Fo y yea s ago Mu ay Sidman (1971) published an in l uen ial
a icle abou «eme gen » o de i ed beha iou . His wo k
demons a ed ha when e bal humans lea ned di e en a bi a y
condi ional disc imina ions sha ing common elemen s (e.g., A-B
and B-C), hey could la e ela e hose s imuli in un ained bu
p edic able ways.
Ba nes, Hega y and Smee s (1997) p o ed ha his ype o
aining could p oduce u he ou comes. Pa icipan s la e exposed
o a non- ein o ced ma ching o sample p ocedu e wi h compound
s imuli consis en ly ma ched equi alen samples wi h equi alen
compa isons and non-equi alen samples wi h non-equi alen
compa isons. Fo example, a e aining A1-B1-C1, A2-B2-C2
and A3-B3-C3, in he p esence sample A1B1 pa icipan s choose
A2C2 as compa ison ins ead o A3B2 (equi alence-equi alence),
while in he p esence o A2C3 hey choose A3B2 (non-equi alence-
non-equi alence). This beha iou was gene ally labelled as
Equi alence-Equi alence (Eq-Eq). As he au ho s no ed, Eq-Eq
beha iou ( ela ing ela ions) closely esembles human analogical
easoning, despi e some a guable di e ences (e.g., Ca pen ie ,
Smee s, & Ba nes-Holmes, 2003a). The expe imen al pa adigm o
Eq-Eq esponding was la e e i ned and ex ended as a beha iou
analy ical model o human analogical easoning (Ca pen ie e
al., 2003a; Ca pen ie , Smee s, Ba nes-Holmes, & S ewa , 2004;
Lipkens & Hayes, 2009; S ewa , Ba nes-Holmes, & Roche, 2004;
S ewa , Ba nes-Holmes, Roche, & Smee s, 2001, 2002). See
S ewa & Ba nes-Holmes (2004) o a e iew. In hese wo ks, Eq-
Eq was ound wi hin a b oad a ie y o expe imen al condi ions:
di e en s imuli, di e en numbe o classes and class membe s,
and di e en aining and es ing p ocedu es. See also Ga cía,
Psico hema 2011. Vol. 23, nº 3, pp. 407-414 ISSN 0214 - 9915 CODEN PSOTEG
www.psico hema.com Copy igh © 2011 Psico hema
Fecha ecepción: 27-8-10 • Fecha acep ación: 16-2-11
Co espondencia: Vicen e Jesús Pé ez Fe nández
Facul ad de Psicología
Uni e sidad Nacional de Educación a Dis ancia
28040 Mad id (Spain)
e-mail: [email p o ec ed]
Facili a ion o he equi alence - equi alence esponding
Vicen e Jesús Pé ez Fe nández1, And és Ga cía Ga cía2 and Jesús Gómez Bujedo3
1 Uni e sidad Nacional de Educación a Dis ancia, 2 Uni e sidad de Se illa and 3 Uni e sidad de Huel a
Equi alence-Equi alence esponding, based on equi alence class o ma ion, is a key concep o he
unc ional-analy ic model o analogical easoning held by RFT heo is s. Rela ional s imulus con ol
is supposed o play an impo an ole in his a bi a y ela ional esponse. P e ious esea ch showed
ha me e aining o he p e equisi es o equi alence class o ma ion is no always enough o he
de i a ion o equi alence-equi alence esponding, e en in adul s. In he i s expe imen , wi h 12
adul pa icipan s, we designed a ma ching- o-sample aining and es ing p ocedu e ha , al hough
i p o ided all necessa y condi ions, did no lead o Equi alence-Equi alence esponding in mos
pa icipan s, so ha he e i cacy o a acili a ion p ocedu e could be assessed. In Expe imen 2, wi h 32
alid pa icipan s, a ma ching- o-sample p ocedu e based on non-a bi a y ela ions was in oduced o
assess i s e i cacy in enhancing s imulus con ol by he ela ional p ope ies o sample and compa isons.
Resul s showed a mode a e e ec : 40.6% o he pa icipan s passed he es a e being exposed o a
non-a bi a y ela ional ma ching ask (bu none wi hou i ). This esea ch unde lines he impo ance o
non-a bi a y ela ional esponses in he de i a ion o mo e complex epe oi es.
