Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 129
APPENDIX E
Analysis of Error in the Estimation of
Nutrient Intake Using Three Sample
Data Sets
The impact of two different kinds of error on the preva-
lence estimate is described in Chapter 7. There, the sub-
cammittee examined in detail two potential sources of error
that can affect the estimation of nutrient intake:
errors in estimating the composition of the food item
consumed and
errors in estimating or recording the amount of each
food item consumed.
In this appendix, the committee ex ~ nes the potential
impact of unmeasured errors of this kind on the probability
approach. A distinction will be made between random errors
(deviations moving in both directions around a true mean)
and systematic errors or biases (consistent under- or over-
estimat~on of the true value). A distinction will also be
made between the impact of error in assessing a single serv-
ing of a single food and in calculating intake from a ser-
ies of servings of foods in one day. Emphasis is placed on
the ef feet of these errors on the estimated distribution of
usual intakes across people rather than on actual intakes of
particular individuals. These constructs are first illus-
trated using actual data, and then their theoretical implica-
tions are developed. The initial assumption of this analyses
is that the food composition analyses are correct (e.g., no
systematic bias) but that there is variation in reported
composition.
129
OCR for page 130
130
VARIABILITY OF FOOD COMPOSITION
The most recent reference tables on food composition
developed by the U.S. Department of Agriculture (USDA, 1976-
1984) provide come information about the nether of samples
analyzed and the standard error of the mean for some foods.
For these foods, the standard deviation (SD) of the nutrient
composition can be calculated, and the coefficient of
variation (CV = 100 x SD/mean) can be derived. Although the
standard error (SE) is dependent upon the nether of sam-
ples analyzed and describes the reliability of the estimate
of the mean, the SD is not dependent on the number of sam-
ples per se (provided there are sufficient samples and anal-
yses to supply a good description of the full range of foods)
and furnishes a description of the range of values that can
be taken by a specific sample of the food. The SE is a mea-
sure of the variability of the mean of the population and in
that sense is a measure of the error that might be encoun-
tered in accepting the average composition of a particular
food as the reference data. In the Chapter 6 analysis,
therefore, the SE has been used to calculate confidence
limits. For present purposes, however, the SD is more
meaningful than the SE of the mean. The CV expresses this
variability in relation to the mean, and it is useful in
this exercise for comparing error in estimating nutrient
content between several foods and for considering the Impact
of the error on the estimate of the daily intake of a
nutrient, as used in dietary evaluation.
Because the SD cannot be estimated from the reference
tables for all food items, the available SDs were examined
and used to make a judgment about the possible CV or range
of CVs that might apply for foods with missing data. The
food composition tables indicate that the relative varia-
bility of micronutrients is greater than the variability of
protein; this difference seems biologically plausible. The
USI)A provides no CV estimates for energy, because the
ref erence data for energy concentration are computed rather
than measured values.
Two kinds of data analyses were used to examine the impact
of variability on dietary evaluation. In the first analysis,
hypothetical variance estimates are assigned to a food record
for a vegetarian diet. The variability estimates used for
this analysis are shown in Table E-1. The subcommittee
assumed that the magnitude of the CV is different for various
nutrients, but the level of nutrient was not taken into
account. Subsequent analyses, based as much as possible on
OCR for page 131
131
TABLE E-1. Assumed Variability in Food Composition
Data Used in Estimating the Errora
Class of Vector Range of CVs (%)
Energy
Protein
Other nutrients
-
aData from G. H. Beaton, University of Toronto, per-
sonal ca~unication, 1985.
10-30
10-20
10-45
reported variance estimates and complemented by imputed vari
ances, are presented in a later section of this Appendix.
These variance estimates were applied with a simulation
procedure to the dietary intake record of a vegetarian sub-
ject studied in Toronto. The food composition data reported
by USDA (1976-1984) were used to estimate the average
composition of each of the 21 foods included in the record.
