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Brief communication Measurement size precision and reliability in craniofacial anthropometry Bigger is better.

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Brief Communication: Measurement Size, Precision, and
Reliability in Craniofacial Anthropometry: Bigger is Better
Department of Anthropology, Indiana Uniuersity, Bloomington, Indiana
47405 (P.L.J J ; Department of Anthropology, Indiana Uniuersity, Purdue
Uniuersity, Indianapolis, and Oral Facial Genetics, Indiana Uniuersity
School of Dentistry, Indianapolis, Indiana 46202 (R.E.W.)
Intraobserver error, Repeatability, Measurement
magnitude, Scale
In this paper we examine the results of an intraobserver
measurement error study involving 49 craniofacial variables that ranged in
size from less than 1cm to approximately 20 cm. Repeat measurements were
taken on 10 male and 10 female adult subjects (19-59 years old). Our focus is
on the relationship between measurement size and measurement error across
the 49 variables. We found that the size of the variable showed no relationship
with the magnitude of the error as measured by the technical error of measurement. When the error was expressed as a coefficient of relative variation
(Malina et al.: Vital and Health Statistics, Series 11, No. 23. Washington, DC:
US Department of Health and Human Services, 19731, this quantity was
negatively associated with the size of the measurement. Conversely, reliability (Fleiss: The Design and Analysis of Experiments. New York: John Wiley &
Sons, 1986) was positively correlated with measurement size. We did not find
effects of scale (Marks et al.: Am. J. Epidemiol. 130.578-587,1989) within the
individual measurements. Thus, for the range of size of the craniofacial measurements in this study, measurement size must be added to the list of factors
such as ease of locating landmarks, measurement technique, and systematic
bias in the application of the technique that can affect precision and reliability
in anthropometry. o 1993 WiIey-Liss, Inc.
Over the past 60 years, several authors
have speculated that the size of anthropometric measurements may affect their reliability (i.e., Davenport et al., 1935; Gavan,
1950; Malina et al., 1973). Recently, Marks
et al. (1989)reported a relationship between
measurement size and measurement error
within several skinfold measurements, i.e.,
error increased as the size of the individual
measurement increased. In our own anthropometric research (Ward and Jamison,
1991) we have reported that craniofacial dimensions less than 6 cm were not as reliably
ascertained as larger dimensions. In the
present study we will examine the relationship between craniofacial variables of different size and the precision and reliability
with which they can be measured. In addi0 1993 WILEY-LISS, INC
tion we will examine the “effects of scale”
defined by Marks et al. (1989)on the basis of
errors within individual variables.
Forty-nine craniofacial dimensions described by Farkas (1981),covering the entire
head and face and ranging in average size
from 20 cm down to less than 1 cm, were
measured twice on 10 male and 10 female
subjects. All were healthy adults between 19
and 59 years of age. Standard anthropometric equipment (spreading and sliding calipers and tapes) was utilized for all measurements. Measurements were obtained by a
Received December 2,1991; accepted September 16,1992.
trained anthropometrist (R.E.W.)with more
than 5 years of experience in a clinical setting. Depictions of the landmarks and additional details on methodology can be found
in Ward and Jamison (1991). In our original
study we did not “correct” obvious errors
such as inversions and voice errors (i.e., recording 20.1 as 21.0). For the present study
we did adjust nine probable recording or instrument reading errors out of a total of
1,960 data entries.
The earlier measurement error literature
focusing on adults (see references in Jamison and Zegura, 1974; Lohman et al., 19881,
generally described intraobserver and/or interobserver error, usually with two or more
trials by the same or different investigators
spanning a very brief period of time. In contrast, for many of the recent auxological
studies (Cameron, 1986; Himes, 1989; Martorell et al., 1975; Pelletier et al., 1991) the
problems were broader, i.e., multiple observers working with children of different ages
and repeat measurements spanning long
enough periods of time that the subject
would be expected to change from one session to the next. Thus Habicht et al. (1979)
and others who followed their approach (see
Mueller and Martorell, 1988) not only defined and discussed reliability, they also
calculated unreliability, precision and imprecision, and dependability and undependability. Of these, Mueller and Martorell
(1988) conclude that precision and reliability should be reported in every anthropometric study in order to give the reader an
impression of the quality of the data.