Facili ación de la espues a de equi alencia - equi alencia. La espues a de equi alencia - equi alencia,
basada en la o mación de clases de equi alencia, es uno de los concep os cla es del modelo de
azonamien o analógico analí ico uncional p opues o po los au o es de la TMR. El con ol de
es ímulos elacional juega un papel impo an e en es a espues a elacional a bi a ia. In es igaciones
an e io es demos a on que el me o en enamien o de los p e equisi os pa a la o mación de clases de
equi alencia no es siemp e su i cien e pa a la de i ación de la espues a de equi alencia - equi alencia,
incluso en adul os. En el p ime expe imen o, con 12 pa icipan es, diseñamos un p ocedimien o de
en enamien o y p ueba que, a pesa de p opo ciona odos los p e equisi os, no condujo di ec amen e
a la espues a de equi alencia - equi alencia, pe o que pe mi ía e alua la e i cacia de un p ocedimien o
de acili ación. En el segundo expe imen o, con 32 pa icipan es álidos, se puso a p ueba la e i cacia
de un p ocedimien o basado en elaciones no-a bi a ias en e los es ímulos pa a inc emen a el con ol
de es ímulo po las p opiedades elacionales de mues a y compa aciones. Los esul ados mos a on
un éxi o mode ado: el 40,6% de los pa icipan es supe a on el es as se expues os a una igualación a
la mues a elacional no a bi a ia (pe o ninguno la supe ó sin el p ocedimien o de acili ación). Es os
hallazgos sub ayan la impo ancia de las espues as elacionales no a bi a ias en la de i ación de
epe o ios más complejos.
VICENTE JESÚS PÉREZ FERNÁNDEZ, ANDRÉS GARCÍA GARCÍA AND JESÚS GÓMEZ BUJEDO
408
Bohó quez, Pé ez, Gu ié ez, & Gómez (2008); Pé ez & Ga cía
(2008).
Howe e , no all subjec s passing aining and equi alence
es showed a consis en Eq-Eq esponse, and esea che s we e
also in e es ed in explaining ailu es o ob ain Eq-Eq esponding.
An ob ious i eld o ha kind o esea ch was de elopmen al
psychology, whe e, in conco dance wi h s udies on classical
analogies, Eq-Eq esponding was ound in adul s and nine yea
old child en, bu no in i e yea old p eschoole s (Ca pen ie ,
Smee s, & Ba nes-Holmes, 2002b). Subsequen s udies ied o
iden i y he causes o he ailu e in young child en and de eloped
« acili a ion» p ocedu es o encou age ela ional esponding,
ollowing he assump ion ha pa icipan s lacked he necessa y
ela ional abili ies (Ca pen ie , Smee s, & Ba nes-Holmes, 2002a;
Ca pen ie e al., 2003a; Pé ez, Ga cía, Gómez, Bohó quez, &
Gu ié ez, 2004).
A complemen a y esea ch a ea was he assessmen o he
condi ions a ec ing Eq-Eq de i a ion in pa icipan s supposed o
domina e i s p e equisi es, since no all adul s passed he Eq-Eq es s,
o equi ed addi ional aining and es ing o do so. Fo example,
in he Ba nes e al., (1997) pionee ing s udy, subjec s equi ed
be ween wo and six non- ein o ced es blocks and addi ional
aining o demons a e Eq-Eq esponding; epea ed aining and
es ing was a cons an since in mos expe imen s. Bu again, a
small numbe o adul s did no show Eq-Eq esponding despi e
o epea ed aining and es ing. (See o example S ewa e al.,
2001). Since he lack o p e equisi es was no a plausible accoun
in his case, some expe imen s analyzed he e ec o al e na i e
s imulus con ol opog aphies (Ray, 1969) compe ing wi h Eq-Eq
o explain heses ailu es (Bohó quez, Ga cía, Gu ié ez, Gómez,
& Pé ez, 2002; Ca pen ie , Smee s, & Ba nes-Holmes, 2003b;
Ga cía, Bohó quez, Gómez, Gu ié ez, & Pé ez, 2001; Ga cía e
al., 2008; Ga cía, Gómez, Pé ez, Bohó quez, & Gu ié ez, 2003;
Ga cía, Gu ié ez, Bohó quez, Gómez, & Pé ez, 2002; S ewa e
al., 2001). Fo example, Ga cía e al., (2008) demons a ed ha
when Eq-Eq en e s in compe ence wi h a non-a bi a y c i e ion
wo main manipula ions in l uenced he p obabili y o an a bi a y
o non-a bi a y ela ional esponse: inc easing baseline aining
and e alua ing simple equi alence inc eased he numbe o
subjec s passing he Eq-Eq es s.
Since Eq-Eq beha iou can be conside ed as ma ching a bi a y
ela ions, he beha iou o he pa icipan s mus be unde he
con ol o he a bi a y ela ion (equi alence o non-equi alence)
sha ed by he elemen s o he compound sample and compa isons.