A variability was assigned to each food item by random
selection within the ranges presented in Table E-1 by using
the algorithm
CV (food item X) = 10 + RNDt 1) x Y.
where Y = 20 for energy, 10 for protein, and 35 for other
-
nutrients . Thus, for each food item and each nutrient, there
was a mean composition and CV. his procedure was used to
randomly assign a specific composition for each food item or
nutrient combination. A random value from the normal distr~-
bution, represented by the mean and CV for that food item,
was chosen. Table E-2 presents the results that accrued from
1,000 repetitions of this exercise and computations of the SD
and CV for the computed nutrient intake. The results show
that the relative error is decreased for the total record of
food intake in comparison to the individual food items. me
exercise could be repeated by selecting new random values
for the CVs of the food items and then obtaining composite
error estimates, which would not be expected to differ mar-
kedly from those shown in Table E-2. The table also presents
the direct calculation of the variances and the SD and CV of
the total intake as the sum of variances of the individual
item by conventional statistical approaches. Given the
assumptions of normality for the individual composition
distributions, this is a much more rapid approach than the
OCR for page 132
132
TABLE E-2. Potential Error in a Person's Estimated
Nutrient Intake Attributable to Variance
in Ford Componition Data on Sample
Vegetarian D4eta~b
Food Composition Data
With Variance Added to Food Compositions
Nutrient No Variance, By Randomization Approach By Statististical Formula
Vector Mean Mean SD CV (I) Mean SO CV (I)
Energy
(keel/day) 2,610.4 2,619.6 146.37 5.60 26,10.4 146.02 5.59
Protein
(g/day) 68.8 68.7 3.96 5.76 68.8 4.04 5.87
Calcium
(mg/day) 814.1 812.7 86.49 10.64 814.1 87.29 10.72
Iron
(mg/day) 29.1 29.4 3.48 11.85 29.1 3.43 11.76
Vitamin A
(It//day) 13,085.5 13,070.0 1,912.67 14.63 13,085.5 1,880.3 14.37
Thicken
(mg/day) 2.3 2.3 0.3 12.69 2.3 0.29 12.73
Vitamin C
(mg/day) 303.6 302.8 29.52 9.75 303.6 30.91 10.18
aMean and standard deviation. based on 1,000 iterations with normally randomized
variables in randomization approach. Statistical formula represents addition of
variances under the resumption that each variance is normally distributed with mean
and CV as described. For the CV of ford composition randomly assigned to each
nutrient, see Table E-~. There CVs we as high as 45% for individual foods.
bData from G. H. Beaton, University of Toronto, personal communication, 1985.
repeated calculations based on random selections. The com-
parison of the two methods in Table E-2 shows that the
results are practically identical.
A member of the subcommittee (H. Cmiciklas-Wright, Penn-
sylvania State University, personal communication, 1985)
provided two food intake records for use in a second set of
analyses. New USDA food composition data and variance
estimates (reported standard errors and number of analy-
ses) were available for most of the foods in these records
(USDA, 1976-1984). The data provided by Smiciklas-Wright
were used as more realistic examples for modeling the vari-
ance in estimated intake attributable to variability in the
food composition data.
The first step was to impute variabilities for food com-
position when they could not be derived directly from the
USDA tables. An internalized empirical exercise was used:
CVs were calculated f or all f gods, when data permitted, and
were plotted in relation to the level of nutrient reported
OCR for page 133
133
in the food. me plots suggested that the range of the CV
increased markedly at low concentrations of nutrient. This
increase may reflect limitations of methods for determining
food composition, because an absolute contribution of method-
ologic error may become a large relative error at the lowest
levels of nutrient concentration. Alternatively, it may
simply mean that at low levels, the biological variation is
not proportional to the mean. Nevertheless, it appears that
above a nutrient-specific break point, the variability seems
to relate to the mean, and the range of CVs is diminished.
This apparent relationship was used in imputing CVs in the
two sample diets in the exercise. The stratification of CV
ranges is shown in Table E-3.
Using the ranges shown in Table E-3 and the randomized
approach discussed earlier for the vegetarian diet, the sub-
committee assigned estimates of variability to all foods for
which a direct derivation could not be made from data pro-
vided by the USDA. These data were then examined to deter-
mine the error in the estimated 1-day intake (see Table E-4).
