Obesity and the Consumption Underestimation Bias

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Obesity and the Consumption Underestimation Bias
PIERRE CHANDON
BRIAN WANSINK*
February 2, 2005

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*Pierre Chandon is Visiting Assistant Professor of Marketing at the Kellogg School, Northwestern
University, and Assistant Professor of Marketing at INSEAD, Boulevard de Constance, 77300
Fontainebleau, France. Tel: +33 1 60 72 49 87, Fax: +33 1 60 74 61 84, e-mail:
pierre.chandon@insead.edu. Brian Wansink is the Julian Simon Research Fellow and Professor of
Business Administration, of Nutritional Science, of Advertising, and of Agricultural and
Consumer Economics at the University of Illinois, Urbana-Champaign, 350 Wohlers Hall,
Champaign IL 61820-6980 USA, e-mail: wansink@uiuc.edu.

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ABSTRACT
We contend that people’s perception of the number of calories in a meal follows a compressive
psychophysical power function and therefore becomes less sensitive as the number of calories of
the meal increases. We show, mathematically and empirically, that this psychophysical model
solves two enigmatic cross-disciplinary findings: (1) why people systematically underestimate
their consumption and (2) why this consumption underestimation bias is more pronounced for
overweight people. Five experiments show strong support for the hypothesized model across pre-
and post-intake estimations, chosen and nonchosen meals, single and repeated estimations, and
separate and joint estimations. We also find that the psychophysical relationship between the
estimated and actual number of calories of a meal is independent of the respondent’s carelessness,
debiasing knowledge, impression management, or estimation anchor—four explanations that have
been invoked to explain consumption estimation biases. Our finding that calorie underestimation
is caused by meal size and not body size leads to innovative strategies to improve consumption
quantity estimations.

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According to the National Center for Health Statistics, 65% of U.S. adults are either obese1 or
overweight and the obesity epidemic costs $78.5 billion annually in adult medical expenditures
(Hedley et al. 2004). One factor contributing to increasing obesity rates in both America and
abroad is the well-documented tendency that people have to underestimate the number of calories
that they consume per meal (Brownell and Battle Horgen 2003). For example, a mere 5%
underestimation in a 2000 calorie-a-day diet (e.g., the number of calories contained in a glass of
juice) can lead a person to gain up to 10 extra pounds during a year (Newman 2004). In contrast to
the often volitional reasons invoked to explain this bias, we develop a psychophysical model of
calorie estimation that explains the pattern of the bias and offers innovative implications for
improving the accuracy of consumption estimations.
The general consumption estimation bias is robust across self-reported consumption, 24-hour
recall interviews, and food frequency questionnaires (Tooze et al. 2004). In a meta-analysis of 43
studies using the doubly labeled water (DLW) technique2 to objectively measure actual caloric
intakes, Livingstone and Black (2003) find a strong underestimation of consumption (–20% on
average), but wide variations across studies (–55% to +40%). This underestimation bias is even
more extreme for overweight people (Livingstone and Black 2003; Tooze et al. 2004). Although
overweight people eat significantly more than do people with normal weights, they often report
eating less than do people with normal weights (Shah and Jeffery 1991).
In consumer research, considerable progress has been made in understanding how people
process nutrition information (Andrews, Netemeyer, and Burton 1998; Balasubramanian and Cole
1 Following the guidelines of the World Health Organization, persons are classified as overweight if their body mass
index (BMI) is greater than 25 and obese if their BMI is greater than 30. BMI is computed as the ratio of weight,
measured in kilos, to squared height, measured in meters.
2The DLW technique involves the administration of water that contains enriched quantities of the “labeled” isotopes
deuterium (²H) and oxygen-18 (18O). The difference in the elimination rate between these two isotopes is measured by
urine samples taken on the first and last day of the study (typically, a two-week interval). These quantities yield a
measure of carbon dioxide, which can be used to calculate energy expenditure. If weight is maintained during the
study period, energy expenditure is equal to energy intake (Trabulsi and Schoeller 2001).

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2002; Burton and Creyer 2004; Moorman et al. 2004), estimate single consumption occasions
(Krider, Raghubir, and Krishna 2001; Raghubir and Krishna 1999; Wansink and Van Ittersum
2003), and handle health decisions (Moorman 2002; Moorman and Matulich 1993). However, we
still lack a good understanding of why people, especially those who are overweight, underestimate
the number of calories contained in the meals they consume. This is a critical question for
epidemiologists, nutrition researchers, and clinicians: “more fundamentally still, we need to
understand why people misreport food intake” (Livingstone and Black 2003, p. 915S), “the reason
for the association between BMI and underreporting is unclear” (Tooze et al 2004, p. 803), “our
inability to obtain good information on food intake [is] a dilemma for nutrition [but also] an
enigma for psychology’’ Blundell (2000, p. 3).
To address these questions, we develop and test a psychophysical model of calorie estimation
that offers a parsimonious, common explanation for the general underestimation bias and for its
association with obesity. Drawing on psychophysics research, we hypothesize that subjective
caloric content follows a mathematically predictable compressive power function (i.e., a power
function with an exponent lower than 1). That is, people’s subjective experience of the number of
calories of a meal becomes less sensitive as the number of calories of the meal increases. As a
result, people tend to overestimate the number of calories of small meals and fail to notice the
increase in the number of calories as the meals become larger, such that the underestimation bias,
even when measured as a percentage of the actual number of calories, increases as the size of the
meal increases. This suggests that the higher underestimation of overweight consumers might be a
spurious consequence of their tendency to consume larger meals. Once the natural confound
between body size and meal size is eliminated, our model predicts that overweight and regular
persons will have similar consumption estimation biases. In short, calorie underestimation is
caused by meal size, not body size

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This manuscript is organized as follows: We first develop a psychophysical model of calorie
estimation and mathematically show that it can explain the consumption underestimation bias and
the higher bias of overweight people. In Experiment 1, we show that people’s estimations of the
number of calories in a fast-food meal that they just consumed fit with the hypothesized
psychophysical model. Experiment 1 also shows that the difference in bias between overweight
and regular weight people disappears when the size of meal size is controlled for. In the following
four experiments, we replicate these findings in different field and laboratory contexts (pre-/post-
intake estimations, chosen/nonchosen meals, single/multiple observations, and separate/joint
estimations. We also show that the psychophysical bias is independent of the four possible
explanations evoked in the nutrition and epidemiology literature: the respondent’s carelessness
(Experiment 2), lack of debiasing knowledge (Experiment 3), impression management
(Experiment 4), and reliance on outdated estimation anchors (Experiment 5). In the general
discussion, we show that understanding the psychophysical basis of consumption estimation
biases provides some innovative strategies to help consumers, consumer researchers, nutritionists,
and epidemiologists better estimate actual consumption quantity.
A PSYCHOPHYSICAL MODEL OF CALORIE ESTIMATION
To estimate the number of calories consumed during a meal, consumers cannot simply read
nutritional labels, which usually are either absent or hard to find (e.g., provided on discarded
containers, not displayed in a restaurant). In addition, people often fail to pay attention to caloric
content information, even when food labeling is available, but prefer instead to rely on their own
estimations (Balasubramanian and Cole 2002). To help us understand how people estimate the
caloric content of a meal, we draw from a large body of research in psychophysics, which focuses
on the relationship between objective magnitudes and people’s subjective experience of them.
Relating Objective Magnitudes and Subjective Experience