I compe ing s imulus con ol is a possible explana ion o Eq-Eq
ailu es, pe haps addi ional aining o es ing phases could imp o e
he pe o mance in Eq-Eq ela ions in adul s by diminishing
s imulus con ol om ex aneous sou ces and / o acili a ing he
disc imina ion o he ele an sou ces o s imulus con ol.
P e ious expe imen s add essed his issue wi h i e yea old
child en, using amilia ins ead o abs ac s imuli, o os e ing
he ela ional esponse o he compound s imuli (Ca pen ie e
al., 2002a, 2002b, 2003a). Bu hese p ocedu es ailed o p oduce
he expec ed esul s in mos p eschoole s, and also we e applied
sequen ially and no in isola ion, which p e en ed a de ailed
analysis o i s espec i e e ec s. Fu he mo e, he e ec o
epea ed baseline aining and es ing was no add essed. Eq-Eq
es s we e assumed o be ex inc ion ials, since no eedback was
p o ided. Howe e , ecen s udies demons a ed ha subjec s
can lea n du ing ypical Eq-Eq es s (Pé ez & Ga cía, 2009). A
consis en pa e n o esponding, ial a e ial, appea s o wo k
as a ein o ce , an e ec o me ly assessed in simple equi alence
expe imen s (Leonha d & Hayes, 1991). The e o e, he e ec o
epea ed aining and es ing should be aken in o accoun in o de
o assess he e ec i eness o any manipula ion. O he wise, he
acili a ing e ec could be con ounded wi h imp o emen due o
implici lea ning h ough epea ed es ing.
Gi en ha ela ional s imulus con ol is necessa y o Eq-Eq,
and ha compe ing s imulus con ol could explain ailu es in Eq-
Eq es s in adul subjec s, a ask in ended o explici ly o implici ly
ein o ce ela ional s imulus con ol could acili a e he Eq-Eq
esponse. Ou aim was o de elop an app op ia e Eq-Eq aining
and es ing p ocedu e (Expe imen 1) and use i o assess he e ec
o a p ocedu e in ended o s eng hen ela ional s imulus con ol
(Expe imen 2).
EXPERIMENT 1
The objec i e o he i s expe imen was wo old. Rega ding
aining, ou aim was o de elop a aining and es ing p ocedu e
ha , al hough p o ided all necessa y condi ions, did no lead o
di ec Eq-Eq esponding in mos pa icipan s so ha a acili a ion
p ocedu e could be assessed. Rega ding Eq-Eq es ing, subjec s
we e e alua ed only wice: in he i s occasion, o co obo a e hei
ailu e o de i e Eq-Eq esponding, and in he second, o disca d
any imp o emen due o epea ed es ing.
Me hod
Pa icipan s
Twel e adul s pa icipa ed in his expe imen , six women and six
men, anging be ween 18 and 52 yea s o age (mean= 28; s anda d
de ia ion= 10.43). They we e all olun ee uni e si y s uden s and
had no p e ious knowledge o he pu pose o he expe imen .
Ou goal was o coun wi h a leas eigh alid pa icipan s
in each expe imen . A alid pa icipan was de i ned as one who
success ully passed he condi ional disc imina ion aining and he
equi alence es bu ailed he i s Eq-Eq e alua ion.
Appa a us and s imuli
The whole p ocedu e was designed wi h Mac omedia Flash
MX, p og ammed in Ac ion Sc ip and hen compiled. The esul ing
applica ion displayed s imuli and consequences, and also eco ded
esponses.
The s imuli used we e images speci i cally designed o hese
expe imen s. Figu e 1 shows hese s imuli, each wi h a label
indica ing he equi alence class hey we e assigned o.
The gene al p ocedu e consis ed in an a bi a y ma ching o
sample wi h an obse a ion esponse o he sample. When he
esponse was consis en wi h he a anged ela ion among s imuli,
he message «GOOD» («BIEN» in Spanish) was p esen ed o 1.4
sec. in a g een backg ound, and nex ial begun. I he esponse
was no consis en , he message p esen ed in a ed backg ound was
«NO, you made… e o s. The maximum pe mi ed is…» and he
same ial s a ed again.
The sequence o e en s in each ial was a anged as ollows
(see Figu e 2): 1) The sample appea ed alone in he bo om cen e
o he sc een. 2) When he pa icipan emi ed he obse a ion
FACILITATION OF THE EQUIVALENCE - EQUIVALENCE RESPONDING 409
esponse, compa isons appea ed on he igh and le op o he
sc een. 3) A e he subjec selec ed one s imulus wi h he mouse
(wi hou ime es ic ions) he p og ammed consequences we e
displayed (in aining ials) o he/she was ad anced o he nex
ial (in e alua ion blocks).
