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Enhancement Effect
Article in Journal of Experimental Psychology Learning Memory and Cognition · March 2011
DOI: 10.1037/a0021803 · Source: PubMed
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Journal of Experimental Psychology:
Learning, Memory, and Cognition
2011, Vol. 37, No. 2, 368 –377
© 2011 American Psychological Association
0278-7393/11/$12.00 DOI: 10.1037/a0021803
Bogus Concerns About the False Prototype Enhancement Effect
Donald Homa, Michael C. Hout, Laura Milliken, and Ann Marie Milliken
Arizona State University
Two experiments addressed the mechanism responsible for the false prototype effect, the phenomenon
in which a prototype gradient can be obtained in the absence of learning. Previous demonstrations of this
effect have occurred solely in a single-category paradigm in which transfer patterns are assigned or not
to the learning category. We tested the hypothesis that any extraneous variable potentially responsible for
this effect, such as compactness varying with pattern distortion (Zaki & Nosofsky, 2004), may be
functional in the single-category paradigm but not when multiple categories are available at the time of
transfer. In the present study, subjects received a bogus or a real category learning phase, followed by
a transfer test that required assignment into 1 or 3 prototype categories. The results showed that a minimal
prototype gradient was obtained in the bogus conditions, with performance approaching chance levels
when classification into 3 categories was required. In contrast, a substantial prototype gradient effect was
found following learning. We conclude that the prototype gradient typically obtained following multiplecategory learning is primarily driven by real learning and that the false prototype effect is itself an artifact
of the single-category paradigm.
Keywords: prototype, gradient, categorization, paradigm, learning
prototype, whereas the actual data revealed a steeper gradient, as
predicted by prototype theory. Homa, Proulx, and Blair (2008)
explored the shape of gradients around training patterns and the
prototype under variations of category size and number of exception patterns in each category, finding support for exemplar predictions only when category size was small or when larger category sizes contained numerous exception patterns; when category
size was large and the number of exception patterns was small,
sharp gradients around the prototype and flattened gradients to
training instances were obtained. Zaki and Nosofsky (2004) acknowledged the steepness of the prototype gradient was a problem
for exemplar models of classification and “could potentially indicate that some form of prototype abstraction is taking place” (p.
391).
However, Zaki and Nosofsky (2004) questioned whether the
transfer gradient might arise, at least in part, from an artifact. What
they termed the false prototype enhancement effect in dot pattern
categorization refers to the demonstration that a prototype gradient
effect can be obtained in the absence of any prior learning, arguing
that an extraneous variable— compactness of the dot pattern
forms— covaried with distortion.1 They suggested that the algorithm used to create distortions from a dot pattern prototype tended
A continuing dispute is how categorical knowledge is represented. Although the literature contains a myriad of models based
on rules, features, neural nets, and boundaries, the main focus
remains on variations of prototype and exemplar models. Prototype theorists (e.g., Homa, Dunbar, & Nohre, 1991; Smith &
Minda, 1998) generally assert that the categories are constructed
around abstracted central tendencies called prototypes, forged
from the integration of experiences common to each category.
Exemplar theorists (e.g., Nosofsky, 1988; Zaki & Nosofsky, 2001)
contend that our categories are represented solely by the storage of
the particular instances that are encountered, with abstractions
playing no role. An issue critical to these two theories concerns the
shape of generalization gradients: Exemplar theorists predict that
generalization gradients should be steep around stored instances
with a minimal gradient tied to the category prototype; prototype
theorists predict a sharp gradient around the prototype and a
minimal gradient centered on the training instances. These predictions arise because similarity to either the stored instances or the
category prototype should critically determine subsequent transfer
performance of novel instances.
Support for prototype models was claimed by Smith (2002),
who analyzed the shape of gradients from numerous studies that
used a particular paradigm first introduced by Knowlton and
Squire (1993). In general, Smith demonstrated that variations of
exemplar models must predict a flattened gradient around the
1
This criticism applies to the distorted form stimuli used in the present
study, because the distortion algorithm is similar, although line length
rather than compactness is probably more germane. We believe this concern raised by Zaki and Nosofsky (2004) can be avoided by routine
rejection of any prototype that has peculiar characteristics such as points
that cluster near the centroid. Once the coordinate values exceed ⫾10 units
in the 50 ⫻ 50 grid, each distortion has a near 50% chance of moving
closer, rather than farther, from the prototypical value. Regardless, our
contention, repeated in the present study, is that this criticism vanishes in
the multiple-category paradigm, because an extraneous variable such as
compactness (or line length) cannot function as a categorically discriminative cue.
This article was published Online First January 24, 2011.
Donald Homa, Michael C. Hout, Laura Milliken, and Ann Marie Milliken, Department of Psychology, Arizona State University.
We would like to thank Stephen Goldinger and Allen Bodesila for
reading an earlier version of this article.
Correspondence concerning this article should be addressed to Donald
Homa, Department of Psychology, Arizona State University, Tempe, AZ
85287. E-mail: donhoma@asu.edu
368
PROTOTYPE GRADIENTS
to produce distortions that were less compact than the prototype,
with this tendency increasing with level of distortion. In effect, the
obtained accuracy of classification—prototype ⬎ low-level distortions ⬎ medium-level distortions ⬎ high-level distortions—was
not due to a prior prototype abstraction process that guided subsequent transfer but rather to an artifact of pattern compactness,
with compactness decreasing with pattern distortion.
In their experiments, subjects were exposed to a bogus learning
phase and then instructed to assign transfer patterns to the
“learned” category. In actuality, no patterns were shown, and the
transfer test contained four different prototypes and either 40
random high-level distortions (Experiment 1A) or 10 random lowand 30 random high-level distortions (Experiment 1B). Results
showed a slight but significant decline in rate of endorsement as
distortion level increased. A similar result was obtained by Palmeri
and Flanery (1999), who used a bogus learning phase followed by
a transfer phase involving the category prototype, distortions of the
category prototype, and random patterns.
