Judgment and Decision Making, Vol. 4, No. 1, February 2009, pp. 64–81
Psychophysics and the judgment of price: Judging complex objects
on a non-physical dimension elicits sequential effects like those in
perceptual tasks
William J. Matthews and Neil Stewart?
Abstract
When participants in psychophysical experiments are asked to estimate or identify stimuli which differ on a single
physical dimension, their judgments are in?uenced by the local experimental context — the item presented and judgment
made on the previous trial. It has been suggested that similar sequential effects occur in more naturalistic, real-world
judgments. In three experiments we asked participants to judge the prices of a sequence of items. In Experiment 1,
judgments were biased towards the previous response (assimilation) but away from the true value of the previous item
(contrast), a pattern which matches that found in psychophysical research. In Experiments 2A and 2B, we manipu-
lated the provision of feedback and the expertise of the participants, and found that feedback reduced the effect of the
previous judgment and shifted the effect of the previous item’s true price from contrast to assimilation. Finally, in all
three experiments we found that judgments were biased towards the centre of the range, a phenomenon known as the
“regression effect” in psychophysics. These results suggest that the most recently-presented item is a point of reference
for the current judgment. The ?ndings inform our understanding of the judgment process, constrain the explanations for
local context effects put forward by psychophysicists, and carry practical importance for real-world situations in which
contextual bias may degrade the accuracy of judgments.
Keywords: sequential effects; magnitude estimation; price; anchoring
1 Introduction
cal context — by the stimuli presented on the past few
trials — and a number of authors have provided evidence
When people make basic perceptual judgments — about
that the same principal applies to more complex, non-
the brightness of a light or the loudness of a tone, for
perceptual decisions too (e.g., Beckstead, 2008; Vlaev &
example — their responses are greatly in?uenced by the
Chater, 2007). The current article develops this idea by
context in which the stimuli are presented: A square of a
studying sequential effects in a complex judgment task
given size is regarded as large when most of the squares
using the analytical tools and experimental manipulations
in the experiment are of smaller size, but regarded as
employed in psychophysical research.
small when most of the squares are larger (e.g., Parducci,
The dependency of perceptual judgments on the events
1965). It has long been known that this insight from psy-
of the last few trials has been extensively researched by
chophysics has relevance to more complex, “real world”
psychophysicists. The typical approach is to employ a
situations. Thus, the perceived severity of a moral trans-
regression model in which the current judgment, Jn ,
gression depends upon the ensemble of scenarios pre-
is the dependent variable and the current stimulus and
sented for judgment, even when participants are explic-
stimuli and/or responses from trials earlier in the se-
itly instructed to ignore this context (Parducci, 1968).
quence are predictors. In particular, Jesteadt, Luce, and
Psychophysical studies have therefore demonstrated
Green (1977) advocated the use of the following regres-
the importance of what may be termed the global experi-
sion model:
mental context — the set of stimuli employed — in deter-
mining perceptual judgments, and this insight has proven
Jn = ? + ?0Pn + ?1Pn?1 + ?1Jn?1 +
(1)
useful in more complex and naturalistic judgment tasks.
where Pn is the value of the stimulus presented on the
Yet psychophysical judgments are also in?uenced by lo-
current trial, Pn?1 is the value of the stimulus on the pre-
?This work was supported by Economic and Social Research Coun-
vious trial, and Jn?1 is the value of the judgment made
cil grant RES-000-23-1372. We thank Malik Refaat for help with data
on the previous trial. Equation 1 has been applied to data
collection. Address correspondence to: William Matthews, Department
from a large number of psychophysical experiments. In
of Psychology, University of Warwick, Coventry, CV4 7AL, United
Kingdom. Email: w.j.matthews@warwick.ac.uk. Data for this
these experiments, the participant is presented with a se-
study are available at http://journal.sjdm.org/81104/data.html.
quence of stimuli which differ in one physical attribute,
64

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
65
such as tones which differ in loudness, and asked to form
for the observed sequential effects; the inability to form
some judgment of that attribute; the precise nature of the
accurate long-term representations may push people to-
judgment depends on the psychophysical task. In mag-
wards the use of recent items as a frame of reference.
nitude estimation experiments, the participant is asked
When people make real-world judgments about complex
to assign a number which indicates his or her subjective
items, and when the judgments are of a type with which
impression of the loudness of each tone, either with re-
they are very familiar, it may be that the sequential effects
spect to an explicit standard (e.g., Reynolds & Stevens,
are eliminated as people use only long-term referents and
1960) or on an absolute scale (e.g., Ward, 1987). In
stable internal scales of judgment. Indeed, many of the
cross-modality matching experiments, the participant is
models of sequential effects in psychophysical judgment
asked to adjust the magnitude of one dimension, such as
make assumptions which explicitly concern perceptual
loudness, so that it matches a magnitude on another di-
tasks and which are not readily extended to other situa-
mension, such as brightness (e.g., Ward, 1979). In cat-
tions (e.g., S. D. Brown, Marley, Donkin, & Heathcote,
egory judgment experiments, the participant is asked to
2008).