P ocedu e
The p ocedu e was designed o be comple ed in less han one
hou , and ne e ook mo e han 50 - 60 minu es. Pa icipan s we e
indi idually placed in isola ed desks in on o a compu e . Then
he ollowing ins uc ions (in Spanish) we e p esen ed:
FIRST, WE WOULD LIKE TO THANK YOU FOR
PARTICIPATING IN THIS STUDY
WE WOULD ALSO LIKE TO REMIND YOU OF THE
FOLLOWING:
THIS IS NOT AN INTELLIGENCE TEST.-
THIS IS NOT A PERSONALITY TEST.-
THIS IS NOT A TEST OF SPEED, YOU MAY TAKE AS -
LONG AS YOU NEED.
USE ONLY THE LEFT MOUSE BUTTON, DO NOT -
USE THE KEYBOARD OR THE RIGHT MOUSE BUTTON
A SERIES OF STIMULI WILL NOW APPEAR ON THE
SCREEN. A SAMPLE WILL ALWAYS APPEAR FIRST,
WHICH YOU MUST CLICK ON. SOME POSSIBLE
RESPONSE OPTIONS WILL THEN APPEAR AT THE TOP
OF THE SCREEN. YOU MUST CLICK ON WHICHEVER
YOU THINK IS CORRECT.
The s uc u e o he expe imen had ou s eps: 1) Condi ional
disc imina ion aining and equi alence es . 2) Eq-Eq e alua ion:
Subjec s passing his es i nished he expe imen . O he wise, hey
ad anced o he nex phase. 3) Pa icipan s we e exposed o a
dis ac ion ask in he compu e du ing ou minu es (see below).
4) Eq-Eq was e alua ed again, and he expe imen i nished.
Condi ional disc imina ion aining and equi alence e alua ion
A «one- o-many» p ocedu e was used, wi h «A» s imuli wo king
as node. T aining consis ed o a block whe e A-B ma ching was
ein o ced (A1-B1, A2-B2 and A3-B3); nex , A-C ela ions (A1-
C1, A2-C2 and A3-C3) we e ein o ced in a sepa a e block, and
hen a mixed block combining A-B and A-C ela ions. The i s
wo blocks consis ed o 21 ials each, and only h ee e o s we e
pe mi ed (86% co ec ). Subjec s commi ing ou o mo e e o s
epea ed he block, wi h a maximum o h ee epe i ions. The hi d
block mixed 18 A-B aining ials and 18 A-C ials. The lea ning
c i e ion was i e e o s o less (86% co ec ).
A e passing he h ee aining blocks, a pa ial equi alence
es was adminis e ed. De i ed C-B condi ional disc imina ions
we e assessed (C1-B1, C2-B2 and C3-B3). This block consis ed
o 15 non- ein o ced ials whe e C1, C2 o C3 we e he samples
and B1, B2 and B3 as compa isons. The c i e ion i xed o pass his
es was 2 e o s o less (86% co ec ); in case i was accomplished,
he subjec ad anced o he Eq-Eq e alua ion phase. B-C ela ions
we e no es ed o educe i s e ec on Eq-Eq es s.
Fi s Eq-Eq e alua ion
This e alua ion block was composed o 36 ials wi h bo h
compound sample and compa isons. Two equi alen s imuli
o med he sample in hal o he ials, and wo non-equi alen
s imuli in he o he hal . One o he compa isons was o med by
equi alen s imuli and he o he by non-equi alen ones. Figu e 3
shows an example o each ype o ial.
I he pa icipan esponded in acco dance wi h he Eq-Eq
c i e ion ( i e e o s o less, 86% co ec ) he expe imen ended.
In case he subjec did no each he c i e ion, he/she was exposed
o he dis ac ion ask.
Dis ac ion ask and second Eq-Eq e alua ion
The objec i e o his phase was o delay he second Eq-Eq
e alua ion ou minu es, an in e al simila o ha o he acili a ion
p ocedu e used in Expe imen 2. In he beginning o he phase he
ollowing ins uc ions we e p o ided: «Now, se e al s imuli will
appea in di e en pa s o he sc een, you ha e o click on hem
Figu e 1. Expe imen 1. S imuli used
Figu e 2. Expe imen 1. S anda d sequence o ials and consequences.
Le : sample s imuli. Middle le : sample (bo om) and compa isons ( op).
Middle igh : posi i e ein o ce (GOOD). Righ : posi i e punishe «NO,
you commi ed x e o s. The maximum allowed is y»
Figu e 3. Expe imen 1. Examples o equi alence-equi alence (EQ) and
no-equi alence (NoEQ) es ials
VICENTE JESÚS PÉREZ FERNÁNDEZ, ANDRÉS GARCÍA GARCÍA AND JESÚS GÓMEZ BUJEDO
410
be o e hey disappea . I you manage o do i , he wo d «GOOD»
will appea on a g een sc een. Click on he a ow o begin».
