Reference-point Reasoning and Comparison Asymmetries

Abstract

Comparison asymmetries are most often explained in terms of underlying asymmetries in the perceived sim i- larity of the comparison items, which in turn are seen as arising from the differential weighting of distinctive fe a- tures of the target and base representations. In two e x- periments, we fail to confirm the predictions of the sta n- dard account. Rather, comparison asymmetries seem to follow from two general principles. First, certain item s act as cognitive reference points that other, less prom i- nent category members are located in terms of or assim i- lated to. And second, the target and base terms of a comparison play different semantic roles, with the ta rget acting as the figure and the ba se acting as the ground.

Full text

Reference-point Reasoning and Comparison Asymmetries
Brian F. Bowdle (bbowdle@indiana.edu)
Department of Psychology, Indiana University
1101 East Tenth Street
Bloomington, IN 47405 USA
Douglas L. Medin (medin@nwu.edu)
Department of Psychology, Northwestern University
2029 Sheridan Road
Evanston, IL 60208 USA
Abstract
Comparison asymmetries are most often explained in
terms of underlying asymmetries in the perceived simi-
larity of the comparison items, which in turn are seen as
arising from the differential weighting of distinctive fea-
tures of the target and base representations. In two ex-
periments, we fail to confirm the predictions of the stan-
dard account. Rather, comparison asymmetries seem to
follow from two general principles. First, certain items
act as cognitive reference points that other, less promi-
nent category members are located in terms of or assimi-
lated to. And second, the target and base terms of a
comparison play different semantic roles, with the target
acting as the figure and the base acting as the ground.
Introduction
The notion that similarity is a symmetric relation is
highly intuitive. After all, if one claims that limes are
similar to lemons, this would seem to entail that lemons
are also similar to limes. This notion is further sup-
ported by the observation that many comparisons can
be stated either directionally, as in Limes are similar to
lemons, or non-directionally and reciprocally, as in
Lemons and limes are similar to each other. Neverthe-
less, comparisons often behave asymmetrically. For
example, Tversky (1977) showed that people frequently
prefer one direction of comparison (e.g., North Korea is
similar to China) over the other (e.g., China is similar
to North Korea). Such asymmetries are even more pro-
nounced in metaphors and similes, for which only one
direction of comparison may be meaningful. For ex-
ample, whereas Time is like a river is an informative
statement, A river is like time is nonsensical. The gen-
eral observation is that, whenever two items differ in
prominence due to such factors as familiarity, salience,
or concreteness, the less prominent item is compared to
the more prominent item.
What is the source of these comparison asymmetries?
That is, given that two items are recognized as being
similar, why should one direction of comparison be
more natural and meaningful than the other? Clearly,
the answer to this question is important to any psycho-
logically plausible model of comparison. Indeed, the
existence of comparison asymmetries has been used to
argue for and against different theories of similarity
(e.g., Tversky, 1977) and metaphor comprehension
(e.g., Glucksberg & Keysar, 1990; Ortony, 1979). In
this paper we evaluate two different accounts of the
cognitive factors underlying comparison asymmetries.
The Standard Account
Comparison asymmetries are most commonly ex-
plained in terms of Tversky’s (1977) contrast model of
similarity which predicts that, under certain circum-
stances, the similarity of item a to item b will actually
seem greater than that of item b to item a. According to
the contrast model, the perceived similarity of item a to
item b, s(a, b), is given by
s(a, b) = θf(A ∩ B) - αf(A - B) - βf(B - A)
where A and B are the features of a and b, f is a measure
of salience, and θ, α, and β are weights assigned to the
feature sets. The basic idea is that the similarity of two
items increases as a function of their common features
and decreases as a function of their distinctive features.
Asymmetries in the similarity of two items are pre-
dicted in terms of the focusing hypothesis: Because the
target (first term) of a directional comparison is the
subject of the statement, it will receive more attention
than the base (second term). This means that the dis-
tinctive features of the target are weighted more heavily
than those of the base – that is, α > β. Thus, the simi-
larity of a to b will seem greater than that of b to a
whenever b possesses the larger or more salient set of
distinctive features.
