Development and validation of skinfold-thickness prediction
equations with a 4-compartment model1–3
Matthew J Peterson, Stefan A Czerwinski, and Roger M Siervogel
ABSTRACT
Background: Skinfold-thickness measurements are commonly
obtained for the indirect assessment of body composition.
Objective: We developed new skinfold-thickness equations by
using a 4-compartment model as the reference. Additionally, we
compared our new equations with the Durnin and Womersley and
Jackson and Pollock skinfold-thickness equations to evaluate each
equation’s validity and precision.
Design: Data from 681 healthy, white adults were used. Percentage
body fat (%BF) values were calculated by using the 4-compartment
model. The cohort was then divided into validation and crossvalidation groups. Equations were developed by using regression
analyses and the 4-compartment model. All equations were then
tested by using the cross-validation group. Tests for accuracy
included mean differences, R2, and Bland-Altman plots. Precision
was evaluated by comparing root mean squared errors.
Results: Our new equations’ estimated means for %BF in men
and women (22.7% and 32.6%, respectively) were closest to the
corresponding 4-compartment values (22.8% and 32.8%). The
Durnin and Womersley equation means in men and women
(20.0% and 31.0%, respectively) and the Jackson and Pollock
mean in women (26.2%) underestimated %BF. All equations
showed a tendency toward underestimation in subjects with
higher %BF. Bland-Altman plots showed limited agreement
between Durnin and Wormersley, Jackson and Pollock, and the
4-compartment model. Precision was similar among all the equations.
Conclusions: We developed accurate and precise skinfold-thickness
equations by using a 4-compartment model as the method of reference. Additionally, we found that the skinfold-thickness equations frequently used by clinicians and practitioners underestimate
%BF.
Am J Clin Nutr 2003;77:1186–91.
KEY WORDS
Body composition, skinfold thickness, body
compartments, anthropometry, adipose tissue, nutritional assessment,
body fat, obesity
INTRODUCTION
Higher amounts of body fat and obesity are associated with
increased risks of adverse health events and greater mortality
(1, 2). Skinfold thicknesses are commonly measured in clinical
and field settings for the assessment of percentage body fat
(%BF) because this method is simple to perform and low in cost
(3). Two of the most widely used skinfold-thickness equations
are those developed by Durnin and Womersley and Jackson and
Pollock (4–6).
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The Durnin and Wormersley equation and the Jackson and Pollock
equation were developed and validated by using a 2-compartment
(2C) model. The 2C model separates the composition of the body
into fat mass and fat-free mass. Using Siri’s equation (7), the 2C
model is written as:
%BF = [(4.95/BD) 4.5] 100
(1)
where BD is whole-body density in g/cc. Use of the 2C-model
equation requires the assumptions that body hydration level and
bone mineral content are both stable. Unfortunately, these assumptions are often violated because of significant variations in hydration levels and mineral contents between ages, sexes, and races
(8–10). The inability of the 2C model to detect these differences
can lead to potentially large errors in estimates of %BF in persons
for whom these assumptions are violated. Thus, use of the 2C
model for development and validation of skinfold-thickness prediction equations is less than ideal (10–14).
Recent advances in in vivo measurement, including 4-compartment
(4C) body composition assessment, have allowed researchers to
assess variations in hydration levels and bone mineral contents
that hydrodensitometry alone cannot measure (13). The 4 compartments of the 4C model are fat, mineral, water, and residual.
By adding measurements of total body water (TBW), bone mineral density [via dual-energy X-ray absorptiometry (DXA)], and
BD (via hydrodensitometry), it is possible to measure individual variances in mineral and water, thus, in theory, leading to
more accurate measurement of %BF. It has been theorized that
multiple measures could lead to the propagation of additive
errors when using the 4C model, however, researchers have
shown negligible additive errors with this model (11). In addition, the 4C model has been used as the criterion method in studies with children, younger and middle-aged adults, and the elderly (3, 10, 11, 15–18).
1
From the VA Medical Center, Geriatric Research, Education and Clinical
Center, Durham, NC (MJP); Wright State University School of Medicine, Lifespan Health Research Center, Kettering, OH (SAC and RMS); and the Center
for the Study of Aging and Human Development, Duke University Medical
Center, Durham, NC (MJP).
2
Supported by the National Institutes of Health, National Institute of Child
Health and Human Development, grant no. R01HD12252.