TABLE E-3. Stratification of CV Ranges for Use in
Assigning Variability of Food Composi-
tion in Nonvegetarian Food Intake
Recordsa
Nutrient
Cutoff
Point CV Range Assumed (%)
(per 100 g) Below Cutoff Above Cutoff
Protein 2 g 5 - 50 5 - lS
Calcium 20 mg 5 - 50 5 - 15
Iron 1 mg 5 - 65 10 - 30
Magnesium 10 mg 5 - 50 10 - 30
Sodium 100 mg 5 - 65 5 - 15
Zinc l mg 5 - 65 lo - 30
Thicken 0.05 mg 5 - 50 10 - 30
Riboflavin 0.05 mg 5 - 50 lo - 30
Niacin 0.5 mg 5 - 65 5 - 15
Vitamin C 7.5 mg 5 - 50 10 - 30
Vitami n B6 0.1 mg 5 - 50 10 - 30
Folacin 20 mg S - 65 lo - 30
Vitals n A 300 IU 5 - 65 10 - 30
aData frae H. Semi ciklas-Wright, Pennsylvania State
University, personal communication, 1985.
OCR for page 134
134
TABLE E-4. Comparison of Potential Error Due to Variability of Food
Composition Associated with Estimated 1-Day Intakes, Non-
vegetarian Dietsa, b
Espy mated 1-Day Intake _ _-
Diet HW1 Diet HW2
Nutrient Mean SD CV ( ~ ) Mean SD CV ( ~ )
Protein 104.6 6.20 5.93 97. 5 2.21 2.27
Calcium 1,540.2 80.77 5.24 1,135.2 61.31 5.40
Iron 8.03 1.19 14.85 10.4 1.66 16.00
Magnesium 250.1 15.70 6.28 222.4 13 .04 5.86
Sodium 4,129.5 157.36 3.81 2,589.8 121.73 4.70
Zinc 11.6 0.909 7.85 13.3 1.64 12.33
Miami n 2.10 0. 37S 17.92 0.715 0. 076 10. 59
Ribof lavin 2 . 60 0 .2 05 7 . 90 2 .13 0 . 154 7. 22
Niacin 15.9 0.908 5.72 13.5 0.879 6.53
Vitamin Be 1.45 0.136 9. 37 1.43 0. 210 14.62
Vitam; n C 153.1 11. 91 7. 77 11. 8 1. 54 13 . 00
Folacin 184.3 19.80 10.74 97.1 ~ 2. 02 12. 38
Vitals n A 3,798.4 281.24 7.40 5,142.0 603.61 11.74
=sylvania State University, per-
sonal communication, 1985.
bSee Tables E-11 and E-12 for diet composition.
Here the variance of 1-day intake was computed by statisti-
cal algorithm rather than by simulation. For most of the
foods reported in the first diet (HW1), there were standard
errors from which variance estimates could be derived (see
Tables E-9 through E-12 at the end of this appendix). The
results are realistic estimates of the potential error of
the estimated 1-day intake. For the second diet (HW2), a
higher proportion of the variability for individual foods
had to be imputed ( see Table E-12).
Differences in the CV of the intake estimate for the two
diets can be attributed to differences in variability asso-
ciated with individual foods. The CV of the diet is also
affected by the relative contributions to intake f rem indi-
vidual foods with particularly high or low variabilities.
OCR for page 135
135
Effect of Increasing the Number of Foods in the Diet
Although it may not be apparent from a comparison of the
three diets, it can be demonstrated by statistical theory
that increasing the number of foods included in the record
will decrease the relative variance of the total intake
estimate. This effect is illustrated in Table E-5. In
this model it is assumed that all foods make an equal con-
tribution to total intake and thus exert the same impact
upon variance of the sum. The table displays the impact of
the number of foods in the record by using several hypo-
thetical CVs for the food composition data.
RANDOM ERROR IN THE MEaSUREMENT OF FOOD INTAKE
-
If the measurement or recording of actual intake of
individual food items includes an implicit error because
some items are underestimated and some are overestimated,
then there measurements will lead to error in estimation of
the 1-day intake of nutrients.