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The “empirical law of sensation” was established by Stevens (1986) but first documented by
Plateau (1872), who discovered that a particular shade of grey always appeared to look “midway”
between black and white regardless of whether it was viewed in bright sunshine or in dim light.
Stevens Law, as it has come to be known, can be expressed as follows:
(1) ∆I/I = n∆S/S.
Equation 1 means that a percentage change in objective magnitude leads to the same
percentage change in subjective magnitude (i.e., equal ratios of intensity are associated with equal
ratios of sensations). The empirical law of sensation predicts that the subjective impact of adding
100 calories to a meal, for example, depends on the size of the meal, but the subjective impact of
doubling the number of calories of a meal is constant, regardless of its size.
Replacing the finite differences in Equation 1 with their corresponding differentials and
integrating both sides yields ln(S) = nln(I) + ln(k), where k is a constant of integration. The
resulting psychophysical function (the mathematical relation between objective magnitudes and
people’s subjective experience of them) is the following power function:
(2) S = aI
n,
where S is the subjective magnitude (or sensation), I is the objective magnitude (or intensity), and
a is a scaling parameter. The exponent n captures the concavity of the power function (i.e.,
whether subjective magnitudes are compressive or expansive). This latter definition is easy to
perceive; if I is multiplied by r, S is multiplied by rn. When n = 1, subjective magnitudes grow as
fast as objective magnitudes. In the special case when a = n = 1, estimations are unbiased (people
are as likely to overestimate as they are to underestimate the actual magnitude). If n < 1, subjective
magnitudes increase at a slower rate than do actual magnitudes, and consumers are more likely to
underestimate magnitudes as they increase. The reverse occurs if n > 1, in which case estimations
grow more rapidly than actual magnitudes and consumers become more likely to overestimate

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quantities as they increase. From Equation 2, we can derive the intensity level at which sensations
are on average accurate (I* = a1/(1 – n)), which also represents the magnitude toward which
sensations are compressed if n < 1.
Calorie Estimations as a Compressive Power Function of Actual Number of Calories
With few exceptions (such as with the perception of the intensity of electric shocks),
sensations are always compressive (Poulton 1989). As Krueger (1989) states, “the true
psychophysical function is approximately a power function whose exponent normally ranges from
0 to 1, and exceeds 1 only in rather special cases.” For example, people perceive that a second
candle adds less brightness than a first candle. Similarly, we also expect that calorie estimations
will follow a compressive power function of the actual number of calories. This expectation
implies that (1) the range of sensations is smaller than the range of stimuli intensity and (2)
sensations increase at a slower rate than intensities. According to the first condition, the accuracy
level I* belongs to the range of observed intensities (i.e., min(I) < I* < max(I)), so that large
intensities (greater than I*) are compressed downward toward I*, whereas small intensities (less
than I*) are compressed upward toward I*. The second condition implies that the exponent of the
power function is smaller than 1 (n < 1). Both are testable predictions.
We expect that our hypothesis will hold for calorie estimations obtained in absolute estimation
tasks, in which consumers directly estimate the number of calories of a meal that they can see in
front of them. . Such a context would minimize a participant’s reliance on their memory and
therefore reduces the biases caused by memory-based estimation strategies (Menon and Raghubir
1995). Absolute magnitude estimation tasks also produce fewer context and response biases than
do traditional relative magnitude estimation tasks, which ask people to compare a stimuli’s
intensity with that of a standard (Gescheider, Bolanowski jr., and Verillo 1992). We use calories
instead of other quantity measures because we can then compare estimations across a variety of

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foods and beverages that otherwise would need to be measured with different units (e.g., ounces,
grams, liters, fluid ounces). In addition, the number of calories in any food is large enough that the
biases cannot be driven by left-truncation at 0 (unlike the number of units or servings). Finally,
unlike other measures of volume, calorie measurement employs a metric ratio scale that is
familiar, easy to use, and directly meaningful for dieting decisions.
We also expect that the hypothesized psychophysical function, because it is driven by low-
level perceptual processes, holds in different contexts, as is supported by the well-established
robustness of power laws in psychophysics research (Krueger 1989). This robustness is also
necessary to explain the magnitude of the biases found in the literature. For example, if pre-intake
estimations were refuted by post-intake sensory experiences, consumers should eventually learn to
correct their biases. We therefore expect that calorie estimations follow a compressive power
function of the actual number of calories whether the estimations are made pre- or post-intake, for
chosen or randomly assigned meals, for single or repeated estimations, and while evaluating meals
separately or comparing their calorie content.
Implications for Consumption Estimation Biases
Biases in calorie estimation are measured as either the percentage deviation from actual caloric
content (PDEV) or the log ratio of estimated to actual calories (LNRATIO). Both measures are
closely related (LNRATIO = ln(S/I), and PDEV = (S–I)/I; hence, LNRATIO = ln(PDEV + 1)). We
use the more intuitive measure, PDEV, to quantify the magnitude of bias in descriptive analyses
but use LNRATIO in the modeling analyses because, unlike PDEV, it is a linear function of the
logarithm of actual consumption quantity if Equation 2 holds (if S = aIn, LNRATIO = ln(aIn/I) = α
+ β*ln(I), where α = ln(a) and β = (n – 1)). The derivatives of PDEV and LNRATIO with respect
to I are both negative if n < 1 (d(LNRATIO)/d(I) = (n – 1)/I, and d(PDEV)/d(I) = (n – 1)I n – 2,
which are both negative if n < 1). Therefore, both measures of bias decrease (i.e., the

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underestimation bias becomes stronger) as actual consumption quantity increases. If, in addition,
min(I) < I* < max(I), the estimated number of calories is greater than the actual number of calories
for small meals and becomes smaller than the actual number of calories for meals above the
accuracy level I*.
--- Insert Figure 1 about here ---
To illustrate how estimation biases reverse as the number of calories increases, we present
Figure 1A, which plots estimated calories S as a function of actual calories I for psychophysical
functions with varying degree of compression. As Figure 1A shows, estimated consumption starts
above the accuracy line and then drops below it as the number of calories increases. Figure 1A
also shows that, as the power exponent n decreases, calorie estimations curves flatten (i.e.,
estimations are less sensitive to actual consumption quantities), and the number of calories at
which estimations are accurate decreases (in Figure 1, I* = 1375 cal when n = .6, and I* = 124 cal
when n = .4). Figure 1B shows the same effects on estimation biases (measured by LNRATIO).
When calorie estimations follow a compressive power function, LNRATIO is a downward-sloping
linear function of the actual number of calories (measured in logs) and the slope is steeper when
the degree of compression is higher (i.e., when n is small).
The empirical finding that overweight people underestimate their consumption more than do
regular weight people appears directly in Figure 1. Overweight persons tend to consume larger
meals than regular weight persons (Subar et al. 2003), which means their estimations pertain to
larger meals, which in turn are more likely to be underestimated, because estimations are
compressive than are the smaller meals consumed by people with regular weights. However, as
Figure 1 shows, the stronger estimation bias of overweight persons can occur even if they rest on
the same psychophysical curve as regular weight people. In other words, no intrinsic differences
between overweight and regular weight persons are required to explain this empirical finding. This

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leads us to the testable prediction that, when the natural confound between people’s body mass
and consumption quantity is eliminated, overweight and regular weight consumers should exhibit
similar consumption estimation biases. For example, Figure 1 shows that if both groups are asked
to estimate the same meal—not the distinct meals they normally would choose—their estimates of
the number of calories it contains would be similar.
Finally, Figure 1 shows why most studies find a strong consumption underestimation bias,
whereas only a minority find consistent overestimation biases. In natural settings, when a broad
cross-section of people are surveyed, the distribution of actual consumption quantity is right
skewed (most observations are below average but a few large values increase the average actual
consumption quantity, Dwyer, Picciano, and Raiten 2003). In these circumstances, the few very
large consumption quantities that skew the mean actual consumption quantity are strongly
compressed and do not skew the average estimated consumption as much. As a result, the average
estimated consumption is lower than the average actual consumption. However, when only a
subset of people or consumption occasions with small consumption quantities are surveyed, the
reverse finding may appear. For example, Livingstone and Black’s (2003) review identifies three
groups with a tendency to overestimate or accurately estimate consumption: persons with a very
low BMI, children aged 6–12 years, and parents estimating the consumption of their children aged
1–6 years. A common characteristics of these three groups is that they consume smaller quantities
than the average person, thus leading to the absence of a general underestimation bias.
EXPERIMENT 1: ESTIMATING CALORIES OF A FAST-FOOD MEAL
The objective of Experiment 1 is to test our central hypothesis that calorie estimations follow a
compressive power function of the actual number of calories in the natural setting of fast-food
restaurants. Experiment 1 also tests our prediction that the higher biases of overweight consumers
are due to their choice of meals that have higher caloric content.