The implication that a potential artifact may be responsible,
wholly or partially, for the prototype gradient is theoretically
important because this interpretation minimizes evidence taken as
support for prototype models in general as well as casts doubt on
a number of secondary, theoretical issues—for example, whether
different memory mechanisms are responsible for classification
and recognition (Knowlton & Squire, 1993), a conclusion emphasized by Zaki and Nosofsky (2004): “The presence of such false
prototype enhancement effects has profound implications, therefore, for the interpretation of results from this classic and highly
influential paradigm” (p. 391). However, there are a number of
inconsistencies and concerns that must be addressed first before
this conclusion is accepted: (a) Results with the bogus learning
category paradigm have not been consistently replicated, and (b)
the generation of a prototype gradient effect may be an artifact
itself, a result of a transfer task involving the assignment of
patterns into a single learned category. These two criticisms are
addressed in order.
The original paradigm that later became the primary focus of the
false prototype effect was introduced by Knowlton and Squire
(1993), who investigated category learning by normal and amnesic
subjects. In their task, amnesic and normal subjects were first
exposed to 40 dot pattern stimuli, all high-level distortions from a
single prototype, followed by a transfer test composed of new
category members at various distortion levels from the prototype
and random patterns (foils from different prototypes). On the
transfer test, subjects were asked to indicate which patterns belonged to the same category as the training instances. A recognition test involving five dot pattern stimuli, tested after a 5-min
delay, was also used. Knowlton and Squire obtained transfer
performance that was similar for the amnesic and normal subjects— both groups revealed a similar prototype gradient on the
transfer test. However, these same subjects differed dramatically
on a recognition test, with the amnesic subjects showing poor
discrimination between old and new patterns. The unimpaired
classification performance, combined with the reduced recognition
by the amnesic subjects, led Knowlton and Squire to conclude that
abstraction mechanisms engaged an implicit memory mechanism
(which was intact in the amnesic patients) whereas recognition was
based on a declarative system (which was damaged in the amnesic
patients).
369
Disputes over this interpretation have come from studies that
have not always produced consistent results. Knowlton and Squire
(1993) also included a bogus learning control condition and found
that transfer performance was significantly reduced by bogus training. In contrast, Palmeri and Flanery (1999) found a significant
prototype gradient effect for the bogus learning condition (subjects
were given the ruse that patterns had been subliminally presented
during a word-identification task) but not following actual learning.2 Zaki and Nosofsky (2004) found a significant gradient in
their bogus full condition but not their bogus subset condition,
even though their model predicted a significant gradient in each
condition.3 In addition, three of the four experiments run by Zaki
and Nosofsky reported results in terms of a judgment on a rating
scale rather than accuracy, rendering comparison to previous studies unclear. Finally, the number of subjects needed to produce a
significant gradient effect following bogus learning was abnormally large, compared with most studies in categorization—179 in
one condition, 123 in a second, 198 in a third, and 185 in a fourth.
Their results suggest that the differences obtained across distortion
levels are real but small in magnitude.
A more critical concern is that the gradient effect following
bogus learning was obtained in what may be considered a singlecategory transfer paradigm. That is, in Knowlton and Squire
(1993), as well as in the studies claiming a bogus prototype effect,
subjects were required to assign transfer patterns if they believed
the patterns belonged or not to the learned (or bogus) category.
Although the single-category transfer paradigm was widely used in
the older category literature that explored rule-learning with welldefined stimuli (e.g., Bourne, 1966; e.g., Category A might contain
only objects that are red and square, and objects that failed this rule
were to be called “not A”), the more recent literature on category
learning rarely has used a single-category transfer paradigm.
Rather, the typical paradigm presents subjects with numerous
patterns that belong to two or more categories in the learning
phase, followed by a transfer test in which the subject is required
to assign patterns to the learned categories. This distinction—
whether transfer occurs to one or multiple categories—is, we believe,
critical to the issue of whether the gradient is an artifact of stimulus
construction or a real outcome produced by prior learning.
2
Palmeri and Flanery (1999) reported a statistically significant effect of
distortion in their learning condition but, as is clear from the degrees
of freedom in their reported F statistics, this analysis included classification
of the random patterns, which were classified far worse than the category
patterns. If analysis is restricted to the reported difference on classification
accuracy of the prototype and high-level distortions (63.8% vs. 62.0%,
respectively), then distortion level is not statistically significant, based on
their reported MS error terms.
3
In their Experiments 2A and 2B, Zaki and Nosofsky (2004) reported a
significant interaction between condition (full and subset) and item type
(prototype, low distortion, high distortion) but failed to report whether the
main effect of item type was significant in the subset condition in either
experiment. The slight difference among the three item types (less than 3%
between the prototype and high distortions in Experiment 2A and less than
.10 on a 5-point scale in categorization judgment in Experiment 2B) and
the outcomes in each experiment (high distortions were classified more
accurately than low distortions) are inconsistent with the predictions of
their own model fits (see Figures 3 and 4).
370
HOMA, HOUT, MILLIKEN, AND MILLIKEN
The concern is not whether the false prototype effect can be
generalized from a one-category to a multiple-category transfer
paradigm; rather, the claim is that the potential artifact raised by
Zaki and Nosofsky (2004) is invalid except when a one-category
transfer paradigm is used. In particular, it is unclear how an
extraneous variable like “compactness” could produce a prototype
enhancement effect when more than one category is learned and
discrimination among these categories is required at transfer. Specifically, compactness by itself could not function as a discriminative cue when multiple categories are considered. To make this
point clear, suppose you knew nothing about the different types of
animals on a particular planet except for one fact—you are told the
best examples of each of three species are the reddest, with
nonexamples being less red in color. If asked to separate the best
members of these three species from the nonexamples, you could do
this with some accuracy. However, if you were asked to sort the
members of these three species into their respective groups, sorting by
redness alone would produce chance performance. The former case—
separating the members from the nonmembers— corresponds to the
one-category paradigm used by Zaki and Nosofsky. The latter case—
sorting the members of these three species into their appropriate
groups—was not explored by Zaki and Nosofsky but is investigated
in the present study. Because the vast majority of studies in categorization, from the seminal studies by Fisher (1916) and Hull (1920) to
the modern study of ill-defined categories (Posner & Keele, 1968,
1970), have used a multiple-category learning phase followed by
transfer into these same categories, the finding of a false prototype
effect that was manifested only in a single-category paradigm would
render meaningless the criticism of Zaki and Nosofsky.