The questions of measurement error addressed by Ward and Jamison (1991) were
similar to those of the earlier anthropometric research. The subjects were adults and
one observer took two sets of measurements
over a brief enough time period that subject
change in craniofacial dimensions was not
anticipated. We were concerned with anthropometric precision, defined as the closeness of repeated measurements of the same
quantity (Sokal and Rohlf, 1969). To examine precision we calculated the technical error of measurement (TEM)and what Malina
et al. (1973)call the “coefficientof variation”
for each craniofacial variable. The formula
for TEM is:
where d is the difference between the Time 1
and Time 2 measurements for each subject.
This provides a measure of precision that is
in the original units of measurement.
The coefficient of variation is the TEM divided by the grand mean for each variable.
Malina et al. (1973)note that this provides a
measure of relative variability; i.e., the magnitude of the error relative to the size of the
measurement is reported as a percentage.
This is not a coefficient of variation in the
traditional statistical sense (see Malina et
al., 1973, p. 42); so we have chosen to call it a
coefficient of relative variation (CRV).
In addition to these measures of precision,
we also calculated the intraclass correlation
coefficient of reliability (R) described by
Fleiss (1986).This measure of R is:
+ UZe
where T represents individual “error-free”
scores (the mean of Time 1and Time 2) and e
is the difference between Time 1and Time 2
measurements for each individual. According to Fleiss (1986), the result “is directly
interpretable as a proportion of variance. It
is the proportion of the variance of an observation due to subject-to-subject variability
in error-free scores” (p. 3). Thus the higher
the value the more reliable the measure.
Bivariate plots and regression statistics
were obtained to examine the relationships
between these measures of precision and reliability and the size of the craniofacial variables. Both linear and curvilinear regressions were calculated using the Statistical
Package for the Social Sciences (SPSS, Inc.,
1990) implemented at the University Computer Center at Indiana University.
Finally, Fleiss (1986) notes that an assumption of the intraclass correlation statistic is independence between the distribution
of errors and the value of T (p. 2). Marks et
al. (1989) found that for some skinfold measurements this assumption is violated because the error increases in size with the
size of the measurement. They refer to this
as the effect of scale. We tested this assumption in our data by running correlations between Time 1vs. Time 2 differences, and the
mean of Time 1 and Time 2 measurements.
These results are also reported below.
TABLE 1. Unrlateral and bilateral craniofacial
measurements: Grand mean (cm), technical error of
measurement (TEM), coefficient of relative variation
(CRVI, and reliability (Ri between Time 1 and Time 2
(measurements ordered bv decreasing size)
mean TEM CRV’
Head circumference
55.92 .27
0.49 .94
31.30 .28
Mandibular curvature
0.88 .95
Table 1 presents basic descriptive data on
28.64 .25
Maxillary curvature
0.87 .96
0.39 .96
the craniofacial anthropometric variables of
Head breadth
15.07 .06
0.40 .98
interest in this study. Included in Table 1is
13.81 .lo
Bitragal breadth
0.74 .96
the grand mean for each measurement, two
Bizygomatic breadth
13.61 .14
1.06 .90
Total facial height
11.97 .26
2.20 .85
indicators of measurement precision (TEM
Minimum frontal breadth
1.16 .89
10.35 .12
and CRV), and one reliability indicator (R).
Bigonial breadth
10.30 .15
1.43 .90
Biocular breadth
8.96 .ll 1.23 .83
In a previous paper (Ward and Jamison,
Lower facial height
7.02 .21
3.00 .88
1991), we discussed other aspects of these
Bipupillary breadth
2.54 .78
6.09 .15
data and noted that in craniofacial dimen5.27 .18
Nose length
3.33 .69
Mouth breadth
2.77 .78
4.92 .14
sions of less than 6 cm the CRV seemed
3.43 .08 2.23 .91
Nose breadth
rather large and conversely, reliabilities
Interocular breadth
3.24 .06
1.73 .90
were low. We concluded that very small
Nasal prominence
2.12 .ll 5.05 .67
1.88 .13 7.04 .58
Nasal root breadth
craniofacial anthropometric measurements
Philtrum length
1.67 .15
8.74 .68
(less than 6 cm) were problematic, especially
Philtrum breadth
0.96 .13 13.62 .44
Columella breadth
0.71 .05 7.77 .54
those small measurements with poorly defined landmarks. Table 1demonstrates this Bilateral
Lower facial depth
(Rt) 13.97 .19
1.35 3 8
(Lt) 13.91 .ll 0.78 .97
0.94 .94
Midfacial depth
(Rt) 12.52 .12
In relation to the effect of scale, only three
1.02 .94
(Lt) 12.43 .13
variables: mouth breadth, nasal root
1.02 .91
Upper facial depth
(Rt) 11.99 .12
breadth, and right ear breadth displayed
(Lt) 11.94 .ll 0.95 .93
Labial-tragial depth
(Rt) 10.80 .20
1.82 .84
significant correlations between Time 1and
(Lt) 10.74 .16
1.47 .89
Time 2 differences and measurement size.