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Method
Trained interviewers approached every fourth person as they were finishing their meals in food
courts operated by different fast-food restaurants in three medium-sized Midwestern U.S. cities
and asked them if they would answer some brief questions for a survey. No mention was made of
food at that time. Of the 200 people who were approached, 147 (73.5%) agreed to participate.
They were first asked what they ate and drank for their meal and to estimate the number of
calories contained in their entire meal. They then answered a few questions about their eating
habits and provided their height (in feet and inches) and weight (in pounds), which were used to
compute their BMI. During this process, the interviewer unobtrusively recorded and confirmed the
type and size of the food and drinks from the packages left on the tray. Nutrition information
provided by the fast-food restaurants then was used to compute the actual number of calories of
each person’s meal.
Unlike DLW, direct observation by trained field researchers allows for unobtrusive
measurements of actual consumption quantities in the field but still yields accurate measures of
dietary intake (Hise et al. 2002). Of the 147 respondents, 91 were classified as regular weight and
56 as overweight on the basis of their self-reported height and weight.
Results
On average, participants underestimated the caloric content of their meal (MS = 613 cal versus
MI = 838 cal, PDEV = –17.5%, t = –7.45, p < .001). However, this average underestimation hides
large differences that depend on the number of calories of the meal. After we dichotomized meals
with a median split, we found that the number of calories of small meals was more accurately
estimated (MS(small meals) = 484 cal versus MI(small meals) = 508 cal, PDEV(small meals) = –.55%, t = –.1, p
= .92), whereas the caloric content of large meals was strongly underestimated (MS(large meals) = 743
cal versus MI(large meals) = 1173 cal, PDEV(large meals) = –34.59%, t = –10.4, p < .001). Respondents

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estimated that larger meals contained, on average, 259 more calories than did smaller meals,
though in reality, they contained 665 more calories, more than twice the estimated amount. We
illustrate these results in Figure 2A, which shows that estimations tend to be above the accuracy
line for small meals but grow more slowly than actual caloric content, so that they quickly fall
below the accuracy line as consumption quantities increase.
--- Insert Figure 2 here ---
Figure 2B shows that the average estimation bias (measured by LNRATIO) for each quartile of
actual quantity forms a straight line, which suggests that consumption estimations follow a power
function of actual consumption. To test this possibility directly, we estimated the power model
shown in Equation 1. The power model fit the data well (R² = .28, F(1, 145) = 55.4, p < .01), and
as we show in Figure 2B, the predicted values fall well within the confidence intervals. To
examine whether the power model fit the data better than a linear model, we computed the mean
average percentage error (MAPE) of the power model and of a linear model (R² = .23, F(1, 145) =
43.7, p < .01). As we expected, the power model fit significantly better than the linear model
(MAPE(Power model)= .38 versus MAPE(Linear model) = .43, t = 4.32, p < .01). The best-fitting power
model is S = 17.0*I.52. As expected, the exponent of the model is significantly lower than 1 (t-test
of difference from 1 = –6.76, p < .001), and the intersection point is within the range of intensities
(Min(I) = 180 cal < I* = 384 cal < Max(I) = 1921 cal). Consistent with our hypothesis, these
results show that calorie estimations are compressive, in support of our hypothesis.
Biases for Overweight and Regular Weight Participants. As we expected, the underestimation
bias is more pronounced for overweight (OW) than for regular weight (RW) consumers (PDEVOW
= –30.38% versus PDEVRW = –9.5%, F(1, 145) = 8.90, p < .001). Estimations by overweight
consumers were not statistically different from those of regular weight consumers (MS(OW) = 634
versus MS(RW) = 600, F(1, 145) = .44, p = .51), though their actual consumption was 266 calories

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higher (MI(OW) = 1003 versus MI(RW) = 737, F(1, 145) = 17.0, p < .001). What explains this result?
Because they eat larger meals, the estimations of overweight consumers (black dots) tend more
toward the right in Figure 2A than the estimations of regular weight participants (white dots).
They are therefore on the flatter part of the estimation curve, for which estimations are much
smaller than is accurate. As we show in Figure 2B, the biases (measured by LNRATIO) of
overweight and regular weight consumers fall on the same line. This shows that, when the number
of calories of a meal is controlled for, overweight and regular weight consumers make the same
estimation mistakes.
To test the hypothesis that the differences between overweight and regular weight consumers
are mediated by the number of calories in their meals, we estimated two structural equation
models. In the first, we test the direct effect of a consumer’s overweight status (captured by a
binary variable OW) on estimation biases (measured by LNRATIO). When entered alone, OW is a
significant predictor of LNRATIO (B = –.26, t = –3.2, p < .001). We then estimate the second
model, in which OW has both a direct effect on LNRATIO and an indirect effect through its effect
on actual consumption quantity (I, measured in logs), which itself influences estimation biases. As
we expected, the direct effect of OW on LNRATIO is not statistically significant (B = –.12, t = –
1.6, p = .11), but OW has an indirect effect on LNRATIO because it increases ln(I) (B = .31, t =
3.74, p < .001), which itself decreases LNRATIO (B = –.44, t = –6.0, p < .001). These results show
that, after we control for meal size, there are no differences in the estimation biases of overweight
and regular weight participants.
Discussion
Experiment 1 shows a strong consumption underestimation bias in the context of a single
meal, minutes after the meal is finished and when consumers know that their estimates can be
checked. These result are important because they replicate those of DLW studies and disconfirm

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some researchers’ expectations that biases will disappear when consumers estimate simple meals
or when they believe that their estimations can be readily checked for accuracy (Muhlheim et al.
1998). In addition, Experiment 1 provides strong support for our hypothesis that calorie
estimations are a compressive power function of the actual number of calories. Moreover, it shows
that biases in consumption estimations are stronger for larger meals, even when measured relative
to total quantity, and that the stronger underestimation of overweight consumers is entirely due to
the larger meals they consume. Unlike DLW studies, which operate across a longer time period,
the setting of Experiment 1 precludes the alternative explanation that the size of the meal explains
differences in body mass between overweight and regular weight participants.
The main limitation of Experiment 1 is that it does not rule out carelessness as a driver of the
results. The burden of recording and estimating consumption may lead people to omit food
occasions or alter their reported intake for convenience, especially when consumption quantity is
high (Livingstone and Black 2003). Participants in Experiment 1 might not have been sufficiently
motivated to engage in the effortful estimation strategies that would have produced unbiased
estimations. In addition, the larger meals may have been more difficult to estimate because they
included more food items (such as desserts) or harder-to-estimate items (such as multi-component
sandwiches), not just because of their larger number of calories. Finally, because of self-selection,
Experiment 1 may have included too many participants who cared little about nutrition or the
accuracy of their estimations.
Existing evidence on the effects of carelessness is limited and mixed (Macdiarmid and
Blundell 1997; Mela and Aaron 1997). Heymsfield et al. (1995) find that participants’ self reports
were more accurate for a single meal (for which 86% of actual intake was reported) than for a
more burdensome two-week period (for which only 52% of actual intake was reported). Still, these
results show that consumption underestimation persists even when estimating and reporting