In their discussion, Zaki and Nosofsky (2004) acknowledged
that the false prototype effect might be confined to the singlecategory paradigm:
We should acknowledge that such effects of “compactness” and
“goodness” are likely to be most pronounced in the present type of
single-category paradigm. . . . It is an open question whether similar
stimulus specific effects may also play some role in multiplecategorization paradigms. (footnote 3, p. 398)
The present study addresses precisely this issue.
In Experiment 1, subjects were exposed to either a real or a
bogus learning phase, followed by transfer to a single category or
to multiple categories. In the bogus category conditions, patterns
generated from three different prototypes were presented so briefly
(and followed by a visual noise mask) that nothing could be seen
except for a brief flash. At the time of transfer, the bogus onecategory subjects were told the patterns actually came from a
single category and that they should assign the transfer patterns
into either the category seen subliminally or a junk category. The
bogus three-category subjects received similar instructions, except
they were told that the patterns actually came from three different
categories. On the transfer task, they were instructed to assign
patterns into these three categories (A, B, C) or into a junk
category if the pattern belonged to none of the subliminal categories. The real learning condition required that subjects first learn to
classify the patterns into three categories prior to transfer. The
composition of the transfer task was identical for all conditions,
composed of three prototypes, low-, medium-, and high-level
distortions of these prototypes, and random (unrelated) patterns.
As a consequence, the only difference among the conditions was in
the prior learning phase, either bogus learning with one or three
categories or actual learning with the three categories.
Therefore, if the concerns of Zaki and Nosofsky (2004) are
extendable to multicategory learning using pattern distortions, then
the generalization gradient at the time of transfer should be undiminished by the number of categories available at the time of test,
regardless of learning. However, if the gradient is minimal or
absent following bogus learning for a three-category case and
robust following the learning of three categories, then the demonstration of a false prototype enhancement effect is likely confined
to (or an artifact of) the one-category paradigm. In our discussion,
we examine more fully the factors that are responsible for producing transfer gradients, including why a minimal, nonzero gradient
might be expected following bogus learning for the three-category
case that has little to do with an artifact of stimulus compactness
or goodness.
Experiment 1
In Experiment 1, subjects were exposed to either a bogus learning phase or a real learning phase. For the bogus learning condition, 30 patterns were shown briefly (10 ms) and followed by a
noise mask. This procedure minimized the encoding of pattern
information and, therefore, category information. A postexperiment questionnaire confirmed that subjects rarely reported anything other than a “blink” or, at most, a pattern segment. This
procedure did have the effect, therefore, of convincing the subjects
that something had been shown.4 This bogus learning was followed by a transfer test to one or three categories. The transfer test
contained 93 patterns, 15 patterns each from three prototype categories (five low, medium, and high distortions each), the three
category prototypes, and 45 random patterns (high-distortion patterns from 45 different prototypes). Subjects assigned the transfer
patterns into Category A, B, C, or junk for the three-category
transfer; for the one-category transfer, subjects assigned the transfer patterns into Category A or junk. For the real learning condition, subjects were exposed to a real learning phase involving the
same three categories that preceded the transfer test. During the
learning phase, subjects were shown 30 high-distortion patterns
(the same patterns presented in the bogus conditions) for five
study/test learning trials, where 10 patterns belonged to each of the
three prototype categories. This learning phase was followed by a
transfer test identical to that for the bogus three-category condition
above.
In the bogus one-category condition, subjects were told to assign
the patterns to Category A or junk. In the bogus condition involving three categories at the time of transfer, subjects were told to
assign the patterns to the Categories A, B, C, or junk (identical to
the learning subjects). Subjects were free to use the labels as they
4
Although this issue was not addressed by Zaki and Nosofsky (2004) or
Palmeri and Flanery (1999), our pilot data indicated that some subjects
were suspicious whether anything was actually presented in a bogus
condition that lacked any patterns being presented. To minimize this
concern, we presented the patterns very briefly (10 ms), followed by an
immediate noise mask. This rendered an impression that something
“popped” but was otherwise not discernable. We did include a postquestionnaire that confirmed this, including a test to ask subjects to draw any
pattern, which no subject could.
PROTOTYPE GRADIENTS
wished, with the sole stipulation that they adopt a strategy where
they sorted together under a common label those patterns they felt
belonged together. At the conclusion of the study, scoring was
optimized for each subject by counting, as the subject labels,
whatever labels produced the highest classification score (see also
Homa & Cultice, 1984, where a similar strategy was used in a task
that contrasted learning with and without feedback during learning).5
Method
Subjects. Subjects were 83 Arizona State University undergraduates who received course credit in their introduction to psychology classes for participation in the experiment. There were 27
subjects in each bogus category condition (bogus one-category and
bogus three-category) and 29 in the real learning condition (learn
three-category). One subject was dropped from the learning condition because he placed 85 of the 93 patterns into the junk
category.
Materials and apparatus. Members of three form categories
served as stimuli and have been described previously (Homa,
1978). In brief, a form category is created by first generating a
random nine-dot configuration within a 50 ⫻ 50 grid and then
connecting the dots with lines. This pattern is designated as the
category prototype; different members of this category are then
generated by statistically moving each of the dots of the prototype.
