five training trials was 1.37 for P9072 versus 0.98 for P9075, 1.45 for P9076 versus 0.55 for P9083, and 1.48 for 9074 versus 0.95 for 9085. All the participants were slower in responding during subsequent testing, except for P9072, P9075, and P9083, who responded faster in the second retention test relative to the first retention test.

[FIGURE 4 OMITTED]

Inversed Reaction Time for Derived Relations

During the initial testing, the average InvRT in the separate trial types was always higher for the speed participants than for their matched counterparts (see Fig. 7a), although the differences between P9058 and P9059 were marginal in the baseline and symmetry trials. In addition, the speed participants were always faster than the accuracy participants. Two of three speed participants were roughly twice as fast as their matched counterparts in the symmetry and equivalence trials (Pairs 1 and 2). A comparison of the trial types within participants shows that responses in the baseline relations were fastest for all the accuracy participants and for two of the three speed participants (P9056 and P9058). P9060 responded fastest in the transitivity trials, but for all other participants, responses in the transitivity trials were the third fastest among responses by trial type. No other consistent differences between trial types were found during the initial testing.

In the retention test, the speed participants continued to respond faster than their matched counterparts in all trial types, except P9057 was faster than P9056 in the transitivity trials and nearly equal to P9056 in the baseline trials. A comparison of the matched pairs showed that only the average InvRT in the equivalence trials continued to be higher for the speed participants relative to their matched counterparts. For the baseline relations, all the participants responded more slowly in the retention test than in the initial testing. P9056 responded slower for all trial types during the retention test relative to the initial testing. Moreover, responses in equivalence trials were slower for all accuracy participants during the retention test relative to the initial testing; by contrast, two of the three speed participants had an increased InvRT in the retention test relative to the initial testing. No other consistent differences in InvRT values were found between the test trials and retention test.

[FIGURE 5 OMITTED]

Figures 7b shows the average InvRT for the separate trial types during the initial test and during the subsequent retention phases for Pairs 4-6. In the initial test, the speed participants in Pairs 4 and 5 responded faster relative to their yoked accuracy participants in the baseline trials, while the accuracy participant in Pair 6 was faster than the matched speed participant. In the symmetry trials, the speed participant in Pair 5 responded faster relative to the accuracy participant. In the transitivity trials, the speed participants in Pairs 4 and 5 responded faster than their matched accuracy participants. The speed participants in Pairs 4 and 5 were also faster relative to the accuracy participants in the equivalence trials. In Retention tests 1 and 2, all the speed participants responded faster than the accuracy participants in the baseline trials. This was also the case for the symmetry trials; however, in transitivity and equivalence trials, the pattern was mixed.

Discussion

The present study aimed to determine whether training in speed versus accuracy conditions has differential effects on participants' likelihood of responding according to stimulus equivalence. In the speed condition, one of the six speed participants responded according to stimulus equivalence, compared with five of the six accuracy participants. The low number of correct trials in the testing phase indicates that a speed condition reduces the immediate emergence of equivalence.

A second purpose of the study was to test whether MTS training in either speed or accuracy generates different probabilities of adduction. Ten of the 12 participants, five from each condition, had 93 % to 100 % accuracy in the math problems involving all trial types of symmetry, transitivity, and equivalence. This result demonstrates that the likelihood of adduction is equal after training in either accuracy or speed.

A third purpose of the study was to investigate retention. Three of the six speed participants responded according to stimulus equivalence in the 2-week retention test, compared with none of the accuracy participants. In addition, the only participant to show perfect stability of all the emergent relations over time was speed participant P9058, who responded according to symmetry, transitivity, and equivalence in the initial test and in a 2-week retention test. By contrast, the accuracy participants who initially responded according to all the emergent relations did not show stability of the emergent relations over time. However, symmetric relations remained stable for two accuracy participants (P9061 and P9059) and two speed participants (P9058 and P9060). These results have to be considered to be somewhat mixed; however, they are in accord with Rehfeldt and Hayes (2000): more participants showed retention of symmetry relations than of equivalence or transitivity relations, and the retention of equivalence relations co-occurred with the retention of symmetry relations. It is also noteworthy that the speed participant who did not respond according to the baseline and emergent relations in either testing phase also had the lowest number of acquisition trials among all the speed participants; thus, stable equivalence classes may require overtraining of the baseline relations. Accordingly, the effect of overtraining baseline trials should be systematically tested in a future experiment.