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consumption is easy. It is therefore important to directly test whether respondent’s carelessness
can explain the results of Experiment 1.
EXPERIMENT 2: EFFECTS OF ESTIMATION CARELESSNESS
The objective of Experiment 2 is to test whether the results of Experiment 1 are caused by
respondents’ carelessness in remembering or in estimating some of the food they consumed,
especially for larger meals. Because psychophysical biases are driven by low-level perceptual
processes, we expect that the degree of compression is independent of carelessness. In other
words, we expect that carelessness has only a main effect on calorie estimations (and estimation
biases) but does not interact with the effects of the actual number of calories.
Method
In Experiment 2, we used the same procedure as in Experiment 1, except that the care with
which respondents recorded and estimated the number of calories of their meal was measured. We
first asked participants: “Did you pay attention to nutritional information here?” and provided two
possible answers (yes or no). We also asked respondents to rate their agreement with two
sentences (“I watch what I eat” and “I pay attention to how much I eat”) on a nine-point scale
anchored at 1 (“strongly disagree”) and 9 (“strongly agree”). Averaging their answers to these
three questions produced a reasonably reliable scale (α = .67). We then categorized respondents as
relatively careful or careless through a median split. Because ours is a null hypothesis, we
minimized the risk of type II error by collecting data from a greater number of respondents than
we did in Experiment 1 (n = 352 participants).
The second difference is that we did not ask respondents to report their height or weight. This
omission enables us to explore whether the results of Experiment 1 hold in a context that generates
less motivation to engage in impression management (we carefully examine the effects of
impression management in Experiment 4). To verify this, we asked 153 consumers similar to

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those who participated in Experiments 1 and 2 to rate the extent to which someone like them,
participating in each study, would be concerned about being evaluated unfavorably and motivated
to answer the estimation questions accurately.3 As we expected, Experiment 2 elicited less fear of
negative evaluation than did Experiment 1 (M(Experiment 2) = 6.6 versus M(Experiment 1) = 7.8, F(1,151)
= 22.2, p < .001), as well as more motivation to answer the estimation questions accurately
(M(Experiment 2) = 4.9 versus M(Experiment 1) = 4.0, F(1,151) = 6.0, p < .05). The increase in the response
rate (from 73% to 82%, χ² = 4.5, p < .05) also attests to the lower social demands of Experiment 2.
Results
Replications. The results of Experiment 1 were replicated. On average, participants
underestimated the number of calories of their meal (MS = 618 cal versus MI = 830 cal, PDEV = –
18.53%, t = –8.7, p < .01), though as in Experiment 1, the underestimation bias was smaller for
small meals (MS(small meals) = 485 cal versus MI(small meals) = 508 cal, PDEV(small meals) = –7.18%, t = –
2.1, p < .05) than for large meals (MS(large meals) = 781 cal versus MI(large meals) = 1152 cal, PDEV(large
meals) = –29.88%, t = –12.8, p < .001), and the difference in the magnitude of the bias between
small and large meals was statistically significant (F(1, 350) = 30.8, p < .001). Also as in
Experiment 1, the power model fit the data better than a linear model (power model: R² = .34, F(1,
350) = 178.7, p < .001; linear model: R² = .31, F(1, 350) = 154.2, p < .001), and the difference in
predictive validity between the two models was statistically significant (MAPE(power model) = .48
versus MAPE(linear model) = .42, t = 5.7, p < .01). The best-fitting power model is S = 5.7*I.69. As we
expected, the exponent is less than 1 (t = –5.6, p < .01), and the intersection point is within the
3We measured fear of negative evaluation by averaging the answers to the following four items: “This person would
worry about what her answers would say about her,” “This person would find these questions embarrassing,” “This
person would feel uncomfortable answering these questions,” and “This person would prefer that no one knew her
estimations.” The motivation to estimate consumption accurately was measured with two items: “This person would
try hard to be accurate” and “This person would be very motivated to answer accurately.” All measures were anchored
at 1 = “strongly disagree” and 9 = “strongly agree.” Both measures are reliable (α = .93 and α = .82, respectively).

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range of intensities (Min(I) = 140 cal < I* = 274 cal < Max(I) = 2455 cal), in support of our
hypothesis that calorie estimations follow a compressive power function.
--- Insert Figure 3 here ---
Effects of carelessness. As we expected, the underestimation bias was, on average, smaller for
more careful participants (MS(careful) = 545 cal versus MI(careful) = 686 cal, PDEV(careful) = –13.93%, t
= –4.6, p < .01) than for less careful consumers (MS(careless) = 689 cal versus MI(careless) = 957 cal,
PDEV(careless) = –22.41%, t = –7.3, p < .01), and the difference in the magnitude of the bias
between the two groups was statistically significant (F(1, 350) = 3.9, p < .05). However, these
numbers also show that more careful respondents consumed smaller meals (F(1, 350) = 42.1, p <
.001) than less careful consumers. Therefore, the lower bias of these more careful respondents
may be driven by their lower consumption, not by intrinsic differences between the groups. We
directly test this hypothesis by estimating the following model:
(3) LNRATIO = α + β*ln(I) + γ*CARE + δ*ln(I)*CARE,
where CARE is a mean-centered binary variable that indicates whether consumers were careful,
and ln(I) is the mean-centered log of the actual number of calories.
Instead of estimating Equation 3, we could estimate the power model in Equation 2, in which
estimated consumption is the dependent variable, with an interaction between CARE and I.
However, the advantage of Equation 3 is that it can be represented as a well-known linear model
and thus shows the interaction effects more easily than does a multiplicative power model. The
coefficient for ln(I) was, as we expected, negative and statistically different from 0 (β = n – 1 = –
.31, t = –5.57, p < .001). Neither of the two other coefficients was statistically significant (γ = .03,
t =.47, p = .64; δ = –.03, t = –.28, p = .78). After we control for actual consumption quantity,
respondents who care about what and how much they eat have the same biases as respondents who

19
do not care. We also demonstrate this finding in Figure 3; the point estimates for careful and
careless consumers are almost perfectly aligned.
Discussion
Experiment 2 shows that the compression of calorie estimations is independent of the amount
of care a person devotes to recording and estimating his or her consumption. It also provides
another illustration of the misleading results that emerge when we compare biases across groups
that differ in their average consumption quantity. To measure whether careful and careless
respondents really have different estimation biases, one needs to compare their estimations for
meals of similar quantity.
One limitation of Experiment 2 is that it does not rule out that the results may be driven by
respondents’ lack of information about the bias. Consumers—and researchers—have no intuition
that they typically underestimate consumption quantity at such a high degree, especially for larger
meals (Livingstone and Black 2003). In support of this explanation, Livingstone and Black (2003)
find less underestimation bias among educated people. However, a related stream of research
shows that consumers’ biases in the estimation of the volume contained in or consumed from a
glass (Folkes and Matta 2004; Raghubir and Krishna 1999; Wansink and Van Ittersum 2003), of
surfaces (Krider et al. 2001), or even distances (Raghubir and Krishna 1996) are mostly automatic
and unconscious. Raghubir and Krishna (1996) find that making people aware of the direct-
distance bias actually increases the prevalence of the bias. It is therefore important to directly test
whether lack of information about estimation biases can explain the results of Experiment 2.
EXPERIMENT 3: EFFECTS OF DEBIASING INFORMATION
The objective of Experiment 3 is to test whether the results of Experiments 1 and 2 may be due
to respondents’ lack of knowledge about the biasing effects of meal size. Following the same
reasoning that we used for carelessness, we expect that, debiasing information will only have a