A statistical distortion algorithm is applied to each point in the
category prototype, with the amount of dot displacement determining the distortion level of a pattern. For high-level distortions,
each dot is displaced, on the average, by about 4.6 Euclidean units
from each corresponding dot of the prototype. The topography of
a category can be thought of as a sphere with the prototype located
in the center, and with the high-level distortions on the surface of
the sphere having a radius of 4.6 units. The average distance
between any two learning patterns is about 7.0 Euclidean units,
with no two patterns being closer than 4.5 units. Only high-level
distortions were used in the learning phase. On the transfer test,
new low-level distortion, medium-level distortion, high-level distortion, and random patterns were used. For the low- and mediumlevel distortions, each dot is displaced about 1.2 or 2.8 Euclidean
units, respectively, from the corresponding dot of the prototype.
Random patterns are statistically unrelated to the three prototypes
and range from 10 to 15 Euclidean units from any other pattern.
Subjects were run individually in a small cubicle with all displays on a computer screen; programming, timing, and data recording were controlled by E-Prime 1.2 (Schneider, Eschman, &
Zuccolotto, 2002). In the bogus one-category condition, the subject
pressed either the A or J keys on the transfer test to signify a
pattern in those categories. In the bogus three-category and real
learning conditions, the subject pressed either the A, B, C, or J keys
to signify a pattern in those categories. A brief questionnaire was
administered following completion of the experiment to assess
what, if anything, was observed in the learning phase.
Procedure.
In each bogus learning condition, the subject
engaged in a “subliminal training” phase in which a series of
patterns were briefly shown for 10 ms each. A total of 30 patterns
were presented in a random order, followed by an immediate
visual noise mask. The 30 patterns were composed of 10 high-level
distortions from three different prototypes.
371
Following this phase, each subject in the bogus one-category
transfer task was told that the learning set actually came from a
single category and that his or her job was to assign each transfer
pattern into either Category A if it came from the subliminal
category or Category J (for junk) otherwise.6 Each subject was
then presented with 93 patterns, 16 from each of three prototype
categories and 45 random patterns. The 16 patterns from each
category were composed of the prototype and five low-, five
medium-, and five high-level distortions; the 45 unrelated patterns
were 45 random patterns unrelated to the three prototypes.
For subjects in the bogus three-category condition, the subject
instructions and learning phase were identical to those used in the
bogus one-category condition. At transfer, the subject was told that
the learning set actually came from three categories and that his or
her job was to assign each transfer pattern into either Category A,
B, C, or junk. Immediately following learning, the subject observed the same 93 patterns and composition as the one-category
transfer condition. No feedback was provided following each
response, and the procedure was self-paced. The order of patterns
in the learning and transfer phases was randomized separately for
each subject.
In the learn three-category condition, the procedure was similar
to that for the bogus conditions except that the learning phase was
real and only a three-category condition was used. There were five
learning blocks, each having a different category order. For Learning Block 1, the subject saw the patterns from three prototype
classes, blocked by prototype class (labeled A, B, and C for each
subject), with the pattern label appearing in the upper right corner
for 2 s. This was followed by a blank screen shown for 1 s,
followed by the next pattern from this group. The patterns were
blocked by prototype but otherwise shown in a randomized order.
For example, the 10 patterns from one prototype class were labeled
A1, A2, . . . A10; the 10 patterns from the second prototype class
were labeled B1, B2, . . . B10; and the 10 patterns from the third
prototype class were labeled C1, C2, . . . C10. For Learning Block
1, the subject might see, in order, A1, A7, A3, A4, A6, A2, A10, A8,
5
For example, suppose a subject assigned the 16 patterns from Prototype 1 as follows: 3 in A, 7 in B, 2 in C, and 4 in junk. For Prototype 2,
8 were put in A, 3 in B, 4 in C, and 1 in junk. For Prototype 3, the
assignments were 2 in A, 4 in B, 5 in C, and 5 in junk. Maximizing this
subject’s performance would assume that Prototype 1 was called B, Prototype 2 was A, and Prototype 3 was C, resulting in an overall performance
of 7, 8, and 5 patterns correctly assigned. For subjects in the bogus
one-category condition, no assumptions were necessary, because the subject need only separate the category from the random patterns.
6
In Palmeri and Flanery (1999), subjects were told that the “subliminal”
patterns belonged to a single category; in Zaki and Nosofsky (2004),
subjects were told that the patterns came from five categories (Experiments
1A and 1B) or a single category (Experiments 2A and 2B). In each
experiment, subjects were then asked to assign transfer patterns to the
subliminal category (or categories) or not. In our bogus one-category
condition, subjects were told that the subliminal patterns belonged to a
single category. Because it is unclear whether the number of categories
supposedly presented in the bogus phase matters, at least in the bogus
one-category condition, we also replicated this procedure with the sole
exception that subjects in the bogus one-category condition were told that
the patterns actually came from three categories. The resulting transfer
performance was virtually identical to that in the bogus one-category
condition reported here.
HOMA, HOUT, MILLIKEN, AND MILLIKEN
372
A5, and A9, each for 2 s with the label A appearing in the upper
right corner. This was followed by the B and C sets, which were
also blocked and randomized within the block, but with the labels
B and C shown in the upper right corner. A test block followed
each learning block. On each test, all 30 patterns were presented in
a random order without the category label. After the subject’s “A,”
“B,” or “C” response, the correct label was shown again in the
upper right corner for 1 s. Following feedback, the screen went
blank for 1 s, and then the next pattern was shown. Performance on
the test trials was self-paced, with most responses occurring within
2–3 s.
Learning Blocks 2–5 were identical to Learning Block 1 with
the sole exception that the order of prototype class corresponding
to A, B, and C was randomly changed and the patterns within each
prototype category were randomized again. That is, if the patterns
were shown in the order A, B, C on Learning Block 1, Learning
Block 2 might present these patterns in the order B, C, A, and so
forth. After the fifth learning/test block, the transfer test was given.
The transfer test for the real learning condition was identical to that
of the bogus three-category condition—the 93 patterns were
shown in a random order, and the subject selected Categories A, B,
C, or junk to classify the patterns. No feedback was provided to the
subjects at any time.
Design. A mixed design was used, with condition (bogus
one-category, bogus three-category, learn three-category) as the
between-subjects variable and type of transfer item (prototype,
new-low, new-medium, new-high, random) as a within-subject
variable.