The ask consis ed in selec ing di e se geome ical i gu es
ha appea ed on he sc een. The i gu es could appea o 0.5 o
1 seconds and hen disappea ed. When he subjec clicked on a
i gu e, a g een sc een wi h he wo d «GOOD» («BIEN» in Spanish)
appea ed o one second, o he wise nex ial begun wi hou
eedback. Rega dless o he esul s, he Eq-Eq e alua ion phase
desc ibed abo e was p esen ed again and he expe imen ended.
Resul s
All pa icipan s passed he condi ional disc imina ion aining
and also he C-B e alua ion block. Fou ou o he wel e
pa icipan s succeeded in he i s Eq-Eq e alua ion (wi h 0, 1, 2,
and 3 e o s) and he expe imen ended o hem.
None o he emaining pa icipan s (eigh ) passed he second
equi alence - equi alence e alua ion. In ac , co ec esponses
dec eased 1.87 poin s on a e age (s anda d de ia ion= 3.31). The
Wilcoxon ma ched pai s es con i med he absence o di e ences
be ween p e and pos measu es (z= 1,55; p= 0,12). Figu e 4 shows
he numbe o ials o pass he aining blocks o alid pa icipan s
and he numbe o co ec esponses du ing i s and second Eq-Eq
e alua ion.
Discussion
Thi y h ee pe cen o he pa icipan s (4/12) passed he i s
Eq-Eq e alua ion wi h he cu en aining and es ing p ocedu e.
In he compa able expe imen s e ised in he in oduc ion, he
numbe o pa icipan s passing Eq-Eq in he i s es conside ably
a ied due o di e en aining and es ing condi ions. Fo example,
in he expe imen s ca ied ou by Ba nes e al., (1997, Expe imen s
1 and 2) none o he pa icipan s passed he es in he i s occasion.
Only one ou o eigh pa icipan s passed he i s es in he wo k
o S ewa e al., (2001, Expe imen 1); bu i e ou o se en adul
pa icipan s succeeded in he sys ema ic s udy by Ca pen ie e al.,
(2003c, Expe imen 1, condi ions 1 and 2). Thus, he pe cen age o
pa icipan s passing he i s Eq-Eq es in hese expe imen s was
0%, 12% and 71% espec i ely.
The e a e oo many di e ences be ween hese expe imen s and
wi h he p esen wo k o ad ance a de i ni i e explana ion o he
di e en esul s (e.g., ype o s imuli, numbe o classes and s imuli,
paymen o pa icipa ion, e c.). Bu wo a iables appea o be
pa icula ly impo an o explain he low numbe o subjec s (33%)
passing he i s es . Fi s , ou p ocedu e included a sligh ly less
es ic i e lea ning c i e ion, and hus a lowe numbe o aining
ials and sho e sessions han compa able expe imen s. And
second, he pa ial equi alence es used (ins ead o a comple e es )
could also con ibu e o explain lowe a es o success, since bo h
ac o s p o ed o acili a e Eq-Eq esponding (Ga cía e al., 2008).
Rega ding he second Eq-Eq es , none o ou alid pa icipan s
passed i , and he numbe o e o s was simila in bo h a emp s.
In con as , he accumula ed pe cen age o subjec s passing he
second Eq-Eq e alua ion in he abo emen ioned expe imen s
was 4/12 (33%), 4/8 (50%) and 7/8 (87%), which clea ly shows
an imp o emen compa ed wi h he i s es . This nega i e esul
allows us o disca d any implici lea ning due o epea ed es ing,
as epo ed by Pé ez and Ga cía (2009).
In summa y, ou p ocedu e eliably ained he condi ional
ela ions necessa y o de i e equi alence ela ions, bu ew
subjec s de i ed Eq-Eq in he i s es , and epea ed es ing did
no imp o e he esul s o he second e alua ion. The e o e, we
can use his p ocedu e o sys ema ically s udy he e ec o a
acili a ion p ocedu e in oduced be ween he i s and he second
Eq-Eq e alua ion.