20
main effect (no interaction) on calorie estimations and estimation biases. In addition, Experiment 3
enables to test whether the results of Experiments 1 and 2 hold for pre-intake estimations. Because
they apply to multiple meals, not just the chosen meal, pre-intake estimation biases are more
frequent and influence more consumption decisions than do post-intake estimations. Studying pre-
intake estimations also reduces potential confounds due to product taste, meal duration, or meal
completion. Finally, we conduct Experiment 3 in a more controlled environment than that of
Experiments 1 and 2.
Method
In Experiment 3, we use a between-subjects design in which respondents are assigned to either
a control condition (replicating the instructions of Experiments 1 and 2) or a debiasing condition
(in which they were warned of the consumption underestimation bias). To rule out potential self-
selection biases, we conducted Experiment 3 in a laboratory context and obtain estimations from
all participants. To rule out differences in the recording burdens of different sized meals, all meals
included the same thee items (sandwich, fries, and soda), and only the quantity of each item was
varied. To reduce the motivation to engage in impression management, estimations were fully
private (i.e., participants wrote down their estimations instead of publicly verbalizing them to the
interviewer). In addition, we motivated respondents to provide accurate estimations by telling
them that the three most accurate respondents would be publicly announced and would be awarded
$50 gift certificates to a local book store.
Respondents were 120 university students who participated in the study to fulfill course
requirements (79 participants in the control condition, 41 in the debiasing condition). In one room,
participants viewed nine different items of a fast-food meal disposed in a 3 × 3 matrix. Each row
showed one of the three ingredients of the meal: chicken nuggets, fries, or cola purchased at a
local fast-food restaurant. Each ingredient was available in three sizes—A, B or C—that formed

21
the columns of the matrix. Chicken was available in 3 (A), 6 (B), or 12 (C) nuggets; fries were
available in 1.45 oz. (A), 2.90 oz. (B), or 5.8 oz. (C) sizes; and the soda, a regular, full-calorie
cola, was available in 10 fl. oz. (A), 20 fl. oz. (B), or 40 fl. oz. (C) sizes. The food items were
shown on generic paper plates or glasses with no information about their weight or volume.
Participants were instructed to imagine that they were going to order a chicken nugget meal
and asked to indicate which size (A, B, or C) of the sandwich, fries, and beverage they would
order. Participants in the debiasing condition were told that “when people estimate the number of
calories in the food they select, they nearly always underestimate how many calories are in their
food. The larger the meal, the more they underestimate. For instance, for a 300 calorie meal,
people are fairly accurate, but if it is a 1500 calorie meal, they tend to underestimate by 30%.
Knowing this, what is the total number of calories you think are contained in the meal you
selected?”. Participants in the control condition were simply asked: “What is the total number of
calories you think are contained in the meal you selected?” Finally, all participants indicated their
height and weight. In the control condition, 53 participants were classified as regular weight and
26 as overweight (because the sample is small, we do not distinguish between regular weight and
overweight participants in the debiasing condition).
In a manipulation check, 155 consumers similar to those who participated in Experiments 1
and 2 indicated that Experiment 3 elicited less fear of negative evaluation than did Experiment 2
(same measures as in the previous pretest, M(Experiment 3) = 3.6 versus M(Experiment 2) = 6.6, F(1,152) =
94.3, p < .001) and a higher motivation to answer the estimation questions accurately (M(Experiment 3)
= 6.8 versus M(Experiment 2) = 4.9, F(1,152) = 29.9, p < .001). The procedure thus was successful in
increasing the chances that the results of Experiment 3 are not simply due to impression
management or carelessness.
Results

22
Replications. The results from the participants in the control condition replicated all the results
of Experiments 1 and 2. On average, there was a significant underestimation in the number of
calories (MS = 866 cal versus MI = 991 cal, PDEV = –7.65%, t = –2.0, p < .05), albeit less strong
than in Experiments 1 and 2, probably because of the great effort we undertook to increase care
and reduce impression management. The caloric content of small meals was accurately estimated
(PDEV(small meals) = 3.08%, t = .70, p = .49), whereas that of large meals was strongly
underestimated (PDEV(large meals) = –26.16%, t = –4.5, p < .001), and the difference was statistically
significant (F(1, 77) = 16.0, p < .001), and as in the previous studies, a power model fit the data
better than the linear model (power model: R² = .08, F(1, 77) = 7.0, p < .01; linear model R² = .07,
F(1, 77) = 5.7, p < .05), and the difference in predictive validity between the two models was
statistically significant (MAPE(power model) = .30 versus MAPE(linear model) = .33, t = 3.0, p < .01). The
best-fitting power model is S = 71.0*I.36. Its exponent is significantly lower than 1 (n = .355, t = -
4.8, p < .001), and the intersection point is within the range of intensities (Min(I) = 445 cal < I* =
742 cal < Max(I) = 1780 cal).
As in Experiments 1 and 2, we found greater underestimation by overweight consumers (MS =
902 cal versus MI = 1166 cal, PDEV = –17.90%, t = –2.5, p < .05) than by regular weight
consumers (MS = 848 cal versus MI = 905 cal, PDEV = –2.63%, t = –.6, p = .56). When it is the
only predictor of LNRATIO, the coefficient of the binary variable OW is negative and statistically
significant (B = –.21, t = –2.2, p < .05), but when we add the actual number of calories (ln(I)) to
the regression, the direct effect of OW on LNRATIO becomes insignificant (B = –.06, t = –.6, p =
.53), though OW significantly increases ln(I) (B = .25, t = 3.6, p < .001), which in turn
significantly influences the estimation biases (B = –.61, t = –4.2, p < .001). The estimations of
overweight and regular weight consumers therefore are similar when we control for the number of

23
calories of the meal they select. As we show in Figure 4, the biases of overweight and regular
weight consumers in the control condition fall on the same line.
--- Insert Figure 4 here ---
Effects of Debiasing Information. Participants in the debiasing condition selected meals with
the same number of calories as did participants in the control condition (MI(debias) = 985 cal versus
MI(control) = 991 cal, F(1, 118) < .1, p = .91). However, the estimates were significantly higher in
the debiasing condition than in the control condition (MS(debias) = 1097 cal versus MS(control) = 866,
cal, F(1, 118) = 12.4, p < .001). That is, the debiasing information was successful in eliminating
the consumption underestimation bias and even led to a small overestimation bias (PDEV(debias) =
17.60% versus PDEV(control) = –7.65%, F(1, 118) = 11.7, p < .001). If we consider small and large
meals separately, however, debiasing information does not eliminate compression. Even in the
debiasing condition, there was more underestimation for large meals than for small meals
(PDEV(small meals) = 32.66% versus PDEV (large meals) = –1.65%, F(1, 39) = 6.6, p < .05), which is
consistent with our hypothesis. To test this finding directly, we estimated the following model:
(4) LNRATIO = α + β*ln(I) + γ*DB + δ*ln(I)*DB,
where DB is a mean-centered binary variable that indicates whether consumers were in the
debiasing (DB = .64) or control (DB = -36) conditions, and ln(I) is the mean-centered log of the
actual number of calories. Across both conditions, the coefficient for actual caloric content is
negative and strongly statistically different from 0 (β = –.63, t = –5.78, p < .001). The coefficient
for the simple effect of the debiasing manipulation is positive (γ = .24, t = 3.49, p < .001) and
thereby indicates less underestimation overall in the debiasing condition than in the control
condition. Finally, the coefficient of the interaction is not statistically significant (δ = .05, t = .20,
p = .84), so the degree of compression in calorie estimations is the same in both the control and the
debiasing conditions. We demonstrate the main effect and lack of interaction for the debiasing

24
manipulation in Figure 4 with the parallel lines that represent the model predictions for the control
and debiased conditions. (Figure 4 does not report results for regular weight and overweight
consumers separately because of the limited number of observations.)
Discussion
Experiment 3 shows the robustness of the findings of Experiments 1 and 2, even when
consumers make their estimations before intake and in a context with a 100% response rate, a low
and controlled estimation burden, strong incentives for accuracy, and little incentive for
impression management. In addition, Experiment 3 shows that providing information about
consumption underestimation biases only shifts the mean calorie estimations upward. Despite
learning that estimation biases are stronger for larger meals, participants in Experiment 3
continued to underestimate large meals more than they did small meals, and the degree of
compression of calorie estimation remained constant.
One limitation of Experiment 3, however, is that it does not eliminate the possibility that the
results may be caused by impression management (Leary and Kowalski 1990). Impression
management may explain the consumption underestimation bias because of the widespread belief
that maintaining a low body weight and eating less are socially rewarded (Muhlheim et al. 1998).
It also may explain the greater underestimation by overweight consumers, for whom the perceived
social pressure to minimize consumption is highest (Crandall 1994).
Explanations involving impression management have received generally mixed support.
Muhlheim et al. (1998) attempt to reduce the motivation to engage in impression management by
telling respondents that their two-week self-reports would be verified by DLW. However, this
“bogus pipeline” procedure increased self-reported consumption from 55% to only 61% of true
quantity. McKenzie et al. (2002) tried to reduce the motivation for impression management by
using overweight interviewers, but this method failed to improve estimation accuracy. However,