3
Address reprint requests to MJ Peterson, Durham VAMC (182), Geriatric
Research, Education and Clinical Center, 508 Fulton Street, Durham, NC
27705. E-mail: peter076@mc.duke.edu.
Received May 7, 2002.
Accepted for publication October 24, 2002.
Am J Clin Nutr 2003;77:1186–91. Printed in USA. © 2003 American Society for Clinical Nutrition
SKINFOLD-THICKNESS PREDICTION EQUATIONS
We developed a new skinfold-thickness equation (%BFnew) to
predict %BF by using the 4C model as the reference in younger
and middle-aged adults (18–55 y). We evaluated the performance
of %BFnew compared with %BF estimates derived from 2 commonly used skinfold-thickness equations, namely those of Durnin
and Wormersley (%BFDW) and Jackson and Pollock (%BF JP).
Because technology that allows us to use a 4C model for validation studies is now accessible, we decided it was important to
examine the possibility of providing clinicians and practitioners
with improved skinfold-thickness prediction equations.
SUBJECTS AND METHODS
Subjects
The subjects in the present study are a subset of the participants
in the Fels Longitudinal Study. They were enrolled in the Fels
Longitudinal Study between 1929 and the present, typically soon
after their birth. Most of the Fels participants are white, resided
in southwestern Ohio at the time of their enrollment, and were
selected for enrollment because their parents were willing to allow
them to participate in a long-term, serial study. To date, there have
been > 1200 participants in the study; they are examined at regular intervals throughout their life span. Of these 1200, a total of
900 are participating in the currently funded National Institutes of
Health study. All subjects provided written informed consent.
The Fels Longitudinal Study and its participants have been
described in detail previously (19). The standard body-composition
exam consists of the anthropometric assessment of weight,
stature, and several skinfold thicknesses (chest and abdomen
skinfold thicknesses are not currently measured). Many other
measures of body composition, including DXA, hydrodensitometry, and bioelectrical impedance, are also obtained. The protocol
for this study is reviewed and approved annually by the Wright
State University Institutional Review Board. The study sample is
representative of the national population in terms of its socioeconomic composition, except for a slight underrepresentation of
the lowest socioeconomic group in recent decades. After excluding participants without all of the data needed to derive a %BF
reference from the 4C model (see below), there were a total of
681 healthy, white male (n = 360) and female (n = 321) participants available for derivation of the %BF 4C individual values.
This larger sample was then randomly divided into a validation
sample (274 men and 230 women) to develop the %BFnew equations and a cross-validation sample (86 men and 91 women) used
to compare all the equations.
Development of %BF4C values
DXA scans were performed with a Lunar DPX (Lunar Co,
Madison, WI) with total body scan software version 3.6z. The
Lunar DPX uses a constant X-ray source and a K-edge filter to
achieve a congruent beam of dual-energy radiation. Tissue mass
and bone mass are calculated, and tissue mass is further divided
into fat-free nonskeletal mass and fat mass. Total body bone mineral content is calculated relative to DXA-determined fat-free mass.
Deuterium oxide dilution methods were used to determine
TBW according to the procedures described by Schoeller et al
(20). Briefly, this method involves measuring the degree of dilution of a known dose of deuterium after it has equilibrated with
TBW. Participants emptied their bladders before the collection of
a 6-mL baseline saliva sample and then drank 15 mL deuterium
1187
oxide (99.9% purity; Cambridge Isotope Laboratories, Woburn,
MA) in a solution of 75 mL deionized water. A second saliva sample was collected exactly 2 h later. The 2 samples were centrifuged
and the supernate was collected, sealed, frozen, and transported
to the Kettering-Scott Magnetic Resonance Laboratory (Kettering, OH) for analysis. Nuclear magnetic resonance spectrometry
was used to determine the TBW from each sample. These values
were then divided by 1.04 to account for the estimated 4% H+ nonaqueous exchange (21).
The hydrodensitometry method was used to measure BD
according to the method described by Siri (7). This method determines BD by using standardized hydrostatic weighing with correction for residual volume. Residual volume was measured twice
on land to the nearest 0.1 L by nitrogen washout, using a computerized spirometer (Solatron, Dayton, OH). Underwater weight
was determined with the participant sitting in a chair suspended
from 4 load cells in a tank of water at 35 C. When the participant was completely submerged and at maximal exhalation,
underwater weights were recorded to the nearest 0.002 kg from
a digital display. Ten repeated underwater weights were completed, and the average of the highest 3 weights (because these
are indicative of maximal exhalation) was used to calculate BD
corrected for residual volume.
