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Appendix M
Estimating the Accuracy and Precision of the Digital
Caliper and Faro Laser
This appendix presents the datasets available to the Committee for
assessing the accuracy and precision of the digital caliper and Faro laser as used
in measuring backface deformation (BFD) during body armor testing. As
discussed in Chapter 5 and Appendix G, both accuracy and precision are
important characteristics in determining the suitability of a measurement system
for use in a testing process.
During Phase III, two new data sets were presented to the committee: the
side-by-side comparisons of BFD measurements made by the Aberdeen Test
Center (ATC) (Table M-1) and the side-by-side comparisons of BFD
measurements made by Chesapeake Testing (Table M-2).74 The committee also
had access to Walton et al. (2008), which is a summary report of the ATC
experimental data from the 228-page ATC experimental data report (Hosto and
Miser, 2008). The committee evaluated and reanalyzed data from all of these
sources.
SIDE-BY-SIDE COMPARISONS
Tables M-1 and M-2 are datasets that were collected by ATC and
Chesapeake Testing. Each measures BFDs created during a test of hard body
armor. The ATC data (Table M-1, N = 91) were collected in early 2008 as part of
a Program Executive Officer Soldier (PEO Soldier) product data management
test. The Chesapeake Testing data (Table M-2, N = 83) were collected in
February 2011 during routine PEO-funded R&D testing on a developmental
design prototype (different from that used for the ATC data). Chesapeake Testing
is a National Institute of Justice (NIJ)-certified ballistics laboratory and is also
certified by ATC in the use of the Faro laser. Both data sets were collected using
standard test operating procedures. Plots of the two data sets appear in Figures M-
1 and M-2.
74
The new data contained in Tables M-1 and M-2 were provided via personal
communication between U.S. Army PEO Soldier and Larry G. Lehowicz, committee chair,
September 7, 2011.
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FIGURE M-1 Plot of the paired BFD measurements made by ATC.
FIGURE M-2 Plot of the paired BFD measurements made by Chesapeake Testing.
Consider first the question of relative accuracy. For the ATC data, the
average difference between the laser and caliper measurements is 1.36 mm. Using
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a paired t-test, this difference is statistically significantly different from zero (p <
.0001). There is an outlier in the data, however, with a difference of 11.647 mm.
Removing this data point, the average difference between the laser and caliper
measurements is 1.25 mm, with a 95 percent confidence interval of (0.95, 1.54)
mm (significantly different from zero, with p < .0001). For the Chesapeake
Testing data, the average difference between the laser and caliper is 1.56 mm,
with a 95 percent confidence interval of (0.98, 2.13) mm (significantly different
from zero, with p < .0001). These data strongly suggest that the digital caliper and
Faro laser may have systematic differences in their measurements of between 1.25
and 1.5 mm, with the laser producing a “deeper” measurement, on average.
We can also use these data to estimate the precision of the caliper and
laser and to test whether the precisions of the two systems are different. A
methodology for estimating precision was provided to the committee that depends
on making a few assumptions.75 The primary assumption is that the overall
variance in each measurement is the sum of the variances of two independent
components: that of the underlying “true value,” assumed common to the two
measurements, and the method-specific “measurement error.” A second
assumption is that the collections of measurements are roughly normal and free
from outliers. It is only with roughly normally distributed observations that simple
variance calculations can be relied on. Further, if outliers are present, they can
distort calculations of variance and lead to incorrect conclusions. This second
assumption is reasonable for the ATC data and questionable for the Chesapeake
Testing data.
For the ATC data, one can calculate the variance of the laser
measurements (18.0), of the caliper measurements (18.9), of the laser
measurement less the caliper measurement (3.07), and of the laser plus the caliper
measurements (70.7). Assume that
L=T+e
C=T+f
where L and C are the observed laser and caliper measurements, T is the true but
unknown measurement value, and e and f are the laser and caliper measurement
errors, respectively. Assume that T, e, and f are mutually independent and
identically distributed with true variances Var(T), Var(e) and Var(f) respectively.
We observe a small systematic difference in the two measurements, which, as
long as it is constant, can be absorbed into the mean of the errors. That is, we
assume the errors have constant, not necessarily zero means. It is an easy
consequence of these equations and assumptions that the following hold:
Var(L) = Var(T) + Var(e) ,
Var(C) = Var(T) + Var(f),
Var(L − C) = Var(e) + Var(f),
Var(L + C) = 4Var(T) + Var(e) + Var(f)
75
The methodology was suggested by Terry Speed, University of California, Berkeley, to
member Thomas Budinger in a personal communication, December 1, 2011.