[FIGURE 6 OMITTED]

In the present study, the emergence of equivalence and symmetry occurred for P9060 and P9074 from the initial testing to the retention test. This result indicates that delayed emergence may occur even after a considerable period of time without exposure to experimental stimuli. It is unclear why this delayed emergence occurred. Holth and Amtzen (1998a) found that a tendency for delayed emergence of consistent responding with repeated testing among a group of 50 participants. Earlier research has also shown that accuracy regarding baseline and emergent relations can improve with repeated testing during retention for some participants (e.g., Rehfeldt and Root 2004).

Retention of adduction continued during the retention test for all participants, wherein all participants had 100 % accuracy, except P9085. The two participants (P9075 and P9076) who did not respond correctly in the adduction test after the first stimulus equivalence test did not do so after Retention tests 1 and 2. Furthermore, two of the six participants who responded correctly in the adduction test in Retention 1 continued to do so in Retention 2. These results serve as a replication of the results obtained during the initial testing; speed and accuracy do not differentially influence the probability of adduction. However, because multiple stimulus relations were presented at once during the adduction test, it is difficult to determine whether adduction is an additional demonstration of participants responding according to the emergent relations. All the participants nevertheless reached their solutions with the same strategy: they wrote down the number related to each arbitrary stimulus before summing them to produce their answer. As this type of response produced stimuli that generated the solution, such a response would be an example of problem solving, a behavior that may have facilitated the adduction of the emergent relations (e.g., Holth and Arntzen 1998b; Holth and Arntzen 2000). Similar results were reported by Rehfeldt and Hayes (2000), who found that equivalence did not emerge in initial MTS testing but did emerge in later generalization tests. The current results also suggest that the establishment of classes through MTS training is not limited to tests bound by specific experimental situations; on the contrary, the MTS training may lead to novel performance outside the experimental situation. The adduction test may nevertheless pose a threat to experimental control, as some practice may have been involved in solving the problems, which might explain why some participants achieved equal or higher accuracy in later MTS retention tests. However, the fact that none of the accuracy participants showed stability nor delayed emergence of the emergent relations after the retention period renders this explanation unlikely.

A fourth purpose of the study was to compare any difference between speed and accuracy by initially yoking accuracy to speed during the baseline trials. The proportionally higher number of errors for the speed participants relative to the accuracy participants during Phase 1 indicates that a speed condition increases the variation in response accuracy in baseline trials to a greater extent than an accuracy condition. A trade-off between speed and accuracy (Imam 2001) in tests for emergent relations has been reported (e.g., Holth and Amtzen 2000; Imam 2001, 2003). Based on the yoking in Phase 1 of the present experiment, this trade-off also occurs during the acquisition of the baseline relations and persists even in the absence of fast-response requirements in testing. These results suggest that the source of the trade-off lies in the reinforcement contingency (see Imam 2006). When the yoking condition was removed, five of the six speed participants required a substantially higher number of trials to reach the criterion level of performance in Phase 2. Similarly, in Imam's (2001, Experiment 1) study, participants who were exposed to a speed contingency were reported to require a higher number of blocks and additional maintenance blocks to reach the performance criteria. In the study by Tomanari et al. (2006), participants needed up to 20,000 trials to reach the performance criteria, and in the study by Amtzen and Haugland (2012), up to 2,934 trials were required. By contrast, in this study, the highest number of acquisition trials was 1,344. The difference in the number of required acquisition trials between the previous two studies and the present study may be attributable to the fact that only arbitrary stimuli were used in the two previous studies, whereas in the present study there was one set of familiar stimuli, the Arabic numerals. Furthermore, it is clear that using four instead of three classes, as used in the Tomanari et al. study, resulted in a higher number of acquisition trials. In addition, the high number of trials required by five of the speed participants (P9058, P9060, P9072, P9074, and P9076) in this study can largely be attributable to the large number of trials in the phases with diminishing consequences. It is possible that with diminishing consequences, a behavioral event, such as naming, is required to facilitate a correct comparison selection (e.g., Home and Lowe 1996). One interpretation is that the speed participants had difficulty achieving the criteria for accuracy as the consequences diminished because the rapid responding limited the time gap available for such a behavioral event to occur.