Results
Learning. Figure 1 shows the mean error rates of learning
across the five trial blocks for the three-category learning condition. The main effect of learning block (1, 2, 3, 4, 5) was significant, F(4, 112) ⫽ 33.10, MSE ⫽ 7.83, 2 ⫽ .542, p ⬍ .001.
Because errors decreased across training blocks, significant learning did occur.
Learning, Experiment 1
0.5
Proportion Error
0.4
0.3
0.2
0.1
0
1
2
3
4
5
Learning Blocks
Figure 1. The mean proportion error rates of learning across the five
trials with junk patterns in the transfer test, Experiment 1.
Transfer: Gradient test. The initial analysis focused on the
shape of the gradient for transfer patterns at varying levels of
distortion (low, medium, high) from the prototype. Figure 2 shows
the mean correct classification rates for the bogus one-category,
bogus three-category, and learn three-category conditions; also
shown are the classification rates for the prototypes. The effect of
condition was significant, F(2, 80) ⫽ 13.35, MSE ⫽ 20.61, 2 ⫽
.250, p ⬍ .001, as was the effect of distortion, F(2, 160) ⫽ 41.50,
MSE ⫽ 3.24, 2 ⫽ .342, p ⬍ .001. The Condition ⫻ Distortion
interaction was also significant, F(4, 160) ⫽ 10.61, MSE ⫽ 3.24,
2 ⫽ .210, p ⬍ .001. A subsequent analysis revealed that the two
bogus conditions (bogus one-category and bogus three-category
learning) did not differ from each other, F(1, 52) ⫽ 0.07, p ⬎ .20,
but both bogus conditions differed from the learning condition
( p ⬍ .05 in each case). The bogus conditions did not interact with
distortion, F(2, 104) ⫽ 1.27, p ⬎ .20. In general, it appeared that
performance decreased across distortion level and that the learn
three-category condition was superior to the bogus conditions.
Because this latter interaction was significant, separate analyses
were done for each condition.
For each of the bogus one-category, bogus three-category, and
learn three-category conditions, the main effect of distortion was
significant, F(2, 52) ⫽ 5.18, MSE ⫽ 3.04, 2 ⫽ .166, p ⬍ .01; F(2,
52) ⫽ 4.96, MSE ⫽ 2.91, 2 ⫽ .160, p ⬍ .05; F(2, 56) ⫽ 48.07,
MSE ⫽ 3.72, 2 ⫽ .632, p ⬍ .001, respectively. There was an
8%–10% change across low-, medium-, and high-distortion levels
for the bogus conditions; in the three-category learning condition,
the gradient was steeper, resulting in a 33% drop.
Transfer: Prototype classification. Classification accuracy
of the category prototype was .84 for the learn three-category
condition, versus .62 and .62 for the bogus one- and bogus threecategory conditions, F(2, 80) ⫽ 5.96, MSE ⫽ .701, 2 ⫽ .13, p ⬍
.01. A Bonferroni test subsequently confirmed that the learn
three-category condition differed from each bogus condition
( p ⬍ .05), with the two bogus conditions not differing from
each other ( p ⬎ .20).
Transfer: Junk classification and a compositional analysis.
Classification of most transfer patterns, including random patterns,
into the learned category would give the appearance of highly
accurate transfer performance. It is, therefore, instructive to measure how often random (unrelated) patterns were correctly classified as “junk” and how often they were incorporated into the
category (or categories) represented in the learning phase. For the
three-category conditions, we can also measure how often intrusions from other categories occurred. Table 1 shows the mean
number of random patterns correctly classified into the junk category; also shown are category intrusions and a compositional
analysis (Homa, Burruel, & Field, 1987), explained shortly.
Correct assignments of unrelated patterns into the junk category
for the bogus one-category, bogus three-category, and learn threecategory conditions were .685, .285, and .724, respectively, F(2,
80) ⫽ 51.73, 2 ⫽ .564, p ⬍ .001. Subsequent tests revealed that
the bogus one-category and learn three-category conditions did not
differ from each other ( p ⬎ .20), with both conditions exceeding
the performance of the bogus three-category condition ( p ⬍ .05).
Thus, the bogus one-category condition produced significant discrimination between the category members and unrelated patterns,
but this discrimination was considerably reduced for the bogus
three-category condition.
PROTOTYPE GRADIENTS
Transfer Accuracy
Proportion Correct
0.9
0.8
0.7
Bogus-1
0.6
Cat-3
Bogus-3
0.5
0.4
Pro Low Med High
Transfer Items
Figure 2. The mean proportion correct classification rates on the transfer
test for the bogus one- and three-category conditions (Bogus-1 and
Bogus-3, respectively) and the three-category real learning condition (Cat3), as a function of distortion level from the prototype (Pro), Experiment 1.
The compositional analysis provides a sensitive index of category knowledge by identifying the kinds of information assigned
to a category, including correct assignments as well as erroneous
category intrusions and unrelated stimuli. The purity measure
(which is separate from the hit rate) reflects the proportion of
information assigned to a category that is correct. For example, in
the bogus three-category condition, the mean number of category
patterns correctly assigned to each category was 0.62 prototypes,
2.64 low-level distortions, 2.20 medium-level distortions, and 2.25
high-level distortions, or a total of 7.71 patterns correctly assigned
to each category out of 16 possible. However, each category also
contained 5.61 category intrusions and 10.80 unrelated patterns,
resulting in an average of 24.12 patterns classified into each of the
three categories. Of these, 7.71 were correct assignments, resulting
in a purity value of .320. In other words, of the patterns assigned
to each category, 32% were correct, and 68% were intrusions from
other categories or unrelated patterns. For comparison, random
assignment of the category patterns into the three categories (with
an equal number of random patterns into each category) would
result in a purity value of .25.