The methods described above can be combined to estimate
%BF by using the equation for the %BF4C model (11):
%BF4C = [2.559/BD 0.734 (TBW/weight)
+ 0.983 (TBBM/weight) 1.841] 100
(2)
where BD is whole-body density in g/cc measured with densitometry, TBW is total body water measured with D2O (in L), TBBM
is total-body bone mineral content measured with DXA (in kg),
and weight is body weight (in kg).
Development of %BFnew equations
We identified the set of skinfold-thickness and anthropometric
sites that best predicted %BF from the 4C model, and we developed prediction equations using %BF obtained from the 4C model
as the reference value. The equation originally included several
skinfold-thickness and circumferential sites and various combinations of skinfold-thickness sites. Circumferential measurements
were included because these measurements are directly affected
by increasing and decreasing regional adiposity and thus they may
aid in developing a more precise estimate of %BF (5, 6). In addition, several variables known to be associated with body composition, including age, height, and weight, were included in the
equations. Body mass index (BMI, in kg/m2) was also included
because this is easily measured (using height and weight) and is
commonly used as an index of obesity. The anthropometric sites
initially included in the new equations were the triceps, subscapular, biceps, midaxillary, suprailiac, midthigh, and lateral calf
skinfold thicknesses and the circumferences of the abdomen, hip,
thigh, calf, and upper arm. Although it would have been most
desirable to also include an abdominal skinfold thickness as a
measure of central adiposity in the initial equations, the Fels Longitudinal Study data collection protocol does not currently include
such a measure. However, we thought that the inclusion of a total
of 7 skinfold-thickness sites and 5 circumferences in the original
equation would result in a strong prediction equation. Two highly
skilled technicians measured each anthropometric site using the
techniques described in the Anthropometric Standardization Reference Manual (22) with Holtain skinfold calipers (Holtain Ltd,
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PETERSON ET AL
TABLE 1
Descriptive characteristics of the validation and cross-validation groups1
Value
Validation group
Men (n = 274)
Age (y)
Height (cm)
Weight (kg)
BMI (kg/m2)
Women (n = 230)
Age (y)
Height (cm)
Weight (kg)
BMI (kg/m2)
Cross-validation group
Men (n = 86)
Age (y)
Height (cm)
Weight (kg)
BMI (kg/m2)
Women (n = 91)
Age (y)
Height (cm)
Weight (kg)
BMI (kg/m2)
1–
x ± SD; range in parentheses.
TABLE 2
Regression coefficients, partial explanation of variance (partial R2), and
significance of independent variables in the new percentage body fat
(%BFnew) equations (validation group)
Variable
36.2 ± 11.0 (18.0–55.4)
179.3 ± 6.6 (158.5–193.6)
79.0 ± 11.6 (45.2–109.0)
24.5 ± 3.2 (15.6–34.6)
Coefficient
Partial R2
P
0.5609
0.0277
0.0192
0.0101
0.6122
0.0091
< 0.0001
0.0082
< 0.0001
0.0002
< 0.0001
0.6420
0.0244
0.0157
0.0150
0.0083
0.6988
0.0063
0.0128
< 0.0001
0.0016
< 0.0001
0.0025
< 0.0001
35.2 ± 14.6 (18.0–55.6)
178.0 ± 7.9 (163.8–192.8)
75.8 ± 13.5 (44.7–106.4)2
24.0 ± 4.5 (16.3–35.0)
Men (n = 273)
Intercept
Age
Stature
Sum4
Sum42
Model R2
Women (n = 229)
Intercept
Age
BMI
Stature
Sum4
Sum42
Model R2
34.8 ± 12.9 (18.0–54.6)
166.1 ± 7.0 (153.5–184.3)
63.0 ± 10.2 (45.9–101.4)
22.8 ± 3.0 (18.0–32.5)
and P < 0.0167 for women. All analyses were performed with SAS
version 8e (SAS Institute Inc, Cary, NC).
35.1 ± 10.3 (18.0–55.6)
166.0 ± 5.6 (154.3–187.0)
63.5 ± 11.6 (43.3–108.6)
23.0 ± 3.7 (16.5–40.6)
2
Significantly different from men in the validation group, P < 0.05
(unpaired t test).