put each stimulus into one of several categories (such
The current article asks whether the pattern of se-
as “very quiet,” “quiet,” “medium,” “loud,” “very loud”;
quential dependencies seen in psychophysical tasks ex-
e.g., Petzold & Haubensak, 2001). In absolute identi?-
tends to situations in which people make judgments about
cation experiments, each stimulus is given a unique label
non-physical dimensions of complex, real-world objects.
— for example, the stimuli are numbered 1–10 — and
In three experiments we asked participants to judge the
the participant is asked to name the stimulus presented
prices of various items. We chose this task because it
on each trial (e.g., Garner, 1953).
corresponds reasonably well to an important aspect of our
Equation 1 has been used to study sequential effects in
economic lives; we are routinely exposed to sequences of
all of these paradigms. The details of the results depend
products and, implicitly or explicitly, assess their proba-
somewhat on the experimental task but the general pat-
ble cost. This task was also attractive because it allowed
tern is robust: The response on the current trial is biased
us to use rich, complex stimuli and to require judgments
towards the judgment made on the previous trial but away
about a property that does not correspond to a simple
from the stimulus presented on that trial (e.g., DeCarlo &
physical aspect of the item presented for judgment.
Cross, 1990; Jesteadt et al., 1977; Matthews & Stewart,
In Experiment 1, we ask whether judgments of price
in press; Mori, 1998; Mori & Ward, 1995; Ward, 1979;
exhibit sequential dependencies of the type seen in psy-
1987). That is, there is assimilation to the immediately
chophysical experiments. In Experiments 2A and 2B we
preceding response but contrast to the immediately pre-
extend the results of Experiment 1 to new stimuli and a
ceding stimulus.
modi?ed procedure, and ask whether experimental ma-
These sequential effects have been given various in-
nipulations known to in?uence sequential dependencies
terpretations, many of which assume that there is some
in psychophysical tasks exert the same effects on judg-
kind of perceptual interference from the previous stimu-
ments of price.
lus and that the previous item and the judgment assigned
to it serve as a point of reference when evaluating the
current stimulus (e.g., DeCarlo & Cross, 1990). It is ar-
2 Experiment 1
gued that even when participants are asked to judge stim-
uli with respect to long-term referents, they use the most
In Experiment 1 participants judged the prices of chairs.
recently experienced events as a framework for judgment
We chose chairs as the to-be-judged items because we felt
(Holland & Lockhead, 1968; Laming, 1984; Stewart, G.
their prices should be relatively obvious from their ap-
D. A. Brown, & Chater, 2005).
pearance (unlike, say, electronic goods, which may have
Many real-world tasks have a structural similarity to
many hidden features). We presented pictures of chairs
magnitude estimation or category judgment, in that peo-
taken from the website of a popular retailer (Ikea). One
ple esimate or classify a sequence of stimuli. However,
can browse this website and purchase chairs based en-
the stimuli are very different. The tones, lights and lines
tirely upon their photographs.
used in psychophysical investigations are very simple and
notoriously dif?cult to store in long-term memory; in-
deed, it is frequently asserted that our capacity for pro-
2.1 Method
cessing such stimuli is limited to about 7 items (Miller,
2.1.1 Participants
1956), in contrast to our capacity to recognise and iden-
tify many thousands of complex objects (e.g., Matthews,
Twenty ?ve staff and students from the University of War-
Benjamin, & Osborne, 2007). The labile mental repre-
wick took part; each was paid £3. All participants had
sentations of psychophysical stimuli may be responsible
been resident in the UK for at least the past 3 years.

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
66
Experiment 1 - Chairs
the decimal point if they wished. Participants were free
to edit their responses (e.g., by deleting the number) and
50
entered their judgment by pressing Enter or Return. The
screen then went blank for 500 ms before the presenta-
40
tion of the next chair. Participants were told not to worry
if they were uncertain and just to enter their best estimate
30
of each item’s price. Each participant judged each item
once, giving 100 trials per participant; the order of pre-
20
sentation was randomized for each person.
Frequency
10
2.2 Results
0
In this experiment, and in those which follow, there were
0
100 200 300 400 500 600
a small number of missing/nonsensical responses (e.g.,
“£0”) and cases where, after completing the experiment,
Price (£)
the participant reported having mis-typed a particular
judgment. Such responses were excluded from the analy-
Experiment 2 - Shoes
sis, as were a handful of extremely large responses (more
30
than ?ve inter-quartile ranges above the upper quartile for
that participant) which were assumed to have been en-
25
tered in error. In the current experiment a total of 0.12%
of responses were excluded.