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Now we calculate the observed variances Var(L), Var (C), Var( L − C),
and Var(L + C) of these four quantities and use them and the above equations to
obtain unbiased estimates of Var(e) and Var(f).We take the difference between
Var(L + C) and Var(L − C) and divide by 4: this estimates Var(T) . Then we
subtract this quantity from Var(L) and Var(C) to give estimates of Var(e) and
Var(f) .
Using this methodology, the estimate of the variance of the caliper is 1.99;
the precision (standard deviation) is 1.41 mm, with a bootstrapped approximate
95 percent confidence interval of (0.38, 2.11) mm. The estimate of the variance of
the laser is 1.09; the precision (standard deviation) is 1.04 mm, with a
bootstrapped approximate 95 percent confidence interval of (0, 1.52) mm.
Because of the possible presence of outliers, the results from the
Chesapeake Testing data are less reliable. However, using the same methodology,
one can calculate the variance of the laser + part (29.0), the caliper + part (27.8),
laser – caliper (6.9), laser + caliper (106.6). The estimate of the variance of the
caliper is 2.83; the precision is 1.68 mm, with a bootstrapped approximate 95
percent confidence interval of (0, 2.47) mm. The estimate of the variance of the
laser is 4.09; the precision (standard deviation) is 2.02 mm, with a bootstrapped
approximate 95 percent confidence interval of (0, 3.11) mm.
Testing formally for equality of variance between the variances of the two
columns (digital caliper and laser arm) in each dataset using the Pitman-Morgan
test on the ATC data and nonparametric test of Sandvik and Olsson (1982) on the
Chesapeake Testing data, one does not reject the null hypothesis of equal
variances.
However, the probability that the data can support a conclusion that there
is no significant difference between the variances of the two measurement
systems is very low; that is, the statistical power for the design of the side-by-side
tests is low. Power is the probability a test will reject the null hypothesis for a
specific effect size, and it depends on both the effect size and the sample size.
With N = 91, the power to detect the difference in precision (square root of
variance) of the laser and the caliper of the size estimated by Walton et al. (2008)
is only 12 percent. Thus the currently available data cannot be construed as
evidence that the variances of the two measurement systems are similar.
The side-by-side ballistic tests do provide important information about the
bias or absolute accuracy of the test instruments. The tests reported here reveal
significant differences in accuracy. While they reveal differences in accuracy,
side-by-side tests such as those reported here cannot be definitive as to which (if
either) system provides desirable accuracy. The consequences of having an
inaccurate test instrument on body armor testing are discussed in Chapter 5 and
Appendix G. The accuracy issue is separate from the issue of relative precision.
Side-by-side procedures can also provide some information about precision of the
measurement procedures, although larger and more carefully designed studies are
needed to provide definitive results about precision. A formal gauge repeatability
and reproducibility study for the laser, caliper, and other potential measuring
instruments is needed to provide reliable information about both accuracy and
precision (see Recommendation 5-3).
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ASSESSMENT OF OTHER TESTING RESULTS
In this section the committee assesses the results from Walton et al. (2008)
and Hosto and Miser (2008) and estimates confidence limits for specific
quantities. These data were collected using a different experimental design than
the side-by-side data. Four BFDs were created in a mounting box using a mold.
Quoting from Walton et al. (2008), “These clay molds, made from actual
indentations in clay during body armor testing, had very rough surfaces, which
showed the individual thread impressions from the Kevlar ‘Soft Body Armor’
backing. The molds also had remnants of small ‘fissures’ that typically form in
the clay during the rapid deformation of ballistic testing.” These mold-created
BFDs were then repeatedly measured by various operators and instruments.
Faro Laser Precision
The original data for these estimates come from Hosto and Miser (2008).
The Faro data, from Tables B-20a (depth, mm, deepest point column) in the
report, are shown in Table M-3 of this appendix.
Table 2 of the NRC Phase I letter report (NRC, 2009), using the results of
Walton et al. (2008), estimated the precision of the Faro laser as 0.0970 mm:
laser combined standard uncertainty laser operator laser error laser instrument spec
ˆ ˆ2 ˆ2 ˆ2
0.04102 0.08172 0.03252
0.0970
The data contain information only about the variation in the operator and
the error. Here the statistical uncertainty of the laser is defined as:
laser statistical uncertainty laser operator laser error
ˆ ˆ2 ˆ2
0.04102 0.0817 2
0.0914.