The purity value for the bogus one-category condition was .625;
random assignment of the entire transfer set, with an equal number
of patterns assigned to Category A and the junk category, would
produce a purity value of .516. For the learn three-category condition, purity was .653 (again, chance with three categories would
produce a purity value around .25). A comparable analysis can be
made for the junk category. A high purity value for junk would
indicate that most patterns assigned to junk were, in fact, patterns
unrelated to the learning categories. For the bogus one-, bogus
three-, and learn three-category conditions, junk purity was .559,
.609, and .779, respectively. This indicates that in both bogus
conditions, random patterns were discriminated from category
patterns with limited success (a .50 –.50 split would indicate no
discrimination), with the two bogus conditions functioning similarly. In contrast, the learn three-category condition was far more
successful in this discrimination.
Discussion
Experiment 1 demonstrated that prior category learning produced a sizable gradient across pattern distortion, with perfor-
373
mance decreasing about 35% from low- to high-level distortions.
The magnitude of this gradient across pattern distortion mirrors
what is typically obtained in categorization research (e.g., Homa &
Little, 1985; Homa et al., 2008). In contrast, bogus learning produced a minimal gradient—about 8%–10%. When transfer required the subject to discriminate among the categories as well
(bogus three-category condition), the generalization gradient became erratic across distortion level, and overall, classification
accuracy was poor. The compositional analysis, which provides an
index of the kinds of information assigned to a category, indicated
that, following bogus learning, purity dropped from over 60% to
less than 35% when subjects were required to discriminate among
the categories. This is because most patterns classified into the
same category were intrusions either from other categories or
random patterns. In effect, any potential extraneous variable that
might be available to discriminate category members from random
patterns could not be effectively used in the multiple-category
condition. Furthermore, the ability to discriminate category from
random patterns was poor, with about 80% of all random patterns
incorporated into the categories.
It is important to realize that performance in the bogus threecategory condition is probably a more accurate measure of the
level of category knowledge acquired during transfer than that in
the bogus one-category condition. That is, if subjects are asked to
discriminate category from random patterns following bogus
learning, the appearance of slight, but significant, performance is
obtained. However, this apparent level of knowledge is somewhat
illusory, because this same training results in subjects who then
demonstrate little ability to accurately sort patterns into the multiple categories. In fact, when we ran about 100 pseudo-subjects
who randomly sorted the transfer stimuli and then maximized their
performance, the obtained accuracy (40%) was only slightly worse
than that obtained by subjects in the bogus three-category condition (48%).7
Because transfer following pattern learning usually entails transfer to multiple categories, not just one, the concerns expressed by
Zaki and Nosofsky (2004) mostly vanish. This is not to deny that
some minimal, nonrandom learning can occur during transfer, only
that its contribution is slight and far less than what is typically
obtained following actual learning.
Experiment 2
Experiment 2 was a replication of the learning condition in
Experiment 1 with the exception that the junk patterns were
removed from the transfer test. All researchers who use a onecategory paradigm typically include random patterns (e.g., Knowlton & Squire, 1993; Palmeri & Flanery, 1999; Zaki & Nosofsky,
2007), and their inclusion is necessary to determine whether subjects can separate category from random patterns in a one-category
task. However, the inclusion of so many random patterns at the
time of transfer is not typically done when real learning is followed
7
Our Monte Carlo runs randomly sorted the 93 transfer patterns into
three learned categories, with the constraint that 21 patterns were sorted
into the junk category, a value that matched the mean rate of the bogus
three-category subjects. Following each run, scoring was then optimized as
it was for the actual subjects. Under these constraints, a mean accuracy of
.40 was obtained.
HOMA, HOUT, MILLIKEN, AND MILLIKEN
Table 1
Compositional Analysis of Bogus and Learned
Category Conditions
Item
Bogus-1
Bogus-3
Learn-3
Category members
Category intrusions
Junk into category
Total classification per category
Proportion correct
Category magnitude
Purity within category
Purity within junk
Junk magnitude
23.70
—
14.19
37.89
.494
0.789
.625
.559
1.225
7.71
5.61
10.81
24.12
.482
1.508
.320
.609
0.459
11.14
1.78
4.14
17.06
.696
1.066
.653
.779
0.930
Note. Maximum number for category members in the bogus onecondition (Bogus-1) category was 48; for the bogus three-condition
(Bogus-3) and learn three-condition (Learn-3) categories, the maximum
was 16. Purity is a measure of the accuracy of information within a
category; magnitude reflects the use of category, indexed by the number of
instances assigned to that category relative to its objective count, where
⬍1.00 indicates underuse and ⬎1.00 indicates overuse.
by transfer to multiple categories. It is, therefore, necessary to
show that the large gradient effect obtained in the three-category
learning condition of Experiment 1 is not diminished when unrelated patterns are excluded from the transfer phase. We hypothesized that the removal of numerous random patterns in transfer
might affect the transfer gradient to a slight degree, because the
inclusion of random patterns can influence decisional processes at
the time of transfer separate from acquired categorical knowledge
(Homa et al., 1987). However, the resulting gradient, if primarily
driven by learning, would be similar to that obtained in Experiment
1 and, therefore, still far greater than that obtained in the bogus
learning conditions.
Method
Subjects. A total of 30 subjects were used, drawn from the
same pool as in Experiment 1, except all of these subjects were in
the three-category condition. Data from one subject were deleted
for failure to show learning across the five learning blocks. Therefore, all analyses were based on the results from 29 subjects.
Materials and apparatus. Subjects were run according to the
same guidelines and stimuli as in Experiment 1.
Procedure. The procedure was identical to that of Experiment 1, except that there were no random patterns in the transfer
test, and patterns were assigned to Category A, B, or C.
Results
Learning. Figure 3 shows the error rates of learning across
the five trial blocks. The main effect of learning block was significant, F(4, 112) ⫽ 40.05, MSE ⫽ 7.51, 2 ⫽ .589, p ⬍ .001.
The initial and terminal error rates mirrored those of Experiment 1.