20.94878
0.1166
0.1166
0.42696
0.00159
22.18945
0.06368
0.60404
0.14520
0.30919
0.00099562
RESULTS
%BFnew equations
Croswell, Crymych, United Kingdom) and a metal or cloth (for
upper arm only) tape measure.
Statistical analyses
The physical characteristics of the validation and cross-validation
groups are presented as means with SDs and ranges. Unpaired t tests
were used to determine significant differences between mean values within each sex between groups (validation and cross-validation
groups) and between the sexes within groups. Sex-specific stepwise regression analyses were used to develop the %BFnew equations in the validation group. Variables included in the initial
analyses included age; height (cm); weight (kg); BMI; the sum of
the triceps, suprailiac, and midthigh skinfold thicknesses (sum3);
and the sum of the triceps, subscapular, suprailiac, and midthigh
skinfold thicknesses (sum4). Squares of sum3 (sum32) and sum4
(sum42) were also included to test for a curvilinear association
between skinfold thicknesses and %BF.
In the cross-validation group, the accuracy of the %BF new,
%BFDW, and %BFJP equations was tested by calculating correlation coefficients. In addition, Bland-Altman plots (23) were used
to determine bias and limits of agreement between equations. Bias
was defined as (predicted %BF %BF4C) plotted on the y axis
and the mean of %BF4C and predicted %BF plotted on the x axis.
Limits of agreement were defined as upper and lower 95% CIs and
were determined by the mean differences ± 2 SD. To determine
each equation’s precision, root mean square error (RMSE) values
were obtained by using univariate analysis. In all the analyses,
%BF4C was used as the method of reference. As described previously, chest skinfold data were not available for men, so analyses
with Jackson and Pollock equations are for women only. Alpha
was set at P ≤ 0.05. We used a Bonferroni adjustment for multiple comparisons of %BF methods and set at P < 0.025 for men
The physical characteristics of subjects in the validation
and cross-validation groups are shown in Table 1. In both
groups, men and women differed significantly in height,
weight, and BMI, but age was not significantly different
between the sexes. Men in the validation group were heavier
than were men in the cross-validation group. Physical characteristics did not differ significantly between women in the
validation and cross-validation groups.
Regression analyses in the validation group (Table 2) revealed
that the sum of the triceps, subscapular, suprailiac, and midthigh
skinfold thicknesses (sum4) explained 56% (partial R2 = 0.56)
of the variance of %BF in men and 65% (partial R2 = 0.64) of
the variance of %BF in women. In men, age, height, and sum42
were also significant contributors to the model, but to a lesser
degree, with no remaining variable’s partial R2 being > 0.027. In
women, in addition to the same set of variables that were significant
in the model for men, BMI was also a significant predictor of %BF,
although its effect size was relatively small (partial R2 = 0.024).
Interestingly, sum3, sum32, circumferential measures, and weight
were not significant predictors of %BF in either model. The final
equations, which were used in subsequent analyses, are as follows
for men and women:
For men: %BFnew = 20.94878 + (age 0.1166)
(height 0.11666) + (sum4 0.42696)
(sum42 0.00159)
(3)
For women: %BFnew = 22.18945 + (age 0.06368)
+ (BMI 0.60404) (height 0.14520)
+ (sum4 0.30919) (sum42 0.00099562)
(4)
where height is in cm and sum4 is the sum of the triceps, subscapular, suprailiac, and midthigh skinfold thicknesses.
SKINFOLD-THICKNESS PREDICTION EQUATIONS
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TABLE 3
Percentage body fat (%BF) estimates and measurements in the
cross-validation group1
Value
Men (n = 86)
%BFnew
22.7 ± 7.1 (11.1–36.6)
%BF4C
22.8 ± 9.5 (4.6–44.3)
%BFJP
—
%BFDW
20.0 ± 7.02 (7.6–34.8)
Women (n = 91)
%BFnew
32.6 ± 5.2 (21.7–43.2)
%BF4C
32.8 ± 7.2 (14.1–46.2)
%BFJP
26.2 ± 5.92 (13.6–39.8)
%BFDW
31.0 ± 5.52 (20.4–43.9)
1–
x ± SD; range in parentheses. 4C, 4-compartment; JP, Jackson and
Pollock; DW, Durnin and Wormersley.