TABLE E-5. impact of the Number of Food Items in a
Record on the Error Term for Computed
Nutrient Intakea
Number of CV (I) of Nutrient Content of Individual
Foods in Food Serving
Record 10 20 30 40 50
2 7.1 14.1 21.2 28.3 35.4
3 5.8 11.6 17.3 23.1 28.9
4 5.0 10.0 15.0 20.0 25.0
5 4.5 8.9 13.4 17.9 22.4
10 3.2 6.3 9.5 12.7 15.8
15 2.6 5.2 7.8 10.3 12.9
20 2.2 4.5 6.7 8.9 11.2
25 2.0 4.0 6.0 8.0 10.0
30 1.8 3.7 5.5 7.3 9.1
aThese calculations assume that all foods make an
equal contribution to the total intake and that all
food servings have the same error terms. The values
are based on a simulated distribution.
OCR for page 136
136
For analysis of measurement error when no variance in the
food composition is taken into account, the considerations
are identical to those discussed in the preceding section.
The solution can be obtained by adding the variances, and
the effects will be exactly as calculated for the
variability of food composition tables.
When the model includes error both from measurement and
from variation in food composition, the variance of a prod-
uct must be computed. Statistical equations for the approx-
imation of this variance have been developed by FAO/WHO/UNU
(in press). If it is accepted that there is no correlation
between the two variations, the following equation can be
used to estimate the variance of the product of intake and
food composition:
V = I2 x v(c) + c2 x V(I) + v(c) x V(I)'
where I2 is the square of reported mean intake of units of
food; c2 is the square of reported mean concentration of
nutrient per unit of food; V is the variance of content of a
food whose content is I x C; V(I) is the variance of the
intake measurement; and V(C) is the variance of the com-
position measurement. Thus the equation assumes no corre-
lation between values of I and C, although approximations
are available for situations in which there is a correla-
tion. The result is a variance for each it-m that is then
summed for the total intake.
To illustrate the impact of variation on estimations of
the actual amount of the food items consumed, a hypothetical
10% CV for measurement will be assumed (see Table E-6). This
illustration is based on the vegetarian diet described ear-
lier. In the simulation, values were selected at random from
two normal distributions (one for the intake estimate and one
for the composition estimate) for each food item, and 1,000
iterations were performed. Using statistical calculations
rather than the simulated approach, a member of the subcom-
mittee performed a similar exercise for the data sets for
diets HW1 and HW2.
Comparison of these variance estimates with those devel-
oped earlier for food composition alone reveal that the
effect of adding a second source of variation, although real,
is less than might have been anticipated. Unless the random
error is very large , there will be a limited additional
effect on the error term generated by food composition varia-
OCR for page 137
137
TA=E E-6. Error Term in 1-Day Intakes Associated with Variability
of Food Composition and E rror in Intake Estimate in
Non~regetarian Diets a
-
Diet - 1 Diet BW2
~ SD CV ( ~ ) Mean SD CV ( ~
Nutrient
Protein 109.6 7.56 7.23 97.5 5.81 5.96
Calcium 1,540.2 103.7 6.74 1,135.2 82.52 7.26
Iron 8.03 1.23 15.35 10.40 1.73 16.62
Magnesium 250. 0 17. 72 7. 08 222 .4 15. 51 6. 97
Sodium 4,129.5 239.3 5.80 2,589.8 180.3 6.95
Zinc 11.58 1.00 8.67 13.32 1.76 13.22
miamin 2.10 0.395 18.85 0.716 0. 080 11.13
Riboflavin 2.60 0.226 8.71 2.13 0.175 8.21
Niacin 15.89 1.18 7.43 13.46 1.29 9.49
Vitamin Be 1.45 0.149 10.26 1.43 0.227 15.83
Vitamin C 153.1 14.78 9.65 11.85 1.61 13.56
Folacin 184.3 21.12 11.46 97. 07 12. 72 13.10
Vitamin A 3,198.4 313.2 8.25 5,142.0 683.0 13.28
~ . .
aData from H. &iciklas-Wright, Pennsylvania State University,
personal communication, 1985. For composition of diets and food
composition variability estimates, see Tables E-ll and E-12. (CV
is based on the ass~mptlon that measurement error in 10. normally
distributed.)
bility. The estimates of protein intake in the HW1 data lead
to a 5.9% CV of the estimate of total protein intake when
only food composition variability is considered (see Table
E-7). However, when measurement error is added, the CV
increases to 7.2% (see Table E-6).
are 14.9% and 15.4%.