Using a parametric bootstrap, the committee estimates a 95 percent
confidence interval for the laser statistical uncertainty as (0.042, 0.141) mm.
Taking the upper end of the confidence interval as a worst case estimate, the
actual laser precision is highly likely to be less than
laser worst case combined standard uncertainty 0.1412 0.03252 0.145 mm.
ˆ
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Digital Caliper Precision
The digital caliper data, reproduced from Table B-21a (deepest point, mm,
corrected depth column) in Hosto and Miser (2008), are shown here as Table M-
4.
Table 2 of the NRC (2009), again using Walton et al. (2008), estimated the
precision of the caliper as 0.823 mm:
caliper combined standard uncertainty caliper operator caliper error caliper instrument spec correction factor
ˆ ˆ2 ˆ2 ˆ2 ˆ2
0.47152 0.362 0.00732 0.57 2
0.823,
Because the data contain information only about the variation in the
operator and the error, the “statistical uncertainty” corresponds to the first two
terms. The correction factor term, which is unique to the caliper, accounts for the
uncertainty in the correction methodology when the deepest point is different
from the aim point. (This difference is called an “offset.”)
The caliper statistical uncertainty is
caliper statistical uncertainty caliper operator caliper error
ˆ ˆ2 ˆ2
0.47152 0.362
0.593.
We can estimate a 95 percent confidence interval for the caliper statistical
uncertainty of (0.367, 0.825) mm. Taking the lower end point of the interval as
the caliper best case for statistical uncertainty, we estimate
caliper best case combined standard uncertainty 0.3672 0.00732 0.572 0.678 mm.
ˆ
Turning to the correction factor term, consider the 0.57 mm uncertainty
associated with the postmeasurement correction made to adjust the caliper
measurements (“how a caliper measurement of a deepest point needs to be
corrected to find the actual depth to the local pristine surface”). Walton et al.
(2008) documents its derivation in that report’s Appendix B. The correction is
geometrically derived, and its uncertainty is estimated using the delta method, a
standard statistical methodology for estimating the variances from complex
functions. Walton et al. (2008) says that “in practice, using aim-points to
reference depth measurements introduces multiple uncertainties (see Appendix B
for quantification), which are found in the assumed and measured values of slope,
offset, shot location on the plate and slope of the impacted surface (not quantified
in this analysis).”
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The data used by Walton et al. to assess this variation are from the Phase I
testing of plates in 2008, not from the data in Hosto and Miser (2008).76 The
committee finds the calculation to have been done in a reasonable and correct
manner.
Issues with Walton et al.
Resolution of the following issues with Walton et al. (2008) would be
accomplished as part of the gauge repeatability and reproducibility studies of
measuring instruments mentioned earlier and is embodied in Recommendation 5-
3.
Caliper measurements were replicated while laser measurements were not.
Obviously, this is not ideal when trying to assess measurement precision.
However, from the data we do have, we can estimate several components of
variation. These results are taken from Table 12 of Walton et al. (2008) (with
calculations replicated by the committee) or were additionally calculated by the
committee.
The variation attributable to the different indentations has standard
deviation 5.28 mm, the variation attributable to different operators (σ 2 laser operator)
has standard deviation 0.040 mm, and the variation attributable to a lack of
repeatability measurement-to-measurement (σ 2 laser error) has standard deviation
0.082 mm. If we calculate a 95 percent confidence interval for the measurement-
to-measurement repeatability using these data, it is (0.045, 0.114) mm.
The measurement-to-measurement repeatability of the data is estimated
using the measurements that operators make on different indentations. Without
replicates, we cannot assess whether the repeatability of the operators is the same
when they are measuring the same indentation multiple times as when they are
measuring different indentations. However, if we make the assumption that these
two variances are the same, then adding replicates does not change our variance
estimate.
Sample sizes are small.
The sample sizes in the side-by-side data and the Walton et al. (2008)
study are not directly comparable due to differences in study design. However,
calculating confidence intervals for precision and accuracy takes into account
both sample size and design differences.
76
Rick Sayre, Deputy Director, OSD DOT&E Live Fire Test and Evaluation, and Tracy
Sheppard, Executive Officer & Staff Specialist, OSD DOT&E, “DoD In Brief to the National
Research Council Study Team,” presentation to the committee, November 30, 2009.