Consistent with the contrast model, asymmetric simi-
larity ratings have been obtained in a wide range of
stimulus domains, such that less prominent items are
seen as being more similar to more prominent items
(e.g., Bartlett & Dowling, 1988; Holyoak & Gordon,
1983; Ortony, Vondruska, Foss, & Jones, 1985; Tver-
sky, 1977). But how does this explain the fact that
people typically prefer one direction of comparison
between two items over the other? The standard an-
swer is that, when interpreting a similarity comparison,
the hearer seeks to maximize the similarity of the items.
In other words, people prefer North Korea is similar to

China over the reverse direction of comparison pre-
cisely because North Korea is judged as being more
similar to China than the reverse – presumably reflect-
ing differences in the featural complexity of the two
items. In support of this position, both Tversky (1977)
and Ortony et al. (1985) found that items in the pre-
ferred comparison order typically received higher simi-
larity ratings than the same items in the non-preferred
order.
To summarize, the standard account of comparison
asymmetries makes two claims. First, comparison
asymmetries reflect underlying asymmetries in the per-
ceived similarity of the items. And second, these un-
derlying asymmetries are due to attentional factors,
such that the distinctive features of the target are
weighted more heavily than the distinctive features or
spatial density of the base.
Cognitive Reference Points
Although the contrast model has been widely adopted,
there is an alternative explanation of comparison
asymmetries – namely, that such asymmetries follow
from principles of reference point reasoning (e.g.,
Gleitman, Gleitman, Miller, & Ostrin, 1997; Roese,
Sherman, & Hur, 1998; Rosch, 1975; Shen, 1989).
One of the central claims of this position is that certain
highly prominent items act as cognitive reference points
that other items are seen in relation to. Some well-
known examples of cognitive reference points are pro-
totypes and ideals, which may be used to understand
less prominent category members (Rosch, 1975), and
the self concept, which serves as a habitual landmark in
social judgments (e.g., Holyoak & Gordon, 1983; Srull
& Gaelick, 1983). The basic idea is that many domains
of knowledge are at least partially structured in terms of
a small number of reference items.
Of course, the claim that non-reference (or deviant)
items are seen in relation to reference items raises the
question of what is meant by “seen in relation to.” One
way in which this relationship may manifest itself is
conceptual location: Cognitive reference points pro-
vide landmarks that can be used to better specify the
location of deviant items in a semantic or perceptual
space. By doing so, reference items lend stability to the
representations of deviant items. For example, it may
be easier to conceptualize and reason with non-standard
quantities (e.g., a length of two feet and nine inches) in
terms of certain standards of measurement (e.g., a
length of one yard). The beneficial use of reference
items as landmarks for locating deviant items has been
demonstrated in several studies of magnitude compari-
sons, where pairs of deviant items were discriminated
with greater speed and accuracy when they were in the
vicinity of a cognitive reference point (e.g., Holyoak &
Mah, 1982; Hutchinson & Lockhead, 1977; te Linde
& Paivio, 1979).
In addition to conceptual location, there is a second
and more complex way in which deviant items may be
seen in relation to cognitive reference points – namely,
conceptual assimilation. The idea here is that deviant
items are more easily assimilated to reference items
than the reverse (e.g., Bowdle & Gentner, 1997; Rosch,
1975; Shen, 1989). Such assimilation effects have
been obtained in numerous studies. For example, peo-
ple are more likely to project new properties from pro-
totypical category members to less prominent members
than vice versa (Rips, 1975), and are more willing to
make inferences and predictions about others based on
the self than vice versa (e.g., Kunda & Nisbett, 1988;
McFarland & Miller, 1990). Whenever such assimila-
tion occurs, the representation of the deviant item is
changed to make it more concordant with that of the
reference item.
The above discussion of the functions of cognitive
reference points suggests that, even prior to being
placed in a comparison, there is a directional or asym-
metric relationship between two items whenever one
makes a better cognitive reference point than the other.
But how does this translate into preferred comparison
orders? An answer commonly given by reference point
models is that the target and base terms of a comparison
play different semantic roles, which specify the place-
ment of deviant and reference items in the comparison
frame.
It has been claimed that items in the subject and com-
plement positions of many sentence types are assigned
the roles of figure and ground, respectively (Gleitman
et al., 1997; Langacker, 1990; Talmy, 1978). The
figure is characterized as a moving or conceptually
movable object whose site or path is the issue of inter-
est. In contrast, the ground is characterized as a sta-
tionary landmark with respect to which the figure’s site
or path is defined. Thus, whichever item makes a more
natural cognitive reference point will be the preferred
ground of the sentence. In directional comparisons, this
predicts that deviant items should be placed in the tar-
get position and reference items in the base position.