2
Significantly different from %BF4C within the same sex, P < 0.05
(Bonferroni-adjusted P; unpaired t test).
Comparison of all equations
FIGURE 2. Bland-Altman plot showing the limits of agreement between
percentage body fat calculated with the 4-compartment-model equation
(%BF4C; the reference equation) and percentage body fat calculated with the
new equation developed in the current study (%BFnew) in women.
The results of the predicted and measured %BF means, SDs,
and ranges for each equation or method are shown in Table 3 for
the cross-validation group. As the reported mean values show, the
%BFnew values are closest to the %BF4C values for both men and
women, with slight overestimations of %BF (0.1% and 0.2% in
men and women, respectively). Jackson and Pollock underestimated %BF in women when compared with the 4C model, with a
mean underestimation of 6.6%. In men and women, Durnin and
Wormersley also underestimated %BF when compared with the
4C model, with mean underestimations of 3.1% and 2.4%, respectively. When considering differences in means between the predicted and %BF4C values, the %BFnew equations were the most
accurate in the cross-validation group.
Bland-Altman plots were used to further assess the accuracy of
each prediction equation. In Figures 1–5, we have shown the bias
and limits of agreement in each prediction equation by plotting
the difference between the measured and predicted values (y axis)
against the mean of the measured and predicted values (x axis).
Differences in %BF4C and %BFnew in men and women were plotted against %BF4C in Figures 1 and 2. The limits of agreement
(mean difference ± 2 SD) were approximately ± 9.5 %BF, with
the exception of the lower confidence limits (10.1%) for women.
This is interpreted as 95% of individuals’ predicted %BF value
could be up to 10% above or below their actual value. Mean differences were close to 0, at 0.18% and 0.25% (P > 0.05) in
men and women, respectively. In Figures 3 and 4, relations
between %BF4C and %BFDW differences and their means in men
and women are shown. Limits of agreement and bias tend to favor
an underestimation by the Durnin and Wormersley equation, with
upper limits at 7.2% and 8.0% in men and women, respectively
and lower confidence limits at 12.9% and 11.4% in men and
women, respectively. There is also an underestimation bias in men
and women when using the Durnin and Wormersley equation, with
mean differences at 2.8% and 1.8% (P < 0.05) in men and
women, respectively. Differences between %BFJP and %BF4C and
FIGURE 1. Bland-Altman plot showing the limits of agreement between
percentage body fat calculated with the 4-compartment-model equation
(%BF4C; the reference equation) and percentage body fat calculated with the
new equation developed in the current study (%BFnew) in men.
FIGURE 3. Bland-Altman plot showing the limits of agreement between
percentage body fat calculated with the 4-compartment-model equation
(%BF4C; the reference equation) and percentage body fat calculated with the
Durnin and Wormersley equation (%BFDW) in men.
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PETERSON ET AL
FIGURE 4. Bland-Altman plot showing the limits of agreement between
percentage body fat calculated with the 4-compartment-model equation
(%BF4C; the reference equation) and percentage body fat calculated with the
Durnin and Wormersley equation (%BFDW) in women.
FIGURE 5. Bland-Altman plot showing the limits of agreement between
percentage body fat calculated with the 4-compartment-model equation
(%BF4C; the reference equation) and percentage body fat calculated with the
Jackson and Pollock equation (%BFJP) in women.
their means in women are shown in Figure 5. Bias with the Jackson and Pollock equation is seen, with a mean difference of
6.6% (P < 0.05). Limits of agreement follow the same tendency
of underestimation, with upper and lower confidence limits at
3.3% and 16.5%, respectively. Relations are evident between the
mean of the measured and predicted values and the individual differences in %BF in both sexes with all equations. In other words,
the relations seen in all equations are a function of %BF, with all
equations having a tendency to produce larger underestimations
as %BF increased.