[FIGURE 7 OMITTED]

A fifth question of the study was whether the InvRT would differ between trial types and between training and test trials. Earlier studies have shown that RTs vary as a function of relational types. For example, Spencer and Chase (1996) found that response speed was an inverse function of relational type, with baseline trials being fastest, followed by symmetry trials and equivalence trials, during both speed and accuracy conditions. Imam (2001) showed a similar pattern with both a speed and an accuracy contingency. No such patterns in InvRT related to either speed or accuracy were found in the present study. In fact, the transitivity trials were nearly as fast as the baseline trials for most participants. In addition, the InvRT values were nearly equal between the equivalence trials and the symmetry trials. These results are unexpected, as the transitivity and equivalence tests have a one-node distance with the LS structure (e.g., Fields et al. 1995). This pattern was also found during the retention period, with minimal reductions in InvRT values for some participants. The differences between this study and earlier studies may be attributable to the higher number of test trials used in previous studies (e.g., Imam 2001, 2003; Spencer and Chase 1996). In addition, this study used a nameable stimulus, which has been shown to eliminate differences in RTs between relational types (Bentall et al. 1993). However, both Tomanari et al. (2006) and Amtzen and Haugland (2012) used entirely arbitrary stimuli and a higher number of test trials than this study, but neither study reported differences in RTs between relational types. It therefore seems unlikely that the nameable stimulus that was used in this study reduced the differences in RTs between trial types. However, some studies (e.g., Imam 2001; Spencer and Chase 1996) that have reported a different substitutability of class members based on speed differences between relational types have analyzed RTs or speed of highly accurate responding. Regarding the speed of the five participants who showed high accuracy in tests for emergent relations in this study, neither the study by Amtzen and Haugland nor that of Tomanari et al. reveals any systematic pattern, which suggests that class members were not differentially related as a function of relational type. The stepwise reduction in LH, or overtraining, may balance the effects of InvRT overtime.

The current results showed that the difference between the last few training trials and the initial test trials was more pronounced for the speed participants than for the accuracy participants. This difference may be attributable to the differential reinforcement of fast responding during the baseline trials. One behavioral interpretation of this difference is that the initially slower responding during the initial test trials indicates precurrent problem solving (e.g., Holth and Amtzen 2000). Thus, the fast response requirements during the baseline trials may have hindered the emergence of stimulus equivalence during the initial test for the speed participants. However, this results contrasts with the results reported by Amtzen and Haugland (2012) and Tomanari et al. (2006), in which the difference was minimal. One additional finding was that the speed condition induced faster responding in the acquisition trials of the speed participants during Phases 1 and 2 of this experiment, and in the majority of the test trials, the speed participants continued to respond more quickly, which continued after a 2-week retention interval. As these MTS performances were clearly influenced by a contingency, this dimension of responding according to emergent relations are likely attributable to the reinforcement contingency (see Sidman 2000). Imam (2003) obtained similar results with a participant who continued to respond quickly on a transfer test to members of an equivalence class, which was not previously trained with a speed contingency.

Variability in InvRT values was higher for the accuracy participants in Phase 1. For example, speed participants P9056 and P9058 had similar variability in InvRT values, but these participants began with a high LH. P9060, who began with a substantially lower LH than the other speed participants, had the highest variability in InvRT values during this phase; the difference between P9060 and his matched participant is most pronounced. His matched counterpart showed a similar variability, although the InvRT values are much lower. For the three pairs in the second group, the pattern of variability is more mixed. It is possible that differential variation in speed or RT indicates stability in the formation of stimulus classes.

Some similarities and differences between the present study and similar studies have to be considered. Unlike many of the previously mentioned studies, which have studied speed conditions, this study introduced tests without an LH. In one part of their experiment, Holth and Amtzen (2000) included a testing condition that was similar to the one used in the current study. In Experiment 3, they exposed participants to MTO training with a 2-s LH, where one testing condition was presented without the LH. The results showed that three of five participants had response patterns that were consistent with equivalence. When the participants were then tested with an LH, the response patterns were consistent with equivalence for only one of the five participants. As such, equivalence formation seems to be more severely restricted if time limits for response are present during testing. For example, Imam (2001, 2003), Tomanari et al. (2006), and Amtzen and Haugland (2012) presented an LH during testing that limited equivalence formation for most of the participants. In the Tomanari et al. study, testing was conducted under the terminal LH values that resulted from training, which were between 0.4 and 0.5 s for samples and between 1.2 and 1.3 s for comparisons. Amtzen and Haugland used a 2.5-s LH on comparisons during testing, and Holth and Amtzen used a 2-s LH during testing. Holth and Amtzen (1998b, 2000) suggested that novel stimulus arrangements during testing require precurrent problem solving, and speed may be a barrier to such problem solving. This interpretation is given further support by the finding that even previously trained fast responding may limit such an intermediate behavior.