Perhaps the most notable distinction between the
standard account of comparison asymmetries and the
reference point account is that the latter does not rely on
the notion of underlying asymmetries in the perceived
similarity of the comparison items. That is, one does
not have to judge whether item a seems more similar to
item b or item b seems more similar to item a in order
to determine their preferred ordering. Rather, compari-
son asymmetries reflect the fact that deviant items are
more concordant with the semantic constrains of the
target position, and reference items with the semantic
constraints of the base position. Simply put, using a
cognitive reference point as the base of a directional
comparison results in a more natural and informative
statement.
Comparing the Positions
Both the standard account and the reference point ac-
count are able to explain many of the comparison

asymmetries that have been observed in the literature,
albeit using different mechanisms. In the present study,
we sought to address an important limitation of existing
research in this area. Specifically, the available evi-
dence almost exclusively involves asymmetries in simi-
larity comparisons, for which the two accounts make
essentially the same predictions concerning which di-
rection of comparison should be preferred. If one turns
to consider the relationship between similarity and dif-
ference comparisons, however, then the two accounts
can be shown to make distinct predictions.
According to the standard account, people prefer the
direction of a similarity comparison that maximizes the
perceived similarity of the target to the base. By anal-
ogy, then, people should also prefer the direction of a
difference comparison that maximizes the perceived
difference of the target from the base. This suggests
that comparison asymmetries should go in opposite
directions for similarity and difference statements, as
asymmetries in similarity and difference ratings tend to
be inversely related (Tversky, 1977). For example, if
North Korea seems more similar to China than the re-
verse, then China will seem more different from North
Korea than the reverse. Therefore, people should not
only prefer North Korea is similar to China over China
is similar to North Korea, they should also prefer China
is different from North Korea over North Korea is dif-
ferent from China. In both cases, the preferred direc-
tion of comparison maximizes the value of the dimen-
sion specified by the comparison predicate.
In contrast to the standard account, the reference point
account states that people simply prefer the direction of
comparison that uses the better cognitive reference
point as the ground, because this ordering maximizes
the informativity of the statement. Given that the posi-
tion of figure and ground in a statement should not be
affected by the particular comparison predicate, the
preferred direction of comparison between two items
should place reference items in the base position for
both similarity and difference statements. Thus, if peo-
ple prefer North Korea is similar to China over the re-
verse, then they should also prefer North Korea is dif-
ferent from China over the reverse.
In addition to making different predictions about the
direction of comparison asymmetries for similarity and
difference statements, the standard and reference point
accounts also make different predictions about the rela-
tive magnitude of such asymmetries. According to
Tversky (1977), difference comparisons will tend to
place more weight on the distinctive feature sets than
will similarity comparisons. Because the standard ac-
count derives asymmetries from distinctive features,
this means that difference comparisons should be more
asymmetric than similarity comparisons. In contrast,
the reference point account suggests precisely the oppo-
site – similarity comparisons should be more asymmet-
ric than difference comparisons. Although the use of
reference items to specify the location of deviant items
is presumably equally important in similarity and dif-
ference statements, conceptual assimilation of deviant
items to reference items should be more likely to occur
in similarity statements. As noted by a number of theo-
rists, informative similarity comparisons do not merely
point out obvious commonalities; rather, they highlight
nonobvious commonalities, and promote the creation of
new ones through processes such as inference projec-
tion (e.g., Bowdle & Gentner, 1997; Medin et al.,
1993). While less work has been done concerning the
communicative functions of difference comparisons, it
is reasonable to assume that difference comparisons are
less likely to invite such modes of conceptual assimila-
tion. This is because difference comparisons serve
more to suggest differences between items than to sug-
gest commonalities. Thus, although there should be a
general preference for comparing deviant items to ref-
erence items, the utility of doing so should be greater
for similarity statements than for difference statements.