20
15
2.2.1 Relationship between true price and judged
price
Frequency
10
We began by plotting the relationship between judged
5
price and true price separately for each participant. The
top panel of Figure 2 shows the results averaged over par-
0
ticipants; each point represents the average judgment for
0 20 40 60 80 100 120 140 160
a given product.
Judged price increases with true price. However, the
Price (£)
distribution of true prices is highly skewed; there are a
large number of low-priced products and fewer expensive
Figure 1: Distribution of prices of stimuli in Experiment
items (see e.g., Stewart & Simpson, 2007, for other exam-
1 (left) and Experiments 2A and 2B (right).
ples of this in price data), giving very high leverage to a
relatively small number of expensive items. In addition,
there is evidence of a curvilinear relationship between
2.1.2 Stimuli
price and judgment, with the curve becoming ?atter at
The stimuli were 100 pictures of chairs available from the
higher prices (this pattern was more obvious in individ-
Ikea furniture store. The prices of the chairs ranged from
ual participant data). We therefore applied a logarithmic
£6.49 to £489 (M = 95.49, SD = 98.86); the distribu-
transformation to both the true price and judgment val-
tion of prices is shown in Figure 1. Each picture mea-
ues. The results, averaged over participants, are shown in
sured 500x500 pixels and was presented on a 19” TFT
the bottom panel of Figure 2. The transformation brought
monitor with resolution 1280x1024 pixels, viewed from
the data into better agreement with the assumptions of lin-
approximately 50cm.
ear regression, so for all subsequent analyses we used the
log-transformed data.
2.1.3 Procedure
To investigate the relationship between price and judg-
ment, we regressed judged prices on true prices. The re-
Participants were tested in individual testing cubicles. On
gression line for the participant-averaged data is shown
each trial, participants were shown one of the chairs. Un-
in the bottom of Figure 2, along with a line of zero inter-
derneath the photo was a box in which the participant
cept and slope of one that indicates the results expected if
typed his or her estimate of the price; participants were
judgments were perfectly accurate — the “veridical” line.
asked to enter the price in pounds and were free to use
The regression line is swivelled with respect to the veridi-

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
67
Experiment 1
to this point later.
Raw data
200
2.2.2 Sequential Effects
To examine sequential effects we applied Equation 1; that
150
is, we regressed the judgment on the nth trial, Jn, on the
true price of the nth item, Pn, the true price of the pre-
100
vious item, Pn?1, and the judgment made for the previ-
ous item, Jn?1 (in all cases using log-transformed vari-
ables). We ?t the data from each participant separately.
50
The results are shown in Table 1. The leftmost columns
Mean Judgment (£)
of Table 1 contain the unstandardized regression coef?-
cients along with associated signi?cance codes. Some
0
researchers (e.g., Beckstead, 2007) have pointed out that
0
100 200 300 400 500 600
the signi?cance of a regression coef?cient depends criti-
True Price (£)
cally upon the number of experimental trials, and that re-
searchers should consider effect sizes when deciding the
Experiment 1
importance of a particular judgment cue. The rightmost
Log-transformed data
column of Table 1 therefore contains the standardized co-
ef?cients (the signi?cance codes for these are, of course,
6
the same as for the unstandardized values, and are not
listed in Table 1).
5
For every participant there is a signi?cant positive re-
4
lationship between actual price and judged price. There
is also evidence of sequential effects, particularly of the
3
preceding judgment. For 23 of the 25 participants the co-
ef?cient for J
2
n?1 is positive, indicating assimilation to
the previous judgment; for 9 of these 23 participants the
1
effect is signi?cant. Neither of the participants with neg-
ln(Mean Judgment)
Veridical
Regression
ative Jn?1 coef?cients show a signi?cant effect. The ef-
0
fects of the preceding item’s actual price, Pn?1, are less
0
1
2
3
4
5
6
7
consistent; 19 of the 25 participants have a negative coef-
?cient, two of which are signi?cant. None of the partici-
ln(True Price)
pants with a positive coef?cient show a signi?cant effect.