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Offsets used by Walton are excessively large.
The offsets reported in the data tables in Hosto and Miser (2008) have
different statistical features from those used to calculate precision as reported in
Appendix B of Walton et al. (2008). In the latter, it is reported that the 95 percent
quantile of N = 654 offsets from an operationally realistic data set made up of
XSAPI of all sizes first-shot data is 0.5512 in. (14 mm). The absolute value of the
offsets from Realistic Clay III as reported in Hosto and Miser (2008) are shown in
Figure M-3. There are two clusters of data: those below 0.5 in. are from
measuring Indent 2, and those above 0.5 in. are from measuring the remaining
three indents.
FIGURE M-3 Absolute value of offsets for caliper measurements from Realistic Clay III.
It is difficult to assess the impact that these differences could have on the
accuracy and precision estimated for the caliper, although we can use the results
of Walton et al. (2008) to explore the effect of some excursions. Appendix B of
Walton et al. (2008) derived the 0.57 mm uncertainty associated with the
postmeasurement correction using the delta method, a standard statistical
approach for estimating the variance of complicated statistics—in this case, the
variability for the correction factor.
One way to gain some insight into how other operationally realistic data
would have affected the uncertainty estimate is to replace the Walton offset mean
and variance used in the Appendix B delta method calculations with the
equivalents from the ATC side-by-side data. During live-fire tests in 2008, ATC
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listed 41 offset measurements with a mean of 3.7 mm and a standard deviation of
3.6 mm.
Recomputing the correction factor uncertainty using these 41 edge-shot
data points in place of the quantities used in Appendix B (offset 14 mm and
standard deviation 0.81 mm) actually increases the correction factor uncertainty
from 0.57 mm to 0.896 mm. This is because, while the mean offset is larger in
Appendix B than for the ATC data, the standard deviation is substantially smaller.
The latter drives the magnitude of the estimated correction factor uncertainty
more than the former.
The previous calculations included 17 shots with a zero offset. One might
suggest that for those shots there is no uncertainty due to the correction factor
and, furthermore, that their inclusion artificially inflates the standard deviation for
the nonzero offsets. Removing the data for these 17 shots results in a mean offset
of 6.3 mm with a standard deviation of 2.4 mm. Recalculating using these values
results in a correction factor uncertainty of 0.723, which is still larger than the
Walton et al. (2008) value of 0.57 mm.
So, while intuition would suggest that smaller magnitude offsets result in
improved caliper precision, using the offset mean and standard deviations from
the ATC data, which has a smaller mean offset but a larger standard deviation,
results in a larger uncertainty estimate.
Measurements in Walton et al. (2008) were on clay indents produced from molds
of clay impressions that were made from ballistic experiments, not on actual
ballistically induced clay impressions.
An advantage of this procedure is that the mold becomes a more-or-less
permanent artifact that allows replicate measurements by laser, caliper, or other
devices after proper validation. In its Recommendation 5-2, the committee
suggests that a standard BFD artifact should be developed to assist in the
assessment of measurement systems.
The Walton et al. (2008) data were not measured at 100°F.
As discussed in the report, the temperature of the clay can have an impact
on the depth of the BFD created during operational testing. However, the
temperature of the clay should not have an impact on the measurement precision
of either the laser or the caliper because the shape and surface characteristics of
the clay impression are determined by the characteristics of the mold. Those
characteristics did depend on the temperature of the clay when the indents were
made, and they should have been made under operational conditions. But the
temperature of the clay should not have an impact on the measurement precision
of either the laser or the caliper. This can be empirically verified as required.
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The average caliper BFD measurement was greater than the average laser BFD
measurement.
This is the reverse of what was observed in the side-by-side analysis and
what has been reported to the committee as a generally observed phenomenon.
The smoothing algorithm used to generate the Walton (2008) data was not
specified:
Indent Indent Indent Indent
1 2 3 4
Laser 29.8 39.8 34.5 41.4
Caliper 33.5 40.2 36.4 41.3
This demonstrates reversal of the direction. Note that in calculations of precision,
the sample means are subtracted from the data as variation is calculated around
the sample mean.
Deriving the "Factor of 10" Heuristic
Let Z be the observed BFD, which is the sum of the true (but
unobservable) BFD, Y, and the instrument measurement error X: Z = Y + X.