Exocanthal-gonial depth (Rt) 9.48 .17
1.79 .88
(Lt) 9.36 .13
1.34 .93
Three significant results out of 49 in a reMandibular depth
(Rt) 9.40 .25
2.69 6 7
peated measures test is approximately 6%
(Lt) 9.48 .22
2.33 .77
or very close to the 5% expected by chance
Exocanthal-tragial depth (Rt) 7.74 .13 1.66 .84
(Lt) 7.70 .14 1.79 .83
alone. In addition, examination of the scatMandibular ramus height (Rt) 6.79 .29
4.25 .56
tergrams indicated that an outlier was re(Lt) 6.63 .30
4.52 .64
sponsible for the significant correlation in
2.00 3 3
Ear length
(Rt) 6.20 .12
2.51 3 1
(Lt) 6.20 .16
each of the three cases. We took this to mean
Exocanthal-glabella depth (Rt) 5.80 .21 3.58 .51
that there was no systematic “effect of scale”
3.24 .59
(Lt) 5.81 .19
Ear attachment length
(Rt) 5.14 .24
4.63 .66
in these three variables. Thus, we feel confi(Lt) 5.10 .19 3.76 .71
dent that we have not violated the assump3.32 .64
Alar depth
(Rt) 3.29 .ll
tion of independence in our application of
(Lt) 3.26 .09 2.75 .76
5.25 .65
Ear breadth
(Rt) 3.22 .17
Fleiss’ R statistic.
4.31 .58
(Lt) 3.28 .14
The overall relationship of mean meaPalpebral fissure breadth (Rt) 3.09 .08 2.55 .67
surement size with, respectively, the TEM,
2.85 .62
(Lt) 3.09 .09
4.82 .61
(Rt) 2.35 .ll
the CRV, and R can be seen in Figure 1and
midline curvature
(Lt) 2.35 .10 4.22 .70
Table 2. Figure 1displays scattergrams and
regression lines for TEM, CRV, and R vs. ‘CRV reported as a percentage
mean measurement size for 49 craniofacial
variables ranging in size from less than 1cm
(columella breadth) to approximately 20 cm (r = .072; P = .624). However, the CRV and
R are both significantly related to size. Ta(head length).
These data indicate no relationship be- ble 2 indicates both linear and curvilinear
tween mean measurement size and TEM statistics for the CRV because the latter pro-
Fig. 1. Relationship between overall measurement size (grand mean) vs. technical error of measurement (A). coefficient of relative variation (B), and reliability (C). Regression statistics can be found in
Table 2.
TABLE 2. Regression statistics for relationship between
size of craniofacial variables (N = 49) and measures of
precision and reliability (variables ranging in size from
i l cm to 20 cm): technical error of measurement (TEM),
coefficient o f relative variation fCRV) and reliabilitv IRJ
TEM vs. size
CRV vs. size
CRVvs. size
R vs. size
Curvilinear regression with x2 term
‘Multiple correlation coefficient.
vides a significant improvement in the fit of
the line. The relationship is negative for
CRV indicating that as the average size of
the craniofacial variables increases, the percentage error decreases (multiple r = - B O O ;
P = .OOO). For R,the relationship is positive
(r = .765; P = .OOO), showing that R increases with increasing size of the measurement.