There is some multicollinearity in the regression model
Figure 2: Relationship between true price and judged
because the Jn?1 and Pn?1 predictors are correlated.
price in Experiment 1. The plots show the mean judgment
Multicollinearity increases the standard errors of the re-
for each product. The top panel shows the untransformed
gression coef?cients (although the coef?cients remain
data; the bottom panel shows the results after logarithmi-
unbiased estimators), reducing the likelihood that a par-
cally transforming both the true prices and the judgments.
ticular coef?cient will be signi?cant. We examined the
The solid line in the bottom panel is the regression line,
variance in?ation factor (VIF) to assess the severity of
indicating the empirical relationship between true price
the multicollinearity. We calculated the VIFs for the re-
and judgment. The dashed line shows the results expected
gression analyses from each participant in each experi-
if judgments were perfectly accurate.
ment (a total of 81 regressions). Each regression had
three independent variables, giving a total of 243 VIF
values. The results indicated that the multicollinear-
cal line; on average, participants overestimated the price
ity was not severe; only 2 of the VIFs were more than
of cheap items and underestimated the price of expensive
3.0 (and then only slightly, 3.01 and 3.03). Some text-
items.
books have suggested that VIFs less than 10.0 indicate
We applied the same approach to the data from each
acceptable multicollinearity (e.g., Neter, Kutner, Nacht-
individual participant. There was a signi?cant positive re-
sheim, & Wasserman, 1996). Nonetheless, some cau-
lationship between true price and judged price for every
tion is needed when interpreting the signi?cance of re-
participant but, as seen in the averaged data, the regres-
sults for individual participants, and in order to estab-
sion lines were rotated towards the horizontal. We return
lish the overall pattern, we used a one-sample t-test to

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
68
Table 1: Regression coef?cients for Experiment 1.
Unstandardized
Standardized
Participant
int
log Pn log Pn?1 log Jn?1 log Pn log Pn?1 log Jn?1
R2
1
0.676
0.653a ?0.035
0.137
0.736
?0.039
0.137
0.540
2
2.131a
0.444a ?0.188b
0.200d
0.764
?0.324
0.203
0.626
3
0.928c
0.505a ?0.041
0.235d
0.713
?0.057
0.240
0.521
4
0.582d
0.462a ?0.026
0.221d
0.692
?0.039
0.224
0.524
5
0.864c
0.432a ?0.105
0.338b
0.704
?0.172
0.341
0.561
6
0.977c
0.636a ?0.066
0.118
0.758
?0.079
0.118
0.566
7
1.807a
0.575a
0.074
0.037
0.735
0.094
0.037
0.557
8
1.408a
0.452a ?0.037
0.032
0.760
?0.063
0.032
0.587
9
?0.484
0.732a
0.051
0.161
0.796
0.055
0.161
0.651
10
0.448
0.652a ?0.040
0.044
0.790
?0.048
0.043
0.632
11
1.219c
0.435a
0.129
0.121
0.541
0.163
0.122
0.363
12
1.950a
0.351a ?0.032
0.175
0.605
?0.055
0.176
0.373
13
0.725d
0.546a ?0.017
0.107
0.677
?0.020
0.109
0.480
14
2.979a
0.311a
0.080 ?0.168
0.634
0.163 ?0.168
0.409
15
2.187a
0.563a ?0.055
0.032
0.668
?0.065
0.032
0.453
16
1.032c
0.455a ?0.174c
0.475a
0.685
?0.261
0.478
0.627
17
0.599
0.542a ?0.111
0.306c
0.704
?0.143
0.308
0.573
18
1.768a
0.608a ?0.046
0.088
0.666
?0.050
0.094
0.454
19
?0.017
0.694a ?0.023
0.363a
0.819
?0.027
0.369
0.677
20
0.183
0.491a
0.031
0.319b
0.615
0.039
0.321
0.512
21
2.287a
0.207a ?0.040
0.147
0.587
?0.112
0.155
0.351
22
1.404a
0.354a ?0.102
0.342b
0.668
?0.194
0.346
0.528
23
1.066c
0.585a
0.009 ?0.061
0.717
0.011 ?0.061
0.532
24
0.751d
0.604a ?0.052
0.138
0.782
?0.068
0.138
0.607
25
0.741d
0.521a ?0.025
0.179
0.722
?0.035
0.185
0.506
M
1.128
0.512
?0.034
0.163
0.702
?0.053
0.166
0.528
SD
0.797
0.126
0.072
0.143
0.069
0.113
0.145
0.090
a p <.0001, b p < .001, c p < .01, d p < .05

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
69
stimuli and responses is described by a power law, Jn =
Table 2: Mean R2 changes for each coef?cient.
kP ?
n . Jesteadt et al. developed the following approach
P
to second order sequential dependencies. First, regress
P
n?1+
n
Pn?1
Jn?1
J
log J
n?1
n on log Pn separately for each participant to obtain
values of k and ?. Second, normalize each response by
Experiment 1
0.491
0.013
0.024
0.037
dividing it by the value expected on the basis of the stim-
Experiment 2A
ulus and the overall power function parameters. Third,
0.416
0.011
0.028
0.039
(No feedback)
group the data according to the difference between log Pn
Experiment 2B
and log Pn?1 (the jump size). Finally, for each jump
0.493
0.026
0.010
0.036
(Feedback)
size, compute the relationship between the current (nor-
malized) response and the previous one, according to the
Note: predictors were log-transformed in Experiment 1.