Experiment 1
In Experiment 1, we tested the central predictions of the
standard and reference point accounts concerning com-
parison asymmetries. Subjects were given directional
similarity or difference comparisons, each of which
contained a less prominent (deviant) item and a more
prominent (reference) item. All comparisons were pre-
sented in both possible orders – with the reference item
in the base position (e.g., A zebra is similar to/different
from a horse) or in the target position (e.g., A horse is
similar to/different from a zebra). For convenience, we
will refer to statements with the first ordering of items
as forward comparisons, and statements with the sec-
ond ordering of items as reverse comparisons. For each
comparison, subjects were asked to indicate the strength
of their preference for one direction of comparison over
the other. Again, the standard account predicts that
comparison asymmetries should go in opposite direc-
tions for similarity and difference statements, and
should be stronger for difference statements. In con-
trast, the reference point account predicts that compari-
son asymmetries should go in the same direction for
similarity and difference statements, and should be
stronger for similarity statements.
Method
Subjects. Forty Northwestern University undergraduates
participated in partial fulfillment of a course requirement.
Materials and Design. Each subject received 32 directional
comparisons between a less prominent (deviant) item and a
more prominent (reference) item. (The relative prominence
of each item was initially determined by the authors and then
confirmed by two judges.) To ensure generality, the 32 com-
parisons involved eight categories of items: animals (e.g.,
zebra – horse), artifacts (e.g., motel – hotel), colors (e.g., tan
– brown), countries (e.g., North Korea – China), emotions

(e.g., admiration – love), famous individuals (e.g., Saddam
Hussein – Adolf Hitler), measurements (e.g., $105.00 –
$100.00), and occupations (e.g., dentist – surgeon).
Half of the subjects received all 32 comparisons as similar-
ity statements (e.g., A zebra is similar to a horse), and half as
difference statements (e.g., A zebra is different from a horse).
Subjects saw each statement in both forward and reverse di-
rections, with the two directions separated by a six-point nu-
merical scale. The order of presentation of the two directions
(forward first versus reverse first) was counterbalanced within
and between subjects.
Procedure. Each subject was given a booklet containing the
32 pairs of comparison statements in a random order. Sub-
jects indicated which direction of comparison they felt was
“stronger, more sensible, or more natural” for each pair by
circling a number on the six-point scale. They were told that
the more strongly they preferred the direction on the left, the
closer their answer should be to 1, and the more strongly they
preferred the direction on the right, the closer their answer
should be to 6.
Results and Discussion
All directional preference ratings were transformed so
that higher numbers indicated a preference for forward
comparisons over reverse comparisons. For similarity
statements, the directional preference (M = 4.77, SD =
0.39) was significantly above the scale midpoint (3.5)
by both subjects and items, t
S
(19) = 14.66, p < .001 and
t
I
(31) = 19.44, p < .001. For difference statements, the
directional preference (M = 4.03, SD = 0.57) was also
significantly above the scale midpoint, t
S
(19) = 4.14, p
< .001 and t
I
(31) = 6.41, p < .001. Thus, subjects con-
sistently preferred comparing deviant items to reference
items in both similarity and difference statements. This
is consistent with the reference point account of com-
parison asymmetries: People prefer the direction of
comparison that places the better cognitive reference
point in the base position, regardless of the particular
comparison predicate used.
Turning to the relative magnitudes of the comparison
asymmetries, the preference for the forward direction of
comparison was higher for similarity statements than
for difference statements, t
S
(38) = 4.83, p < .001 and
t
I
(31) = 10.31, p < .001. Again, this is as predicted by
the reference point account: Because similarity state-
ments are likely to elicit a greater degree of conceptual
assimilation than difference statements, reference point
effects should be stronger in similarity statements.
Asymmetries in Similarity and Difference
Ratings
Contrary to the claims of the standard account, the re-
sults of Experiment 1 suggest that comparison asymme-
tries are not due to underlying asymmetries in the per-
ceived similarity or difference of the comparison items.
If this were the case, then – assuming that hearers seek
to maximize the value of the dimension specified by the
comparison predicate – comparison asymmetries should
have gone in opposite directions for similarity and dif-
ference statements. But how, then, does one explain the
fact that comparison asymmetries are typically associ-
ated with asymmetries in similarity and difference rat-
ings (e.g., Ortony et al., 1985; Tversky, 1977)? We
suggest that such ratings asymmetries might also be due
to reference point reasoning.