25
other studies found no relationship between social desirability and consumption estimation biases
(Horner et al. 2002; Tooze et al. 2004). It is therefore important to directly test whether impression
management can explain the results of Experiment 3.
EXPERIMENT 4: EFFECTS OF IMPRESSION MANAGEMENT
The objective of Experiment 4 is to test whether the results of Experiments 1–3 might be due
to impression management. Following the same reasoning that we provided for the other
alternative explanations, we expect that impression management has only a main effect on calorie
estimations (and estimation biases) but does not interact with the effects of the actual number of
calories. In addition, Experiment 4 enables us to examine whether our results hold when
participants make repeated estimations of different meals rather than a single estimation of a
chosen meal (as in Experiments 1–3).
Method
In Experiment 4, we recruited 55 students from a university campus and asked them to
estimate the number of calories of the same eight meals. This procedure makes meal size
independent of people’s BMI. If, as we argue, the stronger underestimation biases of overweight
consumers are due to their selection of larger meals, there should be no differences between the
estimations of overweight and regular weight consumers in Experiment 4, because everyone is
estimating the same meals. In addition, we measured the motivation to engage in impression
management by measuring social desirability, a personality trait linked to the motivation to engage
in impression management (Crowne 1991; Leary and Kowalski 1990).
Each meal consisted of a sandwich, fries, and colas in different quantities, and total calories
ranged between 190 and 1480. The eight meals were displayed on separate tables, and the order in
which they were viewed was random across participants. Participants provided their height and
weight, which enabled us to split them into regular weight (n = 39) and overweight (n = 16)

26
groups. They then responded to the 10-item M-C social desirability scale, a shorter but reliable
version of the original 33-item M-C social desirability scale, which captures people’s need to
obtain approval by responding in culturally appropriate and acceptable manners (Barger 2002).
The 10-item M-C social desirability scale asks participants to indicate whether each of 10
statements (e.g., “I never hesitate to go out of my way to help someone in trouble”) is true or false
as it pertains to them personally. Answers are coded 1 if they are socially desirable and 0 if not
and then summated. Because we obtained some ties in the M-C scores, we assigned 22
participants to the high social desirability (SD) group and 33 to the low SD group.
In a manipulation check, 160 consumers similar to those who participated in Experiments 3
and 4 indicated that Experiment 4 elicited less fear of negative evaluation than did Experiment 3
(same measures as in the previous pretest, M(experiment 4) = 4.3 versus M(experiment 2) = 6.6, F(1,157) =
63.4, p < .001) and significantly more motivation to answer the estimation questions accurately
(M(experiment 4) = 6.5 versus M(experiment 2) = 4.9, F(1,157) = 28.8, p < .001). The social desirability
scores of overweight and regular weight participants were almost identical (SD(OW) = 5.00 versus
SD(RW) = 5.17, F(1, 53) < .1, p = .76), which already suggests that social desirability cannot
explain the potential differences between the groups.
Results
Replications. All the results from Experiments 1–3 that pertain to the underestimation bias and
the stronger underestimation for larger meals were replicated. There is a significant
underestimation of consumption quantity (MS = 561 cal versus MI = 700 cal, PDEV = –11.4%, t =
–4.8, p < .001), but the caloric content of small meals was estimated accurately (PDEV(small meals) =
2.0%, t = .5, p = .60), the caloric content of large meals was strongly underestimated (PDEV(large
meals) = –24.8%, t = -10.0, p < .001), and the two values were strongly statistically different (F(1,
436) = 34.8, p < .001). As in our previous experiments, the power model fit the data better than a

27
linear model (power model: R² = .65, F(1, 436) = 309.9, p < .01; linear model R² = .62, F(1, 436) =
273.5, p < .001), and the difference in predictive validity between the two models is statistically
significant (MAPE(power model) = .50 versus MAPE(linear model) = .59, t = 8.5, p < .001). The best-fitting
power model is S = 4.0*I.74, the exponent is less than 1 (t = –6.2, p < .001), and the intersection
point is within the range of intensities (Min(I) = 190 cal < I* = 205 cal < Max(I) = 1480 cal).
Effects of Body Mass and Social Desirability. As we expected, the average estimation biases of
overweight and regular weight respondents are identical (PDEV(RW) = –11.1% versus PDEV(OW) =
–12.0%, F(1, 436) < .1, p = .86), and as we show in Figure 5A, the estimations of both groups are
almost perfectly aligned. If we decouple body mass from consumption quantity, the differences
between overweight and regular weight consumers disappear. Also as we expected, the
consumption underestimation bias is stronger for respondents with a high social desirability score
(PDEV(low SD) = –7.8% versus PDEV(high SD) = –16.7%, F(1, 436) = 3.4, p < .07). However, Figure
5B shows that the predictions for high and low social desirability respondents fall on parallel lines,
which suggests that social desirability does not interact with actual consumption quantity. To test
this finding directly, we estimated the following model:
(5) LNRATIO = α + β*ln(I) + γ*SD + δ*OW + ε*ln(I)*OW + θ*ln(I)*SD + λ*OW*SD,
where ln(I) is the mean-centered logarithm of actual consumption quantity, SD is a mean-centered
binary variable that indicates whether consumers have a high score on the M-C social desirability
scale (SD = .60) or not (SD = –.40), and OW is a mean-centered binary variable that indicates
whether consumers are overweight (OW = .71) or not (OW = –.29). Equation 5 incorporates
overweight status as a control variable because it was not independently manipulated.
--- Insert Figure 5 here ---
As we expected, the coefficients of actual consumption quantity and social desirability are
negative (β = –.26, t = –6.26, p < .01; γ = –.15, t = –2.93, p < .01). This indicates two main effects:

28
The underestimation bias is more pronounced for larger meals and with high social desirability
biases. Consistent with our expectations, none of the other coefficients was statistically significant
(δ = .05, t = .81, p = .42; ε = –.06, t = –.62, p = .548; θ = .12, t = 1.4, p = .17; λ = -.15, t = –1.34, p
= 18). The degree of compression of the actual consumption quantity is independent of social
desirability and body mass, and there is no interaction between social desirability and body mass.
In addition, these results cannot be explained by a lack of statistical power. Our sample size (n =
438) is significantly larger than needed to detect the average effect sizes found in the literature at a
.05 (two-tailed) significance level with the conventional .80 power. These sizes are n* = 193 for
the association between body mass and estimation biases (given that r = -.20, as found by
Livingstone and Black 2003) and n* = 58 for the association between social desirability and
estimation biases (given r = -.36, as found by Taren et al. 1999).
Discussion
Experiment 4 shows that social desirability, a personality trait linked to the motivation to
engage in impression management, has only a main effect in reducing the reported number of
calories. Social desirability does not change the degree of compression of actual consumption
quantity. Experiment 4 also shows that, when all respondents evaluate multiple meals and when
body mass is independent of actual consumption quantity, the estimation biases of overweight
persons are indistinguishable from those of regular weight consumers. Finally, Experiment 4
shows that consumption estimations are a compressive function of actual consumption quantity,
even for nonchosen meals and repeated estimations.
One limitation of Experiment 4 is that it does not rule out the final alternative explanation of
our results, namely, that consumers anchor their estimates on the basis of nutritional information
that is outdated and therefore too low. For example, Heymsfield et al. (1995) cite a textbook that
attributes 200 calories per bagel. In reality, the National Institute of Health estimates that modern