300
250
200
150
100
50
0
T ials
Pa icipan s
99
141
78
114
144
228
99
171
Pa icipan s
24 21
17 15
24 23 19 21 19 18
25
16
20 18 21 22
36
30
24
18
12
6
0
Pe cen co ec
EQEQ1
EQEQ2
Figu e 4. Expe imen 1. Top: Numbe o ials needed o pass aining pe alid pa icipan ; bo om: numbe o hi s in bo h equi alence-equi alence es s
(EQEQ 1 and EQEQ 2)
FACILITATION OF THE EQUIVALENCE - EQUIVALENCE RESPONDING 411
EXPERIMENT 2
I adul pa icipan s a e supposed o domina e he p e equisi es
o a bi a y ela ional esponding (Ca pen ie e al., 2002b),
ex aneous s imulus con ol exe ed by o he sou ces han he
expe imen e -de i ned ela ion could be well esponsible o he
ailu e in Eq-Eq es s (Ca pen ie e al., 2003a, 2003c; Ga cía
e al., 2008; Pé ez e al., 2004). Ve bal desc ip ions o he ask
o e ed by he pa icipan s who ailed he es s p o ided addi ional
suppo o his hypo hesis (Pé ez, 2007). Few pa icipan s alleged
o choose andomly; he majo i y ied o ound a ule applicable
ial a e ial, being he mos popula 1) selec ing equi alen
compa ison compounds, ega dless he sample; and 2) simple
equi alence ela ions be ween one elemen o sample and one
elemen o he compa ison. Thus, a acili a ion p ocedu e could
con ibu e o enhance s imulus con ol by he expe imen e -
de i ned ele an ea u es o he ask (i.e., ela ing compound
samples and compa isons, and enhancing he salience o he
ela ion be ween he elemen s o he sample and compa ison
compounds).
S udies on compe ence be ween a bi a y and non-a bi a y
esponse c i e ia in Eq-Eq demons a ed ha a non-a bi a y
ela ion was chosen by mos pa icipan s and iden i i ed by all
(Ga cía e al., 2002), and he e o e a non-a bi a y ela ion could
be used o enhance he s imulus con ol o he a bi a y ela ion
i p ope ly in oduced. The e ec i eness o such a p ocedu e in
p omo ing Eq-Eq was p elimina ily assessed in a o me s udy
(Pé ez e al., 2004). In hese expe imen s wi h 10-11 yea old
child en as pa icipan s, he acili a ion p ocedu e called «Same-
Di e en » (o S/D, see desc ip ion below) was in oduced as a
aining phase and combined wi h o he acili a ion p ocedu es,
wi h pa ial success. In he p esen expe imen , a be ween g oups
wi h epea ed measu es design was implemen ed. The S/D
acili a ion p ocedu e was sys ema ically es ed, bo h as aining
and as an e alua ion phase in sepa a e condi ions. Besides, he
in l uence o an addi ional aining block (A-A / A-B / A-C) be o e
o a e exposi ion o S/D e alua ion was assessed in wo addi ional
condi ions. Eq-Eq was e alua ed be o e and a e he exposi ion o
he acili a ion p ocedu e.
Me hod
Pa icipan s
Fo y wo olun ee uni e si y s uden s pa icipa ed in his
expe imen , 8 males and 34 emales, anging om 20 o 54 yea s o
age (mean= 30.17; s anda d de ia ion= 7.9). They had no p e ious
knowledge o he pu pose o he expe imen .
Pa icipan s we e andomly assigned o ou condi ions: Ten
pa icipan s we e assigned o condi ion 1 (3 men, 7 women); nine
o condi ion 2 (1 man, 8 women); 12 o condi ion 3 (3 men, 9
women) and 11 o condi ion 4 (1 man, 10 women).
Appa a us and s imuli
The same appa a us as in Expe imen 1 we e used. The s imuli
used o equi alence class o ma ion we e also he same. Nine
geome ic i gu es o di e en shapes and colou s we e used in he
S/D acili a ion p ocedu e. See Figu e 5.
P ocedu e
The gene al p ocedu e used was he same as in Expe imen 1,
excep o he (S/D) acili a ion p ocedu e included be ween he
i s and second Eq-Eq e alua ion. The expe imen was di ided
in ou condi ions, depending on he speci i c a angemen o he
acili a ion p ocedu e:
Condi ion 1. S/D e alua ion.
Condi ion 2. S/D e alua ion plus A-A / A-B / A-C aining.
Condi ion 3. A-A / A-B / A-C aining plus S/D e alua ion.
Condi ion 4. S/D aining
Facili a ion p ocedu e: «Same / Di e en »
This p ocedu e consis ed in a ma ching o sample ask wi h
compound s imuli. The sample could be o med by wo iden ical
o di e en geome ic i gu es (e.g., D1D1 o D2D3), while one
o he compa isons was always o med by iden ical i gu es (e.g.,
F1F1) and he o he by di e en i gu es (e.g. F2F3). Sample and
compa isons ne e sha ed indi idual elemen s. The S/D block was
composed o 24 ials; a esponse was conside ed co ec when he
sample and he chosen compa ison main ained he same ela ion
(i.e., same-same o di e en -di e en ). In condi ion 4, he eedback
p o ided was he same as in he condi ional disc imina ion aining
o Expe imen 1. The maximum numbe o e o s allowed ei he
in aining o e alua ion was 2 (91%). A pa icipan wi h h ee
o mo e e o s was d opped om he expe imen . Eq-Eq was
e alua ed again.