According to the reference point account, the target
and base terms of a directional comparison play differ-
ent semantic roles, with the target acting as the figure
and the base acting as the ground. Thus, information
flows directionally from the base to the target, as when
the base is used to generate new inferences about the
target. Assuming that deviant items are more easily
assimilated to reference items than the reverse, this
means that assigning the reference item to the base po-
sition (forward comparisons) should result in a greater
degree of conceptual assimilation than assigning it to
the target position (reverse comparisons). Therefore,
forward comparisons should elicit higher similarity
ratings – and lower difference ratings – than reverse
comparisons.
This explanation of ratings asymmetries is radically
different from that offered by Tversky’s (1977) contrast
model. In this model, the representations of the com-
parison items are assumed to remain static, and asym-
metries are simply due to attentional factors. On the
reference point view, however, the representations of
deviant items may shift towards those of reference
items, thereby making the items more similar. This
view is, in fact, consistent with a fair amount of evi-
dence. Indeed, asymmetries in conceptual assimilation
are often associated with asymmetries in similarity rat-
ings. For example, people not only make more infer-
ences and predictions about others based on the self
than vice versa (e.g., Kunda & Nisbett, 1988; McFar-
land & Miller, 1990), they also rate others as being
more similar to the self than vice versa (e.g., Catram-
bone, Beike, & Niedenthal, 1996; Holyoak & Gordon,
1983; Srull & Gaelick, 1983). We propose that the
latter effect may be largely due to the former – project-
ing novel information from the self to others will make
others seem more similar to the self.
In sum, the reference point account can explain
asymmetries in similarity and difference judgments,
and in fact predicts the same directionalities as the
standard account. As was the case for comparison
asymmetries, however, these approaches make different
predictions about the relative magnitude of asymmetries
in similarity and difference ratings. According to the
standard account, difference comparisons will tend to
place more weight on the comparison items’ distinctive
feature sets than will similarity comparisons. Because
the standard account derives asymmetries from pre-
cisely these stimulus properties, this predicts that direc-
tional difference ratings should be more asymmetric
than directional similarity ratings. According to the
reference point account, however, this pattern of results

should not hold. This is because conceptual assimila-
tion is more likely to occur in similarity comparisons.
Assuming that conceptual assimilation is in fact a pri-
mary source of ratings asymmetries, then, directional
similarity ratings should be more asymmetric than di-
rectional difference ratings.
Experiment 2
In Experiment 2, subjects were given the same direc-
tional comparisons used in Experiment 1, and rated
either the similarity or the difference of both the deviant
item to the reference item (e.g., How similar is a zebra
to a horse?) and the reference item to the deviant item
(e.g., How similar is a horse to a zebra?). Again, the
standard account predicts that difference judgments
should be more asymmetric, whereas the reference
point account predicts that similarity judgments should
be more asymmetric. We also gave a second group of
subjects nondirectional versions these comparison
questions (e.g., How similar are a zebra and a horse?
or How similar are a horse and a zebra?). That is,
these subjects were asked to rate either the similarity of
or the difference between the two items without any
specification of which item was the target and which
was the base.
The inclusion of the nondirectional ratings condition
was inspired by Catrambone et al. (1996), who argued
that if the more prominent of two comparison items
serves as a cognitive reference point for understanding
the other item, then it should act as the implicit base of
a nondirectional comparison. That is, nondirectional
comparisons should be mentally translated into forward
comparisons, in which the deviant item is directionally
compared to the reference item. Supporting this claim,
Catrambone et al. found that nondirectional similarity
comparisons were rated as expressing the same degree
of similarity as forward similarity comparisons, and a
higher degree of similarity than reverse similarity com-
parisons. In the present experiment, we sought to repli-
cate this finding for similarity comparisons, and extend
it to difference comparisons. If both nondirectional
similarity and difference ratings are closer to forward
than reverse ratings, then this would further support the
claim that asymmetries are due to reference point rea-
soning.
Method
Subjects. Eighty Northwestern University undergraduates
served as paid subjects.
Materials and Design. Half of the subjects were assigned to
the directional ratings condition, and half to the nondirec-
tional ratings condition. In the directional condition, subjects
received all 32 directional comparisons used in Experiment 1.
Half of the subjects in this condition were asked to rate the
similarity of the comparison items, and half the difference
between the comparison items. For each comparison, subjects
gave ratings for both the forward direction and the reverse
direction. The order of presentation of the two directions was
counterbalanced within and between subjects.