The present study was conducted in two and three sessions, in contrast to the previously mentioned studies on speed, which were conducted in multiple sessions. Another difference between the present study and previous studies is that the third member of each class was a nameable stimulus in the present study, which may have facilitated the completion of MTS training in just one session (e.g., Amtzen and Lian 2010; Amtzen et al. 2014; Fields et al. 2012). However, the ability of participants to finish the experimental phases in two or more sessions helped avoid the potential influence of external variables on the results and facilitated a quicker comparison of speed and accuracy in an MTS paradigm. For the six participants in the first round, only six test trials were included for equivalence and transitivity, along with 12 symmetry and baseline trials, whereas for the participants in second round, these numbers were 9 and 18, respectively. However, the accuracy criteria for responding according to the emergent relations in this study were different from those in earlier studies. Using a low number of the test trials facilitated an evaluation of whether immediate emergence of equivalence occurred and reduced the possibility of practice with the emergent relations carrying over to the adduction tests. In addition, this study used a concurrent training order, while Amtzen and Haugland (2012) and Tomanari et al. (2006) used an arrangement with trials presented on a serialized basis, in which individual conditional relations were trained separately to the accuracy criteria and then the trials were mixed. The study by Amtzen and Haugland titrated LH down to 1,200 ms and used an 80% accuracy criterion both (a) for the completion of individual titration blocks and (b) across the last few blocks of training. Tomanari et al. used a 95% accuracy criterion across two consecutive blocks. The relatively stricter accuracy criterion of 94% in this study and of 95% in Tomanari et al.'s study may have contributed to the higher number of participants ultimately responding according to equivalence. Another difference between this study and previous studies is that the ITI in this study was 1 s, whereas Tomanari et al. used a 0.4-s ITI and Amtzen and Haugland used a 0.5-s ITI; thus, the overall pace may have been faster in the previous studies, whereas faster responding occurred during the initial trials of the titration in this study. Amtzen and Haugland's study used an OTM structure to train the conditional discriminations, while the present study used an MTO pretraining phrase, followed by an LS structure for the experimental stimuli. In addition, with the exception of Amtzen and Haugland's study, previous studies on equivalence and speed contingencies have not implemented diminishing consequences before the beginning of an extinction phase. For example, Tomanari et al. used a training phase without differential consequences, and this training phase was later mixed with probes for emergent relations. Similar to Amtzen and Haugland's study, this study presented a mixed test of all emergent relations after the baseline training. This study also used a considerably higher start value for the LH than previous studies. This difference may partly explain why more speed participants ultimately responded according to equivalence in this study relative to previous studies. Whether the difference between speed and accuracy is due to the total higher number of trials completed by speed participants during training or the actual speed condition can only be answered by further experimentation. Yoking accuracy to speed throughout all the experimental phases may be one possibility for such a study. It would be interesting to determine how such an arrangement influences adduction. It is possible that the relatively stable InvRT during the titration in this study indicates the stability of class formation. It would be interesting to determine whether the introduction of a titrated LH or a fixed LH affects the stability of equivalence classes. Finally, further research may determine whether speed and accuracy differentially influence the immediate or delayed emergence of stimulus equivalence.

In sum, the present experiment expanded knowledge regarding the effect of speed contingencies on the formation of equivalence classes. The results showed that more participants in the accuracy condition responded in accord with the experimenter-defined classes than participants in the speed condition. However, in the retention tests, only speed participants responded in accord with the experimenter-defined classes. In addition, in the test for adduction after the first stimulus equivalence test, there was no difference between the conditions with respect to the outcome; however, more participants in speed condition had a higher outcome in the adduction tests after Retentions 1 and 2.

DOI 10.1007/s40732-014-0097-9

Published online: 8 October 2014

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Author note There is no conflict of interest to declare for either of the authors. Correspondence concerning this manuscript should be addressed to Erik Amtzen, Oslo and Akershus University College, Department of Behavioral Science, St. Olavs Plass, PO Box 4, 0130 Oslo, Norway. E-Mail: erik.amtzen@equivalence.net. Petur Ingi Petursson is currently affiliated with Ullevalsveien 34, Oslo Kommune Velferdsetaten Postboks 7104 St. Olavs plass 0130 Oslo.