equation:
J
J
log
n
= ? + ? log
n?1 +
(2)
see whether the mean of the (unstandardized) regression
kP ?
n
kI?
n?1
coef?cients collected from the 25 subjects reliably dif-
fered from zero (Lorch & Myers, 1990; see e.g., Ward,
We employed the same approach. (Recall that the
1985; 1987; 1990). For all three predictors (P
skewed distribution of prices in this experiment meant
n, Pn?1,
and J
that we used log-transformed variables, so a straight-
n?1) the mean coef?cients were signi?cantly differ-
ent from zero. As one would expect, the P
forward implementation of Jesteadt et al.’s (1977) ap-
n coef?cient
was positive, t(24) = 20.4, p < .001. The P
proach is appropriate.) We had to aggregate across jump
n?1 coef-
?cient was negative, t(24) = 2.33, p = .029, indicating
sizes to obtain a useable number of trials in each con-
contrast to the true price of the preceding item. Lastly, the
dition; we placed the values of log Pn ? log Pn?1 into
J
?ve bins such that, across the whole experiment, an ap-
n?1 coef?cient was positive, t(24) = 5.70, p < .001,
indicating that the current judgment assimilates towards
proximately equal number of observations fell into each
the previous judgment.
bin. For each bin size we calculated, separately for each
We conducted hierarchical regression, entering the pre-
participant, the correlation between log(Jn/kP ?
n ) and
dictors in the order P
log(Jn?1/kP ?
n, Pn?1, Jn?1, to establish the R2
n?1) . Figure 3 shows the mean correla-
increases for each (see Mori & Ward, 1995; Ward, 1979;
tion coef?cients. As one would expect with so few data
1987, for a similar approach). The mean R2 values (aver-
points, the correlation coef?cients are very noisy, and a
aged over participants) are shown in Table 2. The propor-
one-way within subjects ANOVA indicated no signi?cant
tion of variance attributable to events from the previous
effect of jump size, F (4, 96) < 1. However, inspection
trial is not huge, but is comparable to the results from
of the ?gure suggests slight evidence for the inverted v-
some psychophysical studies. For example, the “high in-
shaped pattern seen in psychophysical studies.
formation” condition of Ward’s (1979) magnitude esti-
mation experiment produced a total R2 change for the
2.2.4 Depth of sequential effects
events of the preceding trial of .019.
Finally, we tried ?tting a regression model which in-
cluded the events from two trials back as predictors; there
2.2.3 Second order effects
was no evidence for a consistent effect of Pn?2 or Jn?2.
The coef?cients were signi?cant for only a handful of
Studies of perceptual judgment have found that the cor-
participants (three showed a signi?cant positive effect of
relation between successive judgments depends upon the
Jn?2; none showed a signi?cant effect of Pn?2) and one
size of the difference between successive stimuli. When
sample t-tests on the mean coef?cients revealed no signif-
Pn and Pn?1 are similar, Jn and Jn?1 are highly corre-
icant effect of Pn?2 (M = 0.006, SD = 0.068, t(24) <
lated; as Pn and Pn?1 move further apart, the correlation
1) or Jn?2 (M = 0.040, SD = 0.112, t(24) = 1.77,
between responses drops away to zero (e.g., Baird, Green,
p = .089). Although these results hint that there might
& Luce, 1980; Jesteadt et al., 1977; Ward, 1979; 1982;
be an effect of Jn?2 on the current judgment, this was not
1985). Looking for such second order dependencies in
borne out in the subsequent experiments.
our data is problematic because of the small number of
trials. Nonetheless, we conducted an exploratory analy-
2.3 Discussion
sis.
The approach we took was based upon that used by
The results of Experiment 1 may be summarized as fol-
Jesteadt et al. (1977; see also Ward, 1979) in studies
lows. Firstly, participants’ judgments were correlated
of magnitude estimation, where the relationship between
with the true prices of the items, but this correlation was

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
70
Experiment 1
tal; participant’s judgments were biased towards the cen-
0.4
tre of the range. Thirdly, and most importantly, there
were sequential effects; the judgment on the nth trial de-
0.3
pended on the events of the previous trial. Speci?cally,
0.2
the current judgment was biased away from the true price
of the previous item but towards the judged price of that
0.1
item; this latter effect was particularly pronounced. These
0
results mimic those found in psychophysical judgments
(e.g., Jesteadt et al., 1977; Mori, 1998; Ward, 1987) and
-0.1
suggest that, just as for judgments about the physical as-
Correlation coefficient
-0.2
pects of very simple stimuli, the immediate experimental
-2
-1
0
1
2
context provides an important in?uence on complex judg-
ments about rich, multidimensional objects.