Assume that Y does not affect X and vice versa. Then the variance of the
observed BFD (Z) is the sum of the variances of the true BFD and measurement
error—that is,
Z Y X , so Z Y X
2 2 2 2 2
Now, we want instrument precision to have a negligible effect on the
variation of the observed BFD. That is, we want Z Y . This is achieved when
X 0.1 Y (equivalently, 10 X Y ), as follows. Given we want Y2 X Y2 ,
2
divide both sides by Y and substitute X 0.1 Y to get 1.01 Y Y 1 , or
2
1.01 1.005 1 .
So, as long as the precision of the measuring instrument is less than one-
tenth of the variation in the actual BFDs, the measurement instrument only
negligibly increases the variation in the observed BFD, where “negligible” is
defined as ≤ 0.005. For the current clay process with an observed BFD standard
deviation of 3.5-4.5 mm or so, this means the precision of the measuring
instrument, in terms of its standard deviation, should be no greater than 0.3 to 0.4
mm.
In Chapter 5, the precision requirement was relaxed to 0.5 mm. The
committee estimated something on the order of a 1 percent increase in BFD
variation attributable to the measurement instrument ( 32 0.52 3 1.014 and
42 0.52 4 1.008 ). While that sounds quite small, Appendix G went on to
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examine the effect of relaxing instrument precision further on the likelihood of
making decision errors under the Office of the Director, Operational Test and
Evaluation test protocol. That part of the analysis found that relaxing the
precision any further than 0.5 mm unacceptably increased the probability of
accepting bad body armor and rejecting good armor.
The committee wishes to emphasize that the above derivation of the
heuristic is dependent only on assuming the actual BFDs are independent of the
instrument measurement error. It is not dependent on the assumption of normality
of the BFDs, nor is it dependent on any information from the Walton (2008) study
and its supporting data.
REFERENCES
Hosto, J., and C. Miser. 2008. Quantum FARO Arm Laser Scanning Body Armor
Back Face Deformation. Report No. 08-MS-25. Aberdeen Proving Ground,
Md.: Aberdeen Test Center Warfighter Directorate, Applied Science Test
Division, Materials and Standards Testing Team.
NRC. (National Research Council). 2009. Phase I Report on Review of the
Testing of Body Armor Materials for Use by the U.S. Army: Letter Report.
Washington, D.C.: National Academies Press.
Sandvik, L. and B. Olsson. 1982. A nearly distribution free test for comparing
dispersion in paired samples. Biometrika 69(2):484-485.
Walton, S., A. Fournier, B. Gillich, J. Hosto, W. Boughers, C. Andres, C. Miser,
J. Huber, and M. Swearingen. 2008. Summary Report of Laser Scanning
Method Certification Study for Body Armor Backface Deformation
Measurements. Aberdeen Proving Ground, Md.: Aberdeen Test Center.
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TABLE M-1 Side-by-Side Comparison of BFD Measurements by ATC
Laser Arm,
Data Digital
Smoothed (mm)
Number Caliper
(mm)
1 39.92 41.398
2 35.79 38.931
3 35.74 38.92
4 31.19 33.656
5 29.94 32.526
6 34.61 35.169
7 30.68 32.412
8 36.76 38.224
9 32.68 32.623
10 36.78 35.804
11 26.87 38.187
12 34.63 35.714
13 37.46 39.456
14 28.03 30.61
15 37.58 37.71
16 35.34 38.503
17 30.99 34.638
18 37.51 40.232
19 40.33 43.751
20 34.86 37.006
21 40.38 40.047
22 30.27 34.191
23 35.22 37.017