29
bagels typically have 350 calories and sometimes contain up to 552 calories (Burros 1994). Using
nationally representative data, Nielsen and Popkin (2003) find that, between 1977 and 1996, food
portion sizes have increased for all categories except pizzas. In addition, they find that the increase
is greater for high-calorie foods such as cheeseburgers (from 381 cal to 485 cal) than for lower
calorie food such as soft drinks (from 125 cal to 155 cal). This shift may explain the higher
underestimation biases of overweight consumers, who are more likely to eat high-calorie food
items. It is therefore important to directly test whether estimation anchors can explain the results
of Experiment 4.
EXPERIMENT 5: EFFECTS OF ESTIMATION ANCHORS
The objective of Experiment 5 is to test whether the results of Experiments 1–4 are due to
estimation anchors. Following the same reasoning as that for the other alternative explanations, we
expect that manipulating the numbers that consumers use as self-generated anchors when
estimating calories has only a main effect on estimation biases but does not interact with the
effects of the actual number of calories. In addition, Experiment 5 enables us to test whether
calorie estimations follow a compressive power function when people make joint estimations
(comparing two meals) as opposed to separate evaluations of single meals.
We might expect lower biases for joint and relative estimations than for the separate and
absolute estimations examined in Experiments 1–4 because they are more frequent (i.e.,
consumption decisions more often involve comparisons between different meals than between a
meal or nothing). Another reason to expect smaller biases is that the difference in the number of
calories in different meals typically is smaller than the number of calories of each meal.
Furthermore, prior research has shown that consumers pay more attention to hard-to-evaluate
attributes in joint evaluations than in separate evaluations (Hsee 1996), and therefore, people

30
should be less likely to underestimate the number of calories (a hard-to-estimate attribute) when
comparing two meals than when evaluating each meal separately.
Method
In Experiment 5, we use a 2 × 4 design with two between-subjects conditions (high versus low
estimation anchors) and four within-subject conditions (four different meal sizes). We recruited 87
university students on campus, showed them four pairs of meals, and asked them to estimate the
difference in the number of calories of the two meals of each pair. In each pair, one meal was a
high-calorie meal and the other low calorie. To improve the external validity of the study, we did
not follow the typical anchoring procedure, which consists of providing external anchors by
asking respondents if the number to be estimated is above or below a certain level. Instead, we
followed the procedure used by Epley and Gilovich (2001) to manipulate self-generated estimation
anchors. Participants in the high (low) estimation anchor condition were asked to imagine that
they had decided to eat the high (low) calorie meal of the pair.
The four pairs of meals were arranged in increasing order of size and identified as A through
D. The high-calorie meal from pair A consisted of chicken nuggets, fries, and a regular cola for a
total of 370 calories. The low-calorie meal from pair A consisted of half a low-calorie turkey
sandwich, baked chips, and diet cola for a total of 190 calories. The number of calories that
participants had to estimate was therefore 180. Pairs B, C, and D contained the same meals as pair
A, but the size of each meal was increased by a factor of 2, 3, and 4, respectively, compared with
the meal in pair A. The number of calorie to be estimated was therefore 360 calories for pair B,
540 calories for pair C, and 720 calories for pair D.
Results and Discussion
Replications. The results of Experiments 1–4 were replicated. Respondents significantly
underestimated the number of calories separating the meals of each pair (MS = 354 cal versus MI

31
= 450 cal, PDEV = –9.7%, t = –2.5, p < .05). In addition, the estimation was more accurate when
the number of calories separating the two meals was small (for pairs A and B, PDEV = 11.23%, t
= 1.7, p = .09) but was strongly below the actual difference when the difference between the two
meals was high (for pairs C and D, PDEV = –30.6%, t = –8.1, p < .001). The difference in the
magnitude of the bias between large and small quantities was strongly statistically different (F(1,
343) = 18.4, p < .001). As in previous experiments, a power model fit the data better than a linear
model (power model: R² = .33, F(1, 343) = 42.3, p < .01; linear model R² = .31, F(1, 343) = 37.6, p
< .01), and the difference in the predictive validity between the two models was statistically
significant (MAPE(power model) = .74 versus MAPE(linear model) = .91, t = 10.4, p < .001). The best-
fitting power model is S = 14.6*I.49, the exponent is significantly lower than 1 (t = –6.9, p < .001),
and the intersection point is within the range of intensities (Min(I) = 180 cal < I* = 192 cal <
Max(I) = 720 cal).
Anchoring Effects. Estimations were accurate in the high anchor condition (PDEV(high anchor) =
6.8%, t = 1.2, p = .22) and significantly below the actual number in the low anchor condition
(PDEV(low anchor) = –26.0%, t = –4.9, p < .01). The difference between the two biases was strongly
statistically significant (F(1,344) = 18.4, p < .001). However, the point estimates and model
predictions, as shown in Figure 6, are almost perfectly parallel across conditions. Therefore, as we
expected, the manipulation of estimation anchors has only a main effect on the estimations. To
provide a direct test of this finding, we estimated the following model:
(6) LNRATIO = α + β*ln(I) + γ*ANCH+ δ*ln(I)* ANCH,
where ANCH is a binary variable that indicates whether consumers were in the high (ANCH = .5)
or low (ANCH = –.5) self-generated estimation anchor condition, and ln(I) is the mean-centered
logarithm of the actual number of calories. As we found in all the previous experiments, the
coefficient for ln(I) was strongly negative (β = –.51, t = –7.29, p < .001). Although the simple

32
effect of ANCH was strongly positive (γ = .47, t = 6.05, p < .001), the interaction effect was not
statistically significant (δ = .10, t = .73, p = .47).
Overall, Experiment 5 shows that consumption estimations are a compressive function of
actual consumption quantity, even when consumers estimate the difference in the number of
calories between two meals. Experiment 5 also shows that manipulating estimation anchors has
only a main effect on consumption estimations. When participants were told that they had chosen
the high-calorie meal of the pair (high estimation anchor condition), their estimations were almost
50% higher than when they were told that they had chosen the low-calorie meal. However, the
degree of compression of these estimations was the same across both conditions.
GENERAL DISCUSSION
Biases in consumption estimations are a significant contributing factor to the obesity epidemic.
Considerable evidence in the epidemiology and nutrition literature shows that people
underestimate the number of calories they consume and that the consumption underestimation bias
is more extreme for overweight people. Yet, despite the importance of understanding the origin of
these biases, none of the explanations developed has proved compelling. In this research, we
develop a psychophysical model of calorie estimation that explains these enigmatic findings. We
argue that people’s perception of the number of calories in a meal follows a compressive power
function of the actual number of calories (i.e., a power function with diminishing sensitivity). We
find strong support for the hypothesized model in five experiments that involve pre- as well as
post-intake estimations, chosen as well as nonchosen meals, single as well as repeated
observations, and separate as well as joint estimations.
The direction and size of the consumption estimation bias depends on the number of calories
of the meal being estimated, even when the bias is measured as a percentage of the true number of
calories. The underestimation bias is stronger for increasingly larger meals, and it decreases as the

33
number of calories to be estimated decreases, to the point that small meals are often overestimated.
We also show, mathematically and empirically, that this explains why the consumption
underestimation bias is more pronounced for overweight consumers. It is not that overweight
consumers are intrinsically worse predictors than regular weight consumers. The higher
underestimation of overweight consumers is a spurious consequence of their tendency to consume
larger meals. Calorie underreporting is a problem with meal size, not body size.
We also find that the psychophysical relationship between objective and subjective
consumption quantity is neither mediated nor moderated by any of the four existing explanations
for consumption estimation biases. Respondents’ carelessness, a lack of information about the
bias, impression management, or anchoring based on outdated nutritional information does not
modify or suppress the effects of the objective number of calories on estimation biases. That these
four factors all have a main effect on consumption estimations implies that the absence of an
interaction between them and the effect of meal size is not due to a lack of power or poor
calibration. Rather, our findings show that psychophysical compression is an independent source
of consumption estimation biases and therefore supplements existing explanations.
Research Implications
Biases in consumption estimations mean that studies that use uncorrected self-reported
consumption data as an independent or dependent variable are biased (Livingstone and Black
2003). Unfortunately, the prohibitive cost of the DLW technique probably means that most
researchers in marketing, nutrition, and epidemiology will still need to depend on self-reported
data in many instances. How can self-reported consumption data be debiased? One existing
technique is to eliminate data from known underreporters (e.g., obese respondents). Unfortunately,
this technique eliminates data from those persons who are of the greatest interest. Another
technique consists of applying a correction factor to all observations or to different groups of