ln(Pn) - ln(Pn-1)
Experiment 1 has several limitations. The principal
problem is that the observed sequential dependencies are
Experiment 2A
open to a number of interpretations. It may be that the
0.4
assimilation to the previous judgment indicates the use
of that judgment as a point of reference (e.g., Laming,
0.3
1995). However, response assimilation might also appear
0.2
if participants simply have a tendency to repeat the pre-
vious response or a reluctance to move very far along the
0.1
judgment scale, as may occur if they are not fully engaged
0
with the task. In addition, it is unclear whether the results
-0.1
of Experiment 1 are speci?c to the stimuli and procedure
employed in this study.
Correlation coefficient
-0.2
We therefore conducted two more experiments using
-60 -40 -20 0 20 40 60
a different class of product (women’s footwear) and a
P
slightly different experimental procedure. The two new
n - Pn-1
experiments differed in whether or not the participants
Experiment 2B
were told the correct value of each product after they had
entered their judgment. In Experiment 2A, no such trial-
0.4
by-trial feedback was provided; in Experiment 2B, feed-
0.3
back was provided after every judgment. If the sequential
effects found in Experiment 1 arise because the previous
0.2
trial serves as a point of reference, the provision of feed-
0.1
back should exert a pronounced in?uence on the form of
these effects. In psychophysical tasks, feedback reduces
0
the dependency on the previous judgment and increases
-0.1
the dependency on the preceding stimulus (e.g., Mori &
Correlation coefficient
Ward, 1995; Ward & Lockhead 1971), presumably be-
-0.2
cause participants now use the true value of the previous
-60 -40 -20 0 20 40 60
item, rather than their own judgment of it, as a point of
Pn - Pn-1
reference (e.g., Stewart et al., 2005). If, on the other hand,
the response assimilation observed in Experiment 1 re-
Figure 3: Effect of jump size on correlation between suc-
sults from some non-speci?c effect, such as a tendency to
cessive responses. Error bars show 95% con?dence in-
repeat responses, the provision of feedback should make
tervals calculated for a within-subject design (Masson &
little difference.
Loftus, 2003). Note that in Experiment 1 (top panel), we
As an additional manipulation, we asked whether ex-
used log-transformed price and judgment values; in Ex-
pertise in?uences the form or magnitude of the sequen-
periments 2A and 2B we used raw values.
tial dependencies. It seems plausible that participants
who know more about the product being judged will be
less reliant on short-term comparisons and less likely to
far from perfect. Secondly, the regression line relating
show sequential effects; improving information about the
judgment to true price was rotated towards the horizon-
stimulus reduces the sequential dependencies in mag-

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
71
nitude estimation and perceptual identi?cation (Mori,
3.2 Results and Discussion
1998; Ward, 1979). Since the products to be judged were
items of women’s footwear, we examined the issue of ex-
The 8 practice trials were excluded from analysis. Partic-
pertise by comparing the results from male and female
ipants failed to enter a response within the 3s window on
participants.
a small minority of trials (2.2%). A handful of additional
responses (0.28% of the total test trials) were excluded
for the reasons described in Experiment 1.
3 Experiment 2A
3.2.1 Relationship between actual price and judged
Whereas in Experiment 1 the item to be judged stayed
price
on-screen until the participant entered a judgment, Ex-
periment 2A presented each item for a ?xed time (3s) and
As can be seen in Figure 1, the distribution of prices was
then provided a ?xed window for the participant to enter
much less skewed than in Experiment 1. (This more even
his or her judgment (another 3s). The time between suc-
distribution was fortuitous; the items were sampled at
cessive items was therefore ?xed, which is potentially im-
random from the Topshop website.) The top panel of Fig-
portant in judgment tasks (e.g., DeCarlo, 1992; Matthews
ure 4 plots the mean judgment for each item against the
& Stewart, in press).
item’s true price, and indicates a linear relationship be-
tween price and judgment, with errors which do not sys-
tematically vary with price. The results from individual
3.1 Method
participants showed the same patterns, and we therefore
used untransformed prices and judgments in the regres-
3.1.1 Participants
sion analyses for this experiment.
Twenty eight participants took part, 14 males aged 19-26
We regressed judged price on true price for each partic-
years (M = 21.0, SD = 1.9) and 14 females aged 19-22
ipant. The coef?cients were positive for all participants
(M = 20.1, SD = 0.9). All had been resident in the
and signi?cant for all but one. The participant-averaged
United Kingdom for at least the past 3 years.
data in Figure 4 suggest over-estimation of cheap prod-
ucts and under-estimation of expensive ones. The same
3.1.2 Stimuli
pattern appeared in individual participants’ data.