To address issues of precision, RMSEs of predicted %BF in the
cross-validation groups were investigated. %BFnew had a RMSE
for men of 4.6% when predicting %BF, and the corresponding
value for %BFDW was 4.9%. In women, %BFnew equations had a
RMSE of 5.0%. The corresponding values for %BFDW and %BFJP
in women were both 4.9%. Overall, RMSEs were quite similar
among all the prediction equations.
groups similar to the one presented here. Bland-Altman plots provided additional information regarding the underestimation of
%BF by the Durnin and Wormersley and Jackson and Pollock
equations. With the Durnin and Wormersley equations, the lower
limits of agreement (mean differences 2 SD) were 12.9% and
11.4% in men and women, respectively. These lower limits of
agreement are considerably larger than the upper limit values, at
7.2% and 7.9% in men and women, respectively. On the basis of
these data, a man or woman is more likely to have their %BF
underestimated using the Durnin and Wormersley equations. This
tendency to have the limits of agreement shifted toward underestimations is even more pronounced in women using the Jackson
and Pollock equation, with upper and lower limits of agreement
of 3.3% and 16.5%, respectively. This indicates that a woman
could have her %BF underestimated by as much as 16.5%. These
underestimations are most likely a result of systematic overestimations of BD. For example, the mean BD value with the Durnin
and Wormersley equation was higher, at 1.032 g/mL, than the
value of 1.028 g/mL that was measured by hydrodensitometry.
Although 0.004 g/mL may initially appear to be a small difference
in BD estimates, when using these 2 values to predict %BF, the
differences in mean predicted %BF values are almost 2%. A relatively small under- or overestimation of BD can result in considerable errors in predicted %BF values.
%BFnew, %BFJP, and %BFDW all had similar estimates of precision, as shown by the similar RMSE values. A prediction equation’s RMSE is certainly important, however, it should not be considered the only criterion when choosing a proper equation.
Although %BF DW and %BF JP values were similar in terms of
RMSE values and precision, we showed that accuracy was less
than desirable in the Durnin and Wormersley and Jackson and Pollock equations in a cohort similar in age and physical characteristics to their derivation samples.
Providing precise and accurate body-composition information
is of great importance. The comparisons provided in this paper
should aid in making a more informed decision, considering precision and accuracy, when choosing among popular equations for
predicting %BF. In summary, we have shown that our newly
developed generalized equations, which use the 4C model as a reference, can accurately predict %BF in healthy, white adults. Our
DISCUSSION
We developed new skinfold-thickness prediction equations and
compared them with the equations of Durnin and Wormersley and
Jackson and Pollock, and with a 4C model, which we used as the
reference equation. To our knowledge, no previous study has used
a 4C model to cross-validate several skinfold-thickness prediction
equations. We chose the Durnin and Wormersley and Jackson and
Pollock equations because of their popularity in the field and in
research settings (18, 24–31). Previous studies have explored the
predictive accuracy and precision of the Jackson and Pollock and
Durnin and Wormersley equations in different populations (18,
24–31). Our study is also unique in that we present data from
healthy, white men and women who had characteristics comparable to those of the groups used by Durnin and Wormersley and
Jackson and Pollock.
The skinfold-thickness equations developed in our laboratory
had no significant mean differences with the %BF4C model in men
or women in the cross-validation group. In this cohort, %BFDW
and %BFJP means were significantly lower than the %BF4C mean,
which may need to be considered when using the Durnin and
Wormersley and Jackson and Pollock equations to predict %BF in
SKINFOLD-THICKNESS PREDICTION EQUATIONS
newly developed skinfold-thickness equations are important for 2
reasons. First, the %BFnew equations were validated and crossvalidated with large samples of men and women spanning a wide
age range (18–55 y). The validation sample used by Durnin and
Wormersley was similar to ours in size, but they did not crossvalidate their equations. Jackson and Pollock did cross-validate,
but their cross-validation did not provide an analysis of their equations’ potential to over- or underestimate %BF. Second, the
%BFnew equations were developed and validated by using a 4C
model as a reference. The 4C model has been shown to be more
accurate in measuring %BF than the 2C method, which was the
criterion method for Durnin and Wormersley and Jackson and Pollock. When validated against the 4C model, the Durnin and Wormersley equations underestimated %BF in men and women and the
Jackson and Pollock generalized equations underestimated %BF
in women to a relatively high degree. We recommend considering
an equation’s accuracy and precision to fully understand its
strengths and weaknesses. This may require finding the original
source for the derivation of the equation and objectively analyzing the information presented to find the best equation for a specific population.
We thank the participants of the Fels Longitudinal Study and the data collection staff, without whom this work would not have been possible. We also
thank Miriam Morey for her thoughtful review of drafts and for her support of
MJP throughout the writing and revision of this work.
MJP, SAC, and RMS were all involved in the study design and writing of the
manuscript. Data analyses were performed by MJP. The authors had no financial or personal interests in the sponsoring organization.
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