(1) One participant was unable to complete the pretraining and did not move into the experimental phases. One speed participant was unable to complete Phase 1, and another speed participant did not complete Phase

(2.) Two of the remaining speed participants were dropped from the analysis, as they could not be matched.

(2) One participant was unable to complete the pretraining. Three speed participants were unable to complete Phase 1, and one speed participant did not complete Phase 2. Four of the remaining speed participants were dropped from the analysis, as they could not be matched. One participant was tested over two consecutive days.

E. Arntzen ([mail]) * P. I. Petursson * P. Sadeghi * C. Eilifsen

Department of Behavioral Science, Oslo and Akershus University College, St. Olavs Plass, PO Box 4, 0130 Oslo, Norway

e-mail: erik.amtzen@equivalence.net

Present Address:

P. I. Petursson

Ullevalsveien 34, Oslo Kommune Velferdsetaten Postboks 7104 St. Olavs plass, 0130 Oslo, Norway
Table 1 Trial Number Completed in Each Training Phase

Speed participants

P9056
Trials               Phase 1 (a)   Phase 2    Phase 3
Total                390           108        54
Correct              317           84         52
Incorrect            37            4          0
Missed               36            20         2

P9058
Trials               Phase l (b)   Phase 2    Phase 3
Total                432           72         1,548
Correct              283           58         1206
Incorrect            53            0          11
Missed               96            14         331

P9060
Trials               Phase l (c)   Phase 2    Phase 3
Total                492           72         420
Correct              319           31         198
Incorrect            97            25         162
Missed               76            16         60

Accuracy participants

P9057
Trials               Phase 1       Phase 2    Phase 3
Total                390           18         54
Correct              356           18         54
Incorrect            34            0          0

P9059
Trials               Phase 1       Phase 2    Phase 3
Total                432           18         54
Correct              414           18         53
Incorrect            18            0          1

P9061
Trials               Phase 1       Phase 2    Phase 3
Total                492           18         72
Correct              461           18         68
Incorrect            31            0          4

Note. Shown is the total number of trials that the participants
(P9056-P9061) needed to reach the accuracy criteria in each phase,
subdivided into correct, incorrect, and missed responses to the
comparison stimuli. Missed responses could occur only for the speed
participants. Phase 1 introduced a titrated LH for the speed
participants and a yoked control for the accuracy participants. In
Phase 2, the speed participants were exposed to a fixed LH of 1,000 ms
on the comparison stimuli, and the accuracy participants were no
longer yoked. In Phase 3, the probabilities of programmed consequences
were gradually reduced to 75 %, 25 %, and 0 %. (a) Starting LH value:
4,955 ms. (b) Starting LH value: 3,927 ms. (c) Starting LH value:
1,771 ms.

Table 2 Trial Number Completed in Each Training Phase

Speed Participants

9072
Trials                  Phase 1 (a)   Phase 2    Phase 3
Total                   2,712         756        6,642
Correct                 1,880         492        3,855
Incorrect               203           62         949
Missed                  629           202        1,838

9076
Trials                  Phase l (b)   Phase 2    Phase 3
Total                   1,200         72         450
Correct                 796           59         384
Incorrect               231           4          29
Missed                  173           9          37

9074
Trials                  Phase l (c)   Phase 2    Phase 3
Total                   1,008         198        1,548
Correct                 625           159        1,156
Incorrect               215           17         116
Missed                  168           22         276

Accuracy Participants

9075
Trials                  Phase 1       Phase 2    Phase 3
Total                   2,712         18         72
Correct                 2,469         18         72
Incorrect               243

9083
Trials                  Phase 1       Phase 2    Phase 3
Total                   1,200         18         72
Correct                 1,182         17         72
Incorrect               18            1

9085
Trials                  Phase 1       Phase 2    Phase 3
Total                   1,008         18         72
Correct                 967           18         72
Incorrect               41

Note. Shown is the total number of trials that the participants
(P9072-P9085) needed to reach the accuracy criteria in each phase,
subdivided into correct, incorrect, and missed responses to the
comparison stimuli. Missed responses could only occur for the speed
participants. Phase 1 introduced a titrated LH for the speed
participants and a yoked control for the accuracy participants. In
Phase 2, the speed participants were exposed to a fixed LH of 1,000 ms
on the comparison stimuli, and the accuracy participants were no
longer yoked. In Phase 3, the probabilities of programmed consequences
were gradually reduced to 75%, 25%, and 0%. (a) Starting LH value:
2,068 ms. (b) Starting LH value: 2,474 ms. (c) Starting LH value:
2,012 ms.