Transfer: Prototype and distortions. Figure 4 shows the
three-category real learning condition without junk patterns in the
transfer. For the three-category real learning condition without
random patterns in the transfer, the effect of item type was significant, F(3, 84) ⫽ 53.95, MSE ⫽ 3.82, 2 ⫽ .658, p ⬍ .001.
Because the procedure and patterns for Experiment 2 were virtu-
ally identical to those used in Experiment 1, an analysis that
directly compared the three-category learning conditions (with
random patterns in Experiment 1 and without random patterns in
Experiment 2) was performed. A mixed analysis of variance was
done, with learning condition (three-category learning with and
without junk) as the between-subjects variable and item type
(prototype, low, medium, high) as the within-subject variable. This
analysis revealed that the effect of condition was not significant,
F(1, 56) ⫽ 0.204, MSE ⫽ 24.40, 2 ⫽ .004, p ⬎ .20, nor was the
Condition ⫻ Distortion level interaction, F(3, 168) ⫽ 0.53,
MSE ⫽ 4.60, 2 ⫽ .009, p ⬎ .10, but the effect of distortion level
was significant, F(3, 168) ⫽ 77.04, MSE ⫽ 4.60, 2 ⫽ .58, p ⬍
.001.
Transfer: Gradient test. An analysis confined to the pattern
distortions revealed that the main effect of distortion from the
prototype (low, medium, high) was significant, F(2, 56) ⫽ 69.71,
MSE ⫽ 3.00, 2 ⫽ .713, p ⬍ .001. The two learning conditions
(three-category learning with and without random patterns) did not
differ from each other, F(1, 56) ⫽ 0.46, MSE ⫽ 19.09, 2 ⫽ .01,
p ⬎ .20, nor was the Condition ⫻ Distortion interaction significant, F(2, 112) ⫽ 0.49, MSE ⫽ 3.21, 2 ⫽ .01, p ⬎ .20. However,
the effect of distortion was significant, F(2, 112) ⫽ 119.89,
MSE ⫽ 3.21, 2 ⫽ .68, p ⬍ .001.
A comparison of the transfer performance for all conditions of
this study—the three conditions from Experiment 1 and the threecategory learning without random patterns condition from Experiment 2—is shown in Figure 5. Inspection of Figure 5 reveals the
close similarity in performance for the two learning conditions and
the dramatically worse performance for the two bogus conditions
(which also produced similar results to each other).
General Discussion
In their study, Zaki and Nosofsky (2004) claimed the prototype
enhancement effect—the tendency for classification accuracy at
transfer to be highest for the low-level distortions, intermediate
Learning, Experiment 2
0.5
0.4
Proportion Error
374
0.3
0.2
0.1
0
1
2
3
4
5
Learning Blocks
Figure 3. The mean proportion error rates of learning across the five
trials without junk patterns in the transfer test, Experiment 2.
PROTOTYPE GRADIENTS
Proportion Correct
0.9
0.8
0.7
0.6
0.5
0.4
Pro
Low
Med
High
Pattern Distortion
Figure 4. The mean proportion correct classification rates on the transfer
test for the three-category real learning condition, as a function of distortion level from the prototype (Pro), without junk patterns in the transfer,
Experiment 2.
for the medium-level distortions, and lowest for the high-level
distortions—typically obtained in categorization research is, partially or totally, a pseudo-outcome, an artifact of the compactness
of the prototype in relation to the other distortion levels. This issue
is important because generalization gradients centered on the category prototype, rather than particular learning instances, have
typically been used as support for a prototype abstraction process
(e.g., Smith & Minda, 2002). However, limitations in the results of
Zaki and Nosofsky should be noted. First, the effect they obtained
was of small magnitude, not consistently obtained in their own
experiments or by other researchers, and required upwards of 200
subjects to obtain statistical significance. Second, Zaki and Nosofsky reported confidence data based on a rating scale in three of
their four experiments, rather than on accuracy rates, and therefore,
direct comparison to other studies cannot be easily made. Third,
and most important, Zaki and Nosofsky used only a one-category
paradigm, and therefore, their results cannot extend to the learning
of and transfer to more than a single category. Compactness, or
any other extraneous variable that is correlated with construction
of the prototype or its distortions, might work to explain transfer
performance with a single category but cannot be logically applied
when more than one category is used. That is, if the prototypes for
all categories are more compact that their instances, then compactness alone cannot function as a distinctive cue to discriminate
among these categories.
In the present experiment, the results revealed a slight but
significant gradient around the prototype in both the bogus oneand bogus three-category conditions, although the gradient for the
bogus three-category condition was erratic, with higher classification for the high-level distortions than the medium-level distortions. In contrast, the magnitude of this gradient was far greater
following learning—about 35%—in both Experiments 1 and 2.
Therefore, it is clear that the magnitude and shape of this gradient
is minimally driven by potential artifacts like stimulus compactness and primarily driven by category learning. In effect, the
pseudo-prototype effect obtained by Zaki and Nosofsky (2004) is
itself a pseudo-effect of the single-category paradigm. Because the
vast majority of studies in human categorization have used paradigms involving multiple categories in learning and transfer, the
concern that a substantial part of the prototype gradient is due to an
artifact is unwarranted.
The results of Experiment 2, in which category learning was
followed by a transfer test lacking the random patterns, largely
mirrored the results of Experiment 1. This result is important
because random patterns are used when transfer is considered for
the one-category condition, where they are necessary, but they are
infrequently used when multiple categories are explored. However, it is clear that the magnitude of the gradient around the
category prototype is unaffected by whether random patterns are
used or not, at least when three categories are learned. As such, our
conclusion that the gradient around the category prototype is due
primarily to actual learning is undiminished by whether the transfer set contains random patterns or not.