To determine whether we were stacking
the deck by including both left and right bilateral measures in the analysis, we looked
at them separately with the unilateral variables. In both analyses the pattern noted
above was seen, i.e., there was no relationship between the TEM and variable size, a
negative relationship between size and the
CRV,and a positive one between size and R.
Malina et al. (1973) discuss the relationship between anthropometric measurement
size and both the TEM and CRV in auxological data. They argue that both indicators of
precision can be affected by variable size
and therefore one should only compare them
“within variables measured by the same instrument and within variables of about
equal magnitude” (p. 45). To examine this
latter assertion, Table 3 presents regression
statistics for 48 unilateral and bilateral
craniofacial variables broken down into
three size categories: 0-5 cm, 5-10 cm, and
TABLE 3. Linear regression statistics for relationship
between size of cranwfacial variables and measures of
precision and reliability for 48 variables (all unilateral
and all bilateral) divided into three size groups: Technical
error of measurement (TEMI, coefficient of relative
variation (CRVI, and reliability (R)
ition. In fact, the magnitude of the error appears to be quite similar between larger and
smaller variables. Thus, in percentage
terms, the CRV becomes smaller as the average size of the variable increases. Not surRegression
prisingly, R displays the converse-it increases with mean measurement size.
Variables from &5 cm (N = 16)
TEM vs. size
Therefore, measurement size must be con-.667
CRV vs. size
sidered along with ease of locating land,635
R vs. size
Variables from 5 1 0 cm (N = 18)
marks, measurement technique, and sys,517
TEM vs. size
tematic bias in the application of that
CRV vs. size
technique when attempting to minimize er.032
R vs. size
Variables from 10-15 cm (N = 14)
ror. Ward and Jamison (1991) concluded
TEM vs. size
,022 that the most unreliable craniofacial an-.184
CRV vs. size
R vs. size
thropometric measurements would be those
with small absolute dimensions and poorly
defined landmarks. To this must now be
added that measurement size, at least at the
10-15 cm. Head length is eliminated from small end of the measurement scale, prothis analysis because it is so far outside the vides a continuous relationship with precisize range represented by the other vari- sion and reliability, not a threshold effect.
ables. Again, no significant relationship is Our study suggests that R increases with
found between TEM and variable size but measurement magnitude while the CRV dethere is a significant negative relationship creases and TEM remains the same.
between size and CRV and a significant posFinally, we note that in order to calculate
itive relationship between size and R. These valid reliabilities, it is important to test the
same results are seen in all three measure- assumption of no relationship between meament size categories.
surement error and measurement size
within each anthropometric variable, i.e.,
the effect of scale. We found this assumption
The present study suggests that for cran- to be correct within our data and we recomiofacial measurements in the size range of mend that future reliability studies include
0-20 cm, the TEM is not affected by size but such tests.
It must be remembered that the overall
both the CRV and R are so affected. Furthermore, when these craniofacial variables are size of the measurements in this study is
subdivided into 5 cm size groups, the same less than 20 cm and for the three measurepattern of relationships holds, i.e., no rela- ment groupings, 15 cm and less. This entire
tionship between mean measurement size craniofacial measurement battery is toand TEM but a negative relationship be- wards the smaller end of the overall anthrotween size and CRV and a positive relation- pometric scale. Thus we cannot as yet genership between size and R. Using 5 cm size alize our results to the rest of the
groups as a criterion of “about equal magni- anthropometric battery, which ranges in
tude” (Malina et al., 1973), this result is con- size up to stature measurements. Nor, withtrary to their expectation that such relation- out further study, can we generalize these
ships would not be found in variables of results to craniofacial measurements taken
on dry skulls. However, it would seem to us
approximately the same size.
Thus the “bigger is better” concept is dem- that our results might have application in
onstrated throughout the measurement size auxological anthropometry. Here, especially
range under consideration here. While it for infant measurements, increase in size
might seem intuitive that the larger the with age would be a potential factor affectcraniofacial measurement the larger the ab- ing measurement precision and reliability.
solute size of the measurement error, the The other potential application of this cauTEM results in this study counter this intu- tion would seem to be for skinfold measure-
ments on subjects of all ages. A well-nourished subject population might be measured
more precisely and with greater reliability
than a poorly nourished sample if the relationships found here for craniofacial anthropometry extend to skinfold determinations.
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