24 29.99 31.114
25 33.61 35.71
26 33.09 33.268
27 36.57 38.336
28 39.88 43.044
29 38.96 42.177
30 37.14 37.344
31 31.17 31.874
32 28.81 30.112
33 30.99 31.905
34 38.97 40.094
35 43.29 42.804
36 38.18 39.775
37 36.08 37.664
38 39.9 42.756
39 35.02 36.424
40 36.97 39.788
41 39.74 40.598
42 35.8 37.023
43 42.54 43.165
44 27.12 28.307
45 40.18 41.751
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46 34.58 34.469
47 29.94 30.144
48 48.04 48.131
49 36.11 38.75
50 33.48 31.311
51 30.58 31.988
52 30.78 31.344
53 36.93 38.403
54 29.38 31.617
55 37.1 38.029
56 36.12 37.304
57 34.95 34.496
58 34.16 35.909
59 32.87 32.859
60 36.06 34.779
61 26.84 27.09
62 33.9 33.583
63 33.77 34.147
64 30.26 30.552
65 29.75 32.086
66 33.88 35.969
67 47.1 47.497
68 36.02 37.586
69 40.37 40.598
70 35.59 35.941
71 38.36 37.334
72 32.53 33.185
73 25.53 26.371
74 33.73 34.724
75 37.05 37.961
76 40.73 41.137
77 33.02 35.199
78 36.78 39.462
79 40.58 39.999
80 40.16 41.819
81 37.93 37.881
82 37.79 37.087
83 39.73 41.94
83 43.17 40.157
85 35.52 36.928
86 35.17 41.413
87 36.12 38.33
88 32.8 35.736
89 36.24 37.67
90 38.85 39.256
91 41.1 42.662
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TABLE M-2 Side-by-Side Comparison of BFD Measurements by Chesapeake
Testing
BFD Digital Faro
Data Caliper Laser
Number (mm) Arm
(mm)
1 32.9 34.6
2 35.7 36.7
3 30.5 35
4 38.8 39.8
5 33.5 37
6 35.4 36.7
7 33.9 35.1
8 35 37
9 31 33.7
10 31.4 36.9
11 29.1 29.5
12 32.5 33.8
13 26.4 28.1
14 33.5 35.3
15 33.3 35.5
16 25.6 29.1
17 32 33.5
18 26.1 28.6
19 22.4 26.5
20 29 34.1
21 31 33.8
22 26.7 28.3
23 34.1 32.1
24 30.7 29.8
25 36.4 34.1
26 37 36.8
27 31.6 33.1
28 31.9 34.2
29 24.9 26.7
30 42 36
31 32.4 35.7
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32 48.3 55.4
33 37.5 39.9
34 34.6 36.4
35 30.7 35.3
36 35.8 37.6
37 37.4 38.2
38 27.4 28
39 29.7 31.4
40 42.1 37
41 29.9 30.9
42 27.6 28.5
43 36.6 36.4
44 35.2 34.1
45 39.8 43.5
46 36 38.7
47 25.5 30.6
48 31.9 33.5
49 32.6 34.2
50 30.4 31.1
51 36.1 23.5
52 25.8 26.9
53 28.3 29.6
54 24 25.8
55 29.8 31.6
56 37.5 38.3
57 38 38.1
58 29.6 33.2
59 30 31.7
60 38.7 39.7
61 35.2 37.3
62 23.6 23.8
63 32.1 34.7
64 31.7 32.6
65 33.5 35.9
66 44.6 46.5
67 36 37.6
68 34.6 37.7
69 32.5 36.2
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70 33.8 35.5
71 35.4 37.1
72 41 40.4
73 33.6 34.7
74 36.2 37.9
75 33.6 35.3
76 35.5 44.6
77 55 55.2
78 34.2 37.8
79 33.1 33.7
80 36 37.7
81 35.4 36.1
82 33.5 37.5
83 36.1 37
TABLE M-3 Faro Data
Impression (j)
O perator (i) 1 2 3 4
29.8130440 39.753433 34.436170 41.442090
1
29.8898140 39.724725 34.581093 41.414619
2
29.8399260 39.951892 34.724191 41.442222
3
29.8008041 39.828403 34.407924 41.457630
4
SOURCE: Hosto and Miser, 2008.
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PREPUBLICATION DRAFT—SUBJECT TO EDITORIAL CORRECTION
TABLE M-4 Caliper Data
Impression (j)
Operator (i) Operator (i) 1 2 3 4
33.12 40.87 36.65 42.05
a
1 32.97 40.74 35.77 41.49
b
33.50 41.32 36.44 40.57
c
33.56 39.48 37.05 41.12
a
2 33.57 39.56 36.95 40.92
b
33.84 39.53 37.28 41.22
c
33.15 40.72 35.45 41.43
a
3 33.17 40.58 35.62 41.68
b
33.31 40.60 35.7 41.67
c
33.69 39.77 36.76 40.85
a
4 34.11 38.85 36.81 40.91
b
33.81 40.36 36.85 41.39
c
SOURCE: Hosto and Miser, 2008.
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OCR for page 340
PREPUBLICATION DRAFT—SUBJECT TO EDITORIAL CORRECTION
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