Resul s
All pa icipan s passed he condi ional disc imina ion aining
and he C-B equi alence es . Eigh ou o 42 pa icipan s (19%)
Figu e 5. Expe imen 2. Geome ic colou ed shapes used in he acili a ion
p ocedu e «Same / Di e en ». R= Red; G= G een; Y= Yellow; P= Pink;
P.b.= Pale blue; D. b.= Da k blue; B = B own; Bl= Black

VICENTE JESÚS PÉREZ FERNÁNDEZ, ANDRÉS GARCÍA GARCÍA AND JESÚS GÓMEZ BUJEDO
412
passed he i s Eq-Eq es (mean= 3.12 e o s; s anda d de ia ion=
1.80). O he emaining 34 pa icipan s, 2 (6.2%) ailed he
S/D aining block (all o hem in condi ion 4). Acco ding o
ou de i ni ion, we coun ed wi h 32 alid pa icipan s, eigh pe
condi ion. Nine een o hem (59.4%) ailed o mee he c i e ion
in he second Eq-Eq es , while 13 (40.6%) passed he second Eq-
Eq es . The Wilcoxon ma ched pai s es showed a signi i can
inc ease in he numbe o hi s in he second Eq-Eq es measu es
(z= 3,02; p= 0,03).
Th ee numbe pa icipan s passed S/D and hen Eq-Eq in
condi ions 1, 2 and 3 (3/8, o 37%). The mean inc ease o co ec
esponses was also simila : 2.62 in condi ions 1 and 2 and 3.87
in condi ion 3. In condi ion 4 (S/D aining only) 50% o he
pa icipan s (4/8) eached he c i e ion in he second Eq-Eq
es . The inc emen in he numbe o co ec esponses was 9.12
on a e age. Ne e heless, K uskal-Wallis analysis showed no
di e ence be ween g oups in he numbe o co ec esponses in
he second Eq-Eq es (p= 0.93). Figu e 6 shows a esume o he
esul s o he pa icipan s in bo h Eq-Eq e alua ions by condi ion.
Condi ion 1
Pe cen co ec
100
80
60
40
20
0
42
28
50 47
67
47
61 69 78
92
78
100
56
100
67 72
EQEQ1
EQEQ2
EQEQ1
EQEQ2
EQEQ1
EQEQ2
EQEQ1
EQEQ2
Condi ion 2
Pe cen co ec
100
80
60
40
20
0
42
56
69
86
61 53 64 69 72
58
69
97
78
100
58 53
Condi ion 3
Pe cen co ec
100
80
60
40
20
0
58
Condi ion 4
Pe cen co ec
100
80
60
40
20
50
53
69 75 75 78
56 58
94
69 61 53
89
64
39
56
86
56 50 53
69
47
94
72
97
56
75
31
56 61
94
Figu e 6. Expe imen 2. Resul s in bo h equi alence-equi alence e alua ions (EQEQ1 and EQEQ2) o e e y alid pa icipan pe condi ion
FACILITATION OF THE EQUIVALENCE - EQUIVALENCE RESPONDING 413
Discussion
Nine een pe cen o he pa icipan s passed he i s Eq-Eq es ,
a pe cen age simila o ha ob ained in Expe imen 1. Fo hose
who ailed, he exposi ion o he non-a bi a y ela ional esponse
phase had a mode a e posi i e e ec . The in oduc ion o he S/D
acili a ion p ocedu e as an e alua ion block (S/D e alua ion,
condi ions 1, 2 and 3) inc eased he numbe o pa icipan s showing
Eq-Eq esponding in he second es . The inclusion o addi ional
baseline aining be o e o a e he acili a ion p ocedu e had no
e ec on hese esul s. Explici aining o non-a bi a y ela ional
esponses (S/D aining, condi ion 4) also inc eased he p obabili y
o Eq-Eq esponding.
The ac ha he exposi ion o a non- ein o ced block (no
explici ly ein o ced, a leas ) in condi ion 1 modi i ed he
subsequen beha iou o he pa icipan s in he second Eq-Eq es
sugges s ha some kind o lea ning occu ed. The non-a bi a y
ela ional esponding was easily iden i i ed by all alid pa icipan s
in his expe imen , as well as in o me s udies (Ga cía e al., 2002),
whe e he salience o non-a bi a y ela ions p o ed o be highe .