In the nondirectional ratings condition, subjects received
nondirectional versions of the 32 comparison statements. As
in the directional condition, half of the subjects were asked to
rate the similarity of the comparison items, and half the dif-
ference between the comparison items. Because nondirec-
tional comparisons lack target and base terms, however, sub-
jects gave only one rating per comparison in this condition.
The order of presentation of the deviant and reference items in
a comparison (e.g., How similar are a zebra and a horse?
versus How similar are a horse and a zebra?) was counter-
balanced within and between subjects.
Procedure. Each subject was given a booklet containing the
32 comparison statements in a random order. Subjects gave
similarity or difference ratings by circling a number on a 20-
point scale below each comparison. For similarity ratings, the
low end of the scale was labeled “not at all similar” and the
high end “very similar”. For difference ratings, the low end
was labeled “not at all different” and the high end “very dif-
ferent”.
Results and Discussion
Focusing first on the directional ratings, subjects gave
higher similarity ratings to forward comparisons (M =
11.02, SD = 2.44) than to reverse comparisons (M =
9.84, SD = 2.69), t
S
(19) = 3.93, p < .001 and t
I
(31) =
6.57, p < .001. Likewise, subjects gave higher differ-
ence ratings to reverse comparisons (M = 13.12, SD =
2.26) than to forward comparisons (M = 12.44, SD =
2.35), t
S
(19) = 3.29, p < .005 and t
I
(31) = 3.42, p < .005.
These results are consistent with both the standard ac-
count and the reference point account. More critically,
however, the directional similarity ratings were more
asymmetric than the directional difference ratings: The
absolute mean difference in ratings between the for-
ward and reverse comparisons was nearly twice as large
for similarity comparisons (M = 1.18, SD = 1.34) as it
was for difference comparisons (M = 0.68, SD = 0.92).
This is only consistent with the reference point account,
according to which conceptual assimilation will result
in asymmetric similarity and difference ratings but is
more likely to occur in similarity comparisons. How-
ever, this difference in the magnitude of the ratings
asymmetries was only marginally significant by items,
t
I
(31) = 1.91, p < .10, and not by subjects, t
S
(38) = 1.38,
p <.20.
Turning now to consider the entire pattern of ratings,
the nondirectional similarity ratings (M = 11.42, SD =
2.71) did not differ from forward similarity ratings, but
were significantly larger than reverse similarity ratings,
t
S
(38) = 2.23, p < .05 and t
I
(31) = 6.41, p < .001. This
replicates the findings of Catrambone et al. (1996).
Likewise, the nondirectional difference ratings (M =
12.10, SD = 3.12) did not differ from forward differ-
ence ratings, but were significantly smaller than reverse
difference ratings by items, t
I
(31) = 4.25, p < .001, but

not by subjects, t
S
(38) = 1.58, p < .20. Thus, subjects
seemed to interpret nondirectional similarity and differ-
ence comparisons as forward comparisons, in which the
reference item played the implicit role of ground. This
result cannot be explained by Tversky’s (1977) contrast
model, and further illustrates the centrality of reference
point reasoning in comparisons.
Conclusions
Our findings suggest that asymmetries in similarity and
difference comparisons cannot be explained in terms of
the differential weighting of static representations.
Rather, they seem to follow from two general princi-
ples. First, certain items act as cognitive reference
points that other items are understood in terms of via
conceptual location or conceptual assimilation. And
second, the target and base terms of a comparison play
different semantic roles – the base, acts as the ground,
is used to understand the target, which acts as the fig-
ure. Thus, comparison asymmetries reflect the fact that
deviant items are more concordant with the linguistic
constrains of the target position, and reference items
with the linguistic constraints of the base position. Di-
rectional comparisons are maximally informative when
a cognitive reference point is used as the base. Further,
this direction of comparison is most likely to result in
higher similarity ratings – and lower difference ratings
– due to the increased potential for conceptual assimila-
tion. In sum, the comparison process would appear to
be far more dynamic than is commonly assumed, with
reference-point reasoning playing a prominent role in
both similarity and difference.
Acknowledgments
We thank Dedre Gentner, Robert Goldstone, Steven
Sherman, and Phillip Wolff for their comments and
suggestions. We also thank Gina Davis, Elizabeth
Frame, Jason Griffith, and Matthew Kinman for their
help with data collection and coding.
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