The stimuli were pictures of 110 items of women’s
3.2.2 Sequential Effects
footwear available from a popular high-street chain (Top-
shop). The prices of the items ranged from £6 to £140
As before, we examined sequential effects by ?tting the
(M = 58.33, SD = 27.27); the distribution of prices is
regression model described in Equation 1. (The ?rst trial
shown in Figure 1. The pictures were sampled from the
of each block was omitted from this analysis because the
Topshop website. All pictures measured 500x500 pixels
time since the presentation of the most recent item de-
and showed a single item of footwear on a white back-
pended on how long a break the participant took between
ground. The stimuli were shown on a 19” TFT monitor
blocks.) The regression coef?cients for each participant
with a resolution of 1280x1024 pixels viewed from ap-
are shown in Table 3.
proximately 50cm.
For every participant but one there is a signi?cant posi-
tive relationship between true price and judged price. For
3.1.3 Design and Procedure
the Pn?1 term, 17 coef?cients are negative (3 signi?cant)
and 11 are positive (1 signi?cant). For the Jn?1 term,
On each trial the participant was shown one picture and
26 are positive (12 signi?cant) and 2 are negative (neither
asked to judge the price of the item. Each item was shown
signi?cant). One sample t-tests on the coef?cients con-
for 3s and followed by a 3s window during which the par-
?rmed the impression given by the results from individual
ticipant typed his or her judgment. At the end of the re-
participants: There was a signi?cant positive dependence
sponse window the screen went blank for 1.5s before pre-
of judgment on actual price, t(27) = 16.1, p < .001,
sentation of the next item. Participants completed eight
a signi?cant negative dependence on the previous item’s
practice trials followed by three blocks of 34 test trials,
price, t(27) = 2.57, p = .016, and a signi?cant posi-
and were allowed to take a short break between blocks.
tive dependence on the previous judgment, t(27) = 6.51,
As the true prices of the items were always integers, par-
p < .001.
ticipants were instructed to enter their judgments to the
Unlike Experiment 1, the time between trials was con-
nearest pound. The order in which the 110 items were
stant in this experiment (with the exception of the self-
presented for judgment was randomized for each partici-
paced breaks between blocks), so we can use trial num-
pant.
ber as a measure of time and ask whether the observed

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
72
Table 3: Regression coef?cients for Experiment 2A (No feedback).
Unstandardized
Standardized
Participant
int
Pn
Pn?1
Jn?1
Pn
Pn?1
Jn?1
R2
1
8.609
0.507a ?0.124
0.179
0.649 ?0.152
0.179
0.428
2
13.835d
0.462a
0.025
0.321c 0.570
0.031
0.311
0.430
3
15.665c
0.344a ?0.278b
0.465a 0.445 ?0.356
0.462
0.378
4
12.132d
0.535a
0.017
0.136
0.699
0.021
0.132
0.525
5
15.936b
0.369a
0.010
0.092
0.624
0.017
0.089
0.402
6
8.956
0.326a ?0.034
0.239d 0.624 ?0.065
0.236
0.403
7
5.645
0.362a ?0.089
0.301c 0.663 ?0.162
0.296
0.497
8
11.169d
0.241a ?0.099
0.335c 0.438 ?0.180
0.336
0.278
9
0.272
0.537a
0.021
0.027
0.766
0.031
0.027
0.595
10
23.845a
0.289a ?0.087d
0.082
0.711 ?0.214
0.083
0.549
11
5.666
0.505a
0.032
0.118
0.629
0.040
0.121
0.391
12
23.386d
0.341c
?0.131
0.034
0.304 ?0.121
0.034
0.121
13
73.594a
0.354
?0.339
0.139
0.190 ?0.179
0.140
0.071
14
20.624b
0.481a
0.012 ?0.025
0.670
0.017 ?0.025
0.447
15
12.699d
0.862a ?0.120
0.060
0.791 ?0.110
0.058
0.635
16
7.017
0.481a
0.008
0.241d 0.721
0.012
0.236
0.624
17
5.544
0.687a ?0.127
0.197d 0.767 ?0.150
0.197
0.644
18
9.407b
0.196a ?0.014
0.113
0.649 ?0.048
0.115
0.443
19
?0.134
0.466a
0.122
0.071
0.593
0.154
0.073
0.384
20
10.051c
0.495a
0.001
0.105
0.790
0.002
0.104
0.668
21
9.173
0.323a
0.009
0.250d 0.472
0.013
0.261
0.256
22
0.607
0.384a
0.130d ?0.145
0.762
0.246 ?0.146
0.575
23
19.059a
0.396a ?0.036
0.036
0.832 ?0.073
0.035
0.696
24
5.465
0.318a ?0.026
0.199d 0.511 ?0.041
0.200
0.329
25
14.684a
0.334a ?0.046
0.219d 0.647 ?0.089
0.238
0.502
26
7.768
0.444a ?0.050
0.227d 0.595 ?0.067
0.235
0.398
27
10.631d
0.390a ?0.140d
0.385a 0.633 ?0.227
0.383
0.462
28
8.563
0.667a ?0.022
0.123
0.777 ?0.025
0.126
0.619
Mean
12.852
0.432
?0.049
0.162
0.626 ?0.060
0.162
0.455
SD
13.449
0.142
0.101
0.131
0.150 0.122
0.131
0.155
a p <.0001, b p < .001, c p < .01, d p < .05

---

Judgment and Decision Making, Vol. 4, No. 1, February 2008
Judgments of price
73
Experiment 2A - No Feedback
for Pn, t(26) = 1.05, p = .301; for Pn?1, t(26) = 1.44,
p = .163; for Jn?1, t(26) < 1).