34
respondents (such as overweight versus regular weight consumers). Our study suggests that better
results can be achieved by applying a different correction factor for each meal size. Consider
Experiment 1. Because consumption was underestimated by an average of 17.5%, a general
correction factor would be to multiply self-reports by 1.21 (1/(1 – .175)). When we compare the
accuracy of self-reported data in Experiment 1 corrected using (1) a single correction factor, (2) a
different factor for overweight and regular weight consumers, and (3) a different factor for small
and large meals, we find that the single-factor correction predicts true consumption as well as the
“obesity” correction (MAPE(single factor) = .40 versus MAPE(overweight vs. regular weight) = .38, t = 1.6, p =
.10) but both are outperformed by the meal size correction (MAPE(small vs. large meals) = .36, t = 2.2, p
< .05).
Another fruitful area for additional research would be to examine whether consumption
estimations can be improved by using different measurement units (such as volume or number of
servings) or by focusing people more on external cues (such as the size of the plate or type of
food) than on biased internal sensations. Another area worthy of research would be to examine the
effects of familiarity and expectations. Our results rule out the idea that consumption estimation
biases are due to a lack of familiarity with large meals (overweight people are no better predictors
than people with a regular weight who are less used to consuming larger meals). Expectations of a
lower-calorie meal might even aggravate the consumption underestimation bias, so that consumers
would be more accurate when estimating a typical high-calorie fast-food meal than when
estimating an objectively healthier meal. Such an analysis would need to control for the
differences in the size of the high- and low-calorie meals, which will create its own biases.
Overall, our study shows that any analyses of factors that affect the biases in consumption
estimation must carefully disentangle improvements that are due to changes in the quantity
consumed from those that are due to intrinsic improvements in estimation accuracy.

35
Public Policy Implications
One important area for public policy research would be to study the link between biases in
calorie estimation and consumption behavior. For example, it would be useful to examine whether
people who tend to underestimate the number of calories of a fast-food meal are more sensitive to
“supersize” promotions that offer larger meals for a modest price increase than people whose
estimations are unbiased. This raises the question of what medical practitioners, clinicians, and
health policy professionals can do to improve consumers’ estimations of the number of calories in
a meal. Our results show that simply informing people about the bias is ineffective. One solution
would be to make nutritional information more salient in restaurants. Whereas, it may not
influence estimates, it may influence choice (Burton and Creyer 2004).
A more general solution might be to tell consumers to separate their meals mentally into
smaller portions and estimate the number of calories of each portion independently. For example,
our model predicts that estimation accuracy would greatly improve if consumers estimated the
number of calories of half of their meal and then doubled that number. In Experiment 1, for
example, the average meal contained 838 calories, but the predicted estimation was 578 calories
(17*838.524). In contrast, the predicted estimation for a “half meal” of 419 calories was 402
calories (17*419.524), which, when doubled, is very close to the true number of calories.

36
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40
FIGURE 1
EFFECTS OF THE DEGREE OF COMPRESSION OF THE PSYCHOPHYSICAL
FUNCTION ON ESTIMATIONS (PANEL A) AND ESTIMATION BIASES (PANEL B)
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
Actual Number of Calories
(I)
Estimated Number of Calories
(S)
a = 18, n = .6
a = 18, n = .4
a = 18, n = .5
-2.00
.00
2.00
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
Actual Number of Calories
ln(I)
Estimation Bias
ln(S/I)
α = ln(a) = 2.89
β = (n - 1) = -.4
α = ln(a) = 2.89
β = (n - 1) = -.6
α = ln(a) = 2.89
β = (n - 1) = -.5
A
B
Over
weight
Regular
weight
Over
weight
Regular
weight

41
FIGURE 2
EXPERIMENT 1: ESTIMATED VERSUS ACTUAL NUMBER OF CALORIES (PANEL A)
AND PREDICTED AND OBSERVED (MEAN AND 95% CI) ESTIMATION BIASES AS A
FUNCTION OF ACTUAL NUMBER OF CALORIES (PANEL B)
0
500
1000
1500
2000
0 500 1000 1500 2000
Actual Number of Calories
(I)
Estimated Number of Calories
(S)
Model predictions
Accuracy line
Regular weight
Overweight
a = 17.0, n = .52,
I* = 384 cal.
-1.00
.00
1.00
5.5 6.0 6.5 7.0 7.5
Actual Number of Calories
ln(I)
Estimation Bias
ln(S/I)
Model predictions
Regular weight
respondents
Overweight respondents
α = 2.83, β = -.48
A
B

42
FIGURE 3
EXPERIMENT 2: PREDICTED AND OBSERVED (MEAN AND 95% CI) ESTIMATION
BIASES AS A FUNCTION OF ACTUAL NUMBER OF CALORIES AND ESTIMATION
CARELESSNESS
-1.00
.00
1.00
5.5 6.0 6.5 7.0 7.5
Actual Number of Calories
ln(I)
Estimation Bias
ln(S/I)
Model predictions
Careful respondents
Careless respondents
α = 1.74, β = -.31

43
FIGURE 4
EXPERIMENT 3: PREDICTED AND OBSERVED (MEAN AND 95% CI) ESTIMATION
BIASES AS A FUNCTION OF ACTUAL NUMBER OF CALORIES AND DEBIASING
KNOWLEDGE
-.75
.00
.75
6.4 6.6 6.8 7.0 7.2 7.4
Actual Number of Calories
ln(I)
Estimation Bias
ln(S/I)
Debiasing condition
(model predictions)
Debiasing condition (all
respondents)
Control condition (model
predictions)
Control condition (regular
weight respondents)
Control condition
(overweight respondents)
α = 4.26, β = -.64
α = 4.01, β = -.58

44
FIGURE 5
EXPERIMENT 4: PREDICTED AND OBSERVED (MEAN AND 95% CI) ESTIMATION
BIASES AS A FUNCTION OF ACTUAL NUMBER OF CALORIES, BODY MASS (PANEL
A), AND SOCIAL DESIRABILITY (PANEL B)
-.75
.00
.75
5.6 6.1 6.6 7.1
Actual Number of Calories
ln(I)
Estimation Bias
ln(S/I)
All respondents
(model predictions)
Regular weight
respondents
Overweight
respondents
α = 1.38, β = -.26
-.75
.00
.75
5.6 6.1 6.6 7.1
Actual Number of Calories
ln(I)
Estimation Bias
ln(S/I)
Low social desirability
respondents (model
predictions)
Low social desirability
respondents
High social desirability
respondents (model
predictions)
High social desirability
respondents
α = .86, β = -.20
α = 1.74, β = -.30
A
B

45
FIGURE 6
EXPERIMENT 5: PREDICTED AND OBSERVED (MEAN AND 95% CI) ESTIMATION
BIASES AS A FUNCTION OF ACTUAL NUMBER OF CALORIES AND ESTIMATION
ANCHOR
-1.25
.00
1.25
4.8 5.3 5.8 6.3 6.8
Actual Number of Calories
ln(I)
Estimation Bias
ln(S/I)
High anchor condition
(model predictions)
High estimation anchor
condition
Low anchor condition
(model predictions)
Low estimation anchor
condition
α = 2.75, β = -.56
α = 2.63, β = -.46