A possible explana ion o he imp o ed esul s in he second es
is ha he non-a bi a y ela ional esponse was applicable ial
a e ial (Pé ez & Ga cía, 2009), and hus ein o ced ela ional
s imulus con ol. The highe inc ease o co ec esponses
obse ed in condi ion 4, hough s a is ically non signi i can , would
be consis en wi h he ac ha explici ein o cemen is usually
mo e in ense, and hus shapes beha iou mo e e i cien ly. An
independen assessmen o he ela i e magni ude o bo h ypes o
ein o cemen should be ca ied ou o con i m his poin .
Gene al discussion
In Expe imen 1 none o eigh adul pa icipan s passed he
Eq-Eq es in wo consecu i e occasions, despi e hey all lea ned
all i s aining p e equisi es and showed de i ed equi alence. The
in oduc ion o a acili a ion p ocedu e augmen ed he numbe
o pa icipan s passing he second Eq-Eq es in Expe imen 2,
al hough he imp o emen was mode a e (13/32, o 40.6%). The
esul s o Expe imen 2 could be ha dly a ibu ed o implici
lea ning, since no imp o emen was no iced in Expe imen 1.
The esul s o Expe imen 2 suppo he s imulus con ol
opog aphy accoun o equi alence - equi alence ailu e in adul s
supposed o domina e i s p e equisi es, since pe o mance could
be imp o ed by enhancing he salience o he ela ional p ope ies
o sample and compa isons and he impo ance o choosing he
compound compa ison in ela ion o he compound sample. These
esul s a e compa ible wi h he i ndings o p e ious s udies (Pé ez
e al., 2004) and also wi h hose epo ed by Ca pen ie e al.,
(Ca pen ie e al., 2003a, 2003b), whe e he au ho s assumed ha
a ailu e in Eq-Eq could be explained because pa icipan s did no
espond o he a bi a y ela ions among he elemen s o compound
samples and compa isons.
Fu u e esea ch e o s should be de o ed o backup his iew by
clea ing up he ole o he di e en s imulus con ol opog aphies
in a bi a y ela ional esponse, i s ela i e impo ance and
beha iou al p e equisi es. Al hough ela ional s imulus con ol
o samples and compa isons appea s o be necessa y o he Eq-
Eq esponse, he e a e many po en ial beha iou al mechanisms
ha can be employed o enhance ela ional s imulus con ol, and
pa icipan s may pass o ail he es s using di e en s a egies.
Mo eo e , he modes acili a i e e ec ob ained in Expe imen 2
should be imp o ed wi h e i nemen s in he acili a ion p ocedu es
ha can h ow mo e ligh abou he beha iou al p ocess in ol ed
in a bi a y ela ional esponding.
As beha iou analy ic au ho s a gued (Hayes, Ba nes-Holmes, &
Roche, 2001; Skinne , 1957; S ewa e al., 2001, 2002), analogies,
me apho s and analogical easoning in e e yday language,
educa ional se ings, psychological ea men s, o e en in scien i i c
language, elay on he abs ac ion o bo h o mal (non-a bi a y) an
a bi a y ela ions. Conside he example p o ided by (Ba nes e
al., 1997): «apple is o o ange as dog is o sheep» (ins ead o , say,
book). The analogy holds because apple and o ange a e equi alen
in he equi alence class « ui », as he same as dog and sheep a e
equi alen in he class «animals» (while dog and book a e no ). Bu
as S ewa e al. (2002) no ed, o anges and apples (as well as dogs
and sheep) also sha e non-a bi a y ela ions: Apples and o anges
a e small and ound; sheep and dog a e hai y, ou legged, e c.
(p. 377). The abs ac ion o o mal p ope ies and ela ing i s non-
a bi a y ela ions (as in he S/D p ocedu e) a e pa o e e yday
analogies, and p obably play an impo an ole in i s de elopmen
(Hayes e al., 2001; Skinne , 1957; S ewa e al., 2001).
P io s udies demons a ed ha non-a bi a y ela ions a e
easily iden i i ed and can block o o e shadow a bi a y ela ional
esponses (Ga cía e al., 2001; Ga cía e al., 2003; Ga cía e al.,
2002). Howe e , his s udy showed ha in some occasions he
simple non-a bi a y ela ional esponse can acili a e he mo e
complex a bi a y ela ional esponse. A be e knowledge abou
he condi ions in which non a bi a y ela ional esponses p e en
o acili a e a bi a y ela ional esponses may help us o unde s and
how his ype o easoning de elops, how o each i , o how o use
i e ec i ely. Pe haps acili a ion p ocedu es as hose desc ibed
could be sys ema ically used in he u u e as a sys ema ic aining
p og amme o indi iduals lacking he ela ional p e equisi es o
analogical easoning (S ewa & Ba nes-Holmes, 2009).
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