140
Veridical
We examined second order effects using the approach
described for Experiment 1. The only modi?cation was
120
Regression
that, in keeping with the rest of our analyses for this ex-
100
periment, we assumed a linear relationship between stim-
ulus price and judgment, J
80
n = ?Pn + k. We therefore
examined the correlation between Jn ? (?Pn + k) and
60
Jn?1 ? (?Pn?1 + k). Similarly, we used Pn ? Pn?1
40
(rather than log Pn?log Pn?1) as a measure of jump size.
The results are shown in the middle of Figure 3. The in-
Mean Judgment (£)
20
verted v-shape seen in psychophysical studies is apparent
0
and the jump size effect is signi?cant, F (4, 108) = 3.54,
p = .009, ?2
0 20 40 60 80 100 120 140
p = .116.
Finally, we tried a regression model which included
events from two trials back as predictors. There was
Experiment 2B - Feedback
no evidence that either predictor in?uenced the current
judgment: For Pn?2, two of the 28 participants had sig-
140
ni?cantly positive coef?cients and one had a signi?cant
negative coef?cient; for J
120
n?2, one participant had a sig-
ni?cant positive coef?cient. One sample t-tests on the
100
mean coef?cients similarly revealed no effect of Pn?2
80
(M = 0.010, SD = 0.120, t(27) < 1) or Jn?2
(M = 0.015, SD = 0.110, t(27) < 1).
60
40
4 Experiment 2B
Mean Judgment (£)
20
0
Experiment 2B was virtually identical to Experiment 2A,
except that participants were told the true price of each
0 20 40 60 80 100 120 140
item after they entered their judgments. Feedback exerts
True Price (£)
a marked effect on perceptual judgments (e.g., Mori &
Ward, 1995), and the effects of feedback on the form of
Figure 4: Relationship between true price and judged
sequential dependencies illuminates the ways in which
price in Experiments 2A and 2B.
participants use local context to make their judgments
(Stewart et al., 2005).
response assimilation is due to systematic drift over the
4.1 Method
course of the experiment. We repeated the sequential ef-
fects analysis with trial number included as a predictor.
4.1.1 Participants
The mean coef?cient for the trial number term was not
Twenty eight new participants were recruited from the
signi?cant (M = ?0.019, SD = 0.075, t(27) = 1.30,
same population as Experiment 2A. None had partici-
p = .204). There was signi?cant assimilation to Jn?1,
pated in Experiment 2A and all were naive to the pur-
(M = 0.124, SD = 0.138, t(27) = 4.76, p < .001, and
poses of the experiment. Fourteen were males aged 19-25
contrast to Pn?1 (M = ?0.037, SD = 0.103), although
years (M = 20.8, SD = 1.7) and fourteen were females
the latter effect missed signi?cance (t(27) = 1.91, p =
aged 18-33 (M = 21.1, SD = 4.2).
.066). The response assimilation we observed therefore
does not seem due to systematic drift over the session, al-
though such effects are an important direction for study
4.1.2 Stimuli, Design, and Procedure
(Petzold & Haubensak, 2001).
The stimuli, design and procedure were identical to Ex-
We used independent-samples t-tests to examine
periment 2A, except that each item’s true price was
whether participant gender in?uenced the regression co-
shown for the ?rst 750-ms of the interval between the end
ef?cients. The results were not signi?cant for any of the
of the response window and the presentation of the next
coef?cients (for the intercept, t(26) = 1.73, p = .096;
item.

---