Table 3 Number of Correct and Incorrect Responses in the Testing Phase

                      Phase 4 (a)

                      Correct choices in the test

Participant    BSL    SYM    TR     EQ     ECF     AD

9056 (Speed)   11#    6      1      1      N       15#
9057 (Acc)     12#    12#    6#     6#     Y#      15#
9058 (Speed)   12#    12#    6#     6#     Y#      15#
9059 (Acc)     12#    11#    6#     6#     Y#      15#
9060 (Speed)   12#    11#    5#     3      N       153
9061 (Acc)     12#    12#    5#     6#     Y#      14#

               Phase 5 (b)


               Correct choices in the test

Participant    BSL     SYM    TR     EQ     ECF    AD

9056 (Speed)   6       9      1      3      N      15#
9057 (Acc)     9       10     2      2      N      15#
9058 (Speed)   12#     12#    6#     6#     Y#     15#
9059 (Acc)     12#     11#    5#     4#     N      15#
9060 (Speed)   12#     12#    5#     6#     Y#     15#
9061 (Acc)     12#     12#    5#     4#     N      15#

Note. Responding that reached accuracy criteria for the directly
trained or emergent relations is shown in bold. Acc = Accuracy; BSL =
baseline; SYM = symmetry; TR = transitivity; EQ = equivalence; ECF =
equivalence class formation; Y = yes: N = no; AD = adduction (this
test comprised 15 different addition problems, each having a distinct
combination of an emergent relation). (a) Initial testing. (b)
Retention test, which was administered after 14 days, except for
P9056 and P9060, who returned after 28 and 16 days, respectively.

Note: Responding that reached accuracy criteria for the directly
trained or emergent relations is shown in bold indicated with #.

Table 4 Number of Correct and Incorrect Responses in the Testing Phase

               BSL    Phase 4 (a)

                      Correct choices in test

                      SYM    TR     EQ     ECF    AD

9072(Speed)    18#    16     9#     8#     N      15#
9075 (Acc)     18#    17#    3      4      N      3
9076 (Speed)   16     10     3      1      N      0
9083 (Acc)     18#    18#    9#     8#     Y#     15#
9074 (Speed)   17     13     4      7      N      15#
9085 (Acc)     18#    18#    9#     9#     Y#     15#

                      Phase 5 (b)

                      Correct choices in test

               BSL    SYM    TR     EQ     ECF    AD

9072(Speed)    18#    18#    8#     8#     Y#     15#
9075 (Acc)     13     8#     5      7      N      3
9076 (Speed)   18#    18#    1      2      N      7
9083 (Acc)     13     12     3      3      N      7
9074 (Speed)   13     13     9#     7      N      15#
9085 (Acc)     13     12     2      3      N      7

                      Phase 6 (c)

                      Correct choices in test

               BSL    SYM    TR     EQ     ECF    AD

9072(Speed)    18#    18#    9#     9#     Y#     15#
9075 (Acc)     15     12     8#     8#     N      10
9076 (Speed)   17     18#    3      5      N      9
9083 (Acc)     12     12     3      3      N      7
9074 (Speed)   18#    18#    8#     8#     Y#     15#
9085 (Acc)     12     11     3      3      N      7

Note. Responding in accord with the accuracy criteria for the directly
trained or emergent relations is shown in bold. Acc = Accuracy; BSL =
baseline; SYM = symmetry; TR = transitivity; EQ = equivalence; ECF =
equivalence class formation; Y = yes: N = no; AD = adduction (this
test comprised 15 different addition problems, each having a distinct
combination of an emergent relation). (a) Initial testing. (b)
Retention test, which was administered after 14 days, except forP9056
andP9060, who returned after 28 and 16 days, respectively. (c)
Retention test; all participants returned 6 weeks and 2 days after the
initial testing, except for P9076 who returned after 6 weeks and 6
days.

Note: Responding in accord with the accuracy criteria for the directly
trained or emergent relations is shown in bold indicated with #.
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Title Annotation:ORIGINAL ARTICLE
Author:Arntzen, Erik; Petursson, Petur Ingi; Sadeghi, Pedram; Eilifsen, Christoffer
Publication:The Psychological Record
Article Type:Report
Date:Mar 1, 2015
Words:12603
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