Three related methodological points deserve comment. First, the
claim that some learning may occur during transfer (Zaki &
Nosofsky, 2004, 2007) is likely true, and therefore, nonchance
performance following bogus training is to be expected. Learning
during transfer is functionally indistinguishable from schematic
concept formation (Evans, 1967; Smallwood & Arnoult, 1974). In
schematic concept formation, researchers explore whether categories can be learned in the absence of external, verbal feedback. In
both cases—a transfer test provided without feedback, and learning in the schematic concept formation task—a series of patterns is
presented, the subject is required to make a classification judgment, and no feedback is provided. The sole difference is that
subjects in the schematic concept formation task explicitly attempt
to learn; in most transfer tasks, any learning that occurs might be
done implicitly. What has been found in the schematic concept
formation task is that significant, but usually minimal, learning
occurred. For example, in the free-sorting task used by Evans and
Arnoult (1967), only 20% of the subjects performed better than
chance. In other studies (e.g., Aiken & Brown, 1971; Brown &
Evans, 1969; Smallwood & Arnoult, 1974), learning increments of
less than 10% were obtained. Homa and Cultice (1984) explored
0.9
Proportion Correct
Exp 2 No Junk Transfer
375
0.8
0.7
B1-C
B3-C
0.6
L3-NJ
L3-J
0.5
0.4
0.3
Pro
Low
Med
High
Pattern Distortion
Figure 5. The mean proportion classification rates on the transfer test for
all four conditions from Experiments 1 and 2 (bogus one-category learning
[B1-C], bogus three-category learning [B3-C], three-category real learning
without junk [L3-NJ], and three-category real learning with junk [L3-J]) as
a function of item type and distortion from the prototype (Pro).
376
HOMA, HOUT, MILLIKEN, AND MILLIKEN
learning with and without feedback in eight conditions, finding
that learning occurred when patterns were low-level, mediumlevel, or a mixture of distortions, although the rate and terminal
level of learning was far greater when feedback was provided.
However, when patterns were exclusively high-level distortions,
little evidence of learning was found; that is, the learning curve
across eight learning blocks was flat, although above chance.
Therefore, in the typical category learning paradigm, the incorporation of mixed distortion levels or the mixing of multiple copies
of the category prototype in the transfer test can produce some
apparent learning following a bogus learning phase. However, as
the present results clearly demonstrate, the magnitude of the generalization gradient around the category prototype, and the overall
level of performance, is far greater when real, rather than bogus,
learning precedes transfer, at least when multiple categories must
be discriminated.
Second, the slight generalization gradient obtained in the bogus
three-category condition is undoubtedly elevated by the maximization of scoring used in the present study. When we ran a Monte
Carlo simulation on 100 pseudo-subjects, with the entire transfer
set randomized, maximizing performance resulted in an overall
classification rate of .40, only slightly below the .48 obtained in
Experiment 1. The addition of a single constraint—assume that the
subject classifies two to three low-level distortions from the same
prototype together and then randomly assigns the remaining patterns—produces an overall classification rate that matches the
level obtained by the bogus three-category condition. This, combined with the compositional analysis, reveals that the transfer
performance was approaching chance levels in the bogus threecategory condition. Specifically, the “best” categories produced by
our subjects resulted in a purity value of 32%. That is, only 32%
of all patterns classified together belonged to the same prototype
category; the remaining 68% of all patterns classified within each
category came from category intrusions and random patterns. This
can be contrasted with the bogus one-category condition, which
had a purity value of .62. This latter value suggests that subjects
could separate category from noncategory patterns but had little
success in separating among categories.
Third, the study of human concepts cannot be adequately investigated in the single-category paradigm. This is not to deny that
preliminary and even provocative findings can be generated by this
paradigm (e.g., Ashby & Maddox, 2005; Knowlton & Squire,
1993), which can be further explored by converging operations.
But what is lacking in the single-category paradigm are stimulus
cues that would permit discrimination between the studied category and any other category of concern, or what Gibson and
Gibson (1955) called distinctive features. Showing the subject a
handful of apparently unrelated objects is like Socrates demonstrating a point to Menon and claiming, “These are all Manks”; it
should leave Menon asking, “But what do non-Manks look like?”
There exists a virtual infinity of features that could, potentially,
discriminate Manks from non-Manks in this situation, and our
hypothetical subject would be left to his or her own devices upon
which to base his or her category decisions on a subsequent
transfer test. This was nicely illustrated by Zaki and Nosofsky
(2007), who demonstrated that the composition of the transfer
set—in this case, multiple copies of a high-level distortion and
numerous low-level distortions of this same pattern— can, following one-category learning, dramatically alter performance. We
disagree, however, that this demonstration requires that researchers “reevaluate whether past results involving the steepness of the
typicality gradient are, in fact, due to the abstraction of a prototype
from the training instances” (Zaki & Nosofsky, 2007, p. 2090).
Rather, the results of the present study make it clear that the
single-category paradigm lends itself to data outcomes that need
not be mirrored in a paradigm requiring discrimination among
multiple categories.
We believe these concerns touch upon a broader issue that needs
to be considered. Any comprehensive theory of human categorization should consider the potential data space shaped by learning
variables (Homa, 1984), especially when generalization gradients
are of major concern. It has been known for some time that small
category sizes produce shallow generalization gradients, whereas
large category sizes produce steep generalization gradients (Homa,
1978). But even the effect of category size, and its role in the
shaping of generalization gradients, can be muted when only two
categories are learned (Homa & Chambliss, 1975), presumably
because the subject need learn only one category, and the second
is learned by default; learning more than two categories, or providing an optional third “none” category, reestablishes the gradient
(Homa & Hibbs, 1978). The integrity of a database in human
categorization experiments is further compromised by the singlecategory paradigm, where the default “noncategory” is undefined
and likely shaped by the composition of the transfer set and the
decisional whims of the subject. Selection of a single category for
study while holding category size constant and then withholding
feedback during a transfer task composed of patterns having,
sometimes, peculiar characteristics—the major characteristics of
the single-category paradigm— can lead only to empirical mischief
and theoretical cost. If researchers wish to study generalization
gradients, tied to either the category prototype or selected training
instances, then considerable attention should be given at the outset
to how the categories are to be defined to the subject and the
suitability of the paradigm.
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Received January 2, 2010
Revision received August 31, 2010
Accepted September 7, 2010 䡲
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