For iron, the two CVs
The magnitude of the effect depends on many factors,
including the relative contributions of various food items
to the final intake (weighting of the relative variances);
the nether of food items as discussed in the preceding sec-
tion for food composition variation; and, importantly, the
magnitude of the two variances. Table E-8 illustrates the
effect of the estimated variability (error teem) for an
individual food item when there is variability both in food
composition and in estimation of food quantity. As shown in
Table E-5, the relative variance of the total intake for many
individual foods would decrease as the number of foods
increases.
OCR for page 138
138
TAME E-7. Error in 1-Day Intakes Attributable to Varia-
bility in Food Composition and Intake Esti-
matea
Sample Diets
HW1
HW2
~ .
Nutrient Mean SD CV (96) Mean SD Cal (9e )
.
Protein 109.6 7.56 7.23 97.5 5.81 5.96
Calcium 1,540.2 103.7 6.74 1,135.2 82.52 7.26
Iron 8.03 1.23 15.35 10.40 1.73 16.62
Magnesium 2SO.0 17.72 7.08 222.4 15.51 6.97
Sodium 4,129.5 239.3 5.80 2,589.8 10.3 6.95
aNormally distributed with CV measurement error assumed to
be 10%.
TABLE E-8. Impact of ~ Random Error in Intake and Food
Composition Data on the CV Calculated for
Nutrient Content of an Individual Serving
of Fooda~b
CV 2 0 10 20 30 40
0 0 10 20 30 40
10 10 14.2 22.4 31.8 41.4
20 20 22.4 28.6 36.6 45.4
30 30 31.8 36.6 43.4 51.4
40 40 41.4 45.4 51.4 58.8
l
aData from NFCS. Values are relative.
ball values expressed as CV = 100 x SD/mean.
not important to know which variable is 1 or 2. m e
error term for a diet comprising several individual
servings of foods would necessitate a summation of
variances (see Table E-5).
OCR for page 139
139
These analyses demonstrate that the true intake of nutri-
ents by a person on a particular day differs from the esti-
mated intake and suggests that the standard deviation of this
error for mixed diets containing 15 to 20 different foods is
likely to fall in the range of 5% to 15%, depending on a
nether of factors. Thus it can be assumed that 95% of the
time the estimated intake will fall within 10% to 30% of the
actual intake of a nutrient. The error in the estimate of a
particular person's intake on a certain day is appreciable.
CONCLUSIONS
These analyses demonstrate that random variation in food
composition (including random errors in analysis) and in the
estimation of food intake introduces an element of variation
in computed nutrient intake across days for 1-day records
and that the relative impact, although not as large as might
have been expected, is nevertheless real. These considera-
tions suggest that part of the reported difference between
calculated intake and chemically determined intake for
duplicate meals or composite diets may arise from random
error and that perfect agreement should not be expected.
In considering the distributions of nutrient intake in
population data, the data on variability of food com-
position discussed in this appendix are not normally
included. That is, the true variability of 1-day intake is
greater than would be estimated with conventional techniques
based on average composition data from the food composition
table.
More import ant in the context of the present report is
the impact of random variation on estimation of the
prevalence of inadequate intake. Part of the unmeasured
variation associated with the 1-day intake estimate would
clearly be factored out by the analysis of variance (ANOVA)
procedure used to estimate the distributions of usual intake
in the population. This part of the variation would have no
final impact on the estimate of prevalence. Thus, there is
no need to measure or estimate its magnitude. To determine
if the entire effect is factored out in the ANOVA, a
statistical model was developed (see Chapter 8). For this
model, SEs were estimated from the food composition table
for the diet HWl presented in this appendix.
OCR for page 140
140
A similar approach for deriving the SE of a 1-day intake
was used to estimate the SD and CV, but SEs rather than SDs
of composition of individual foods were used as the starting
point. The results demonstrate that random variation as dis-
cussed in this appendix influences the confidence 1 ~ ts of
the estimate of usual intake and may also influence the esti-
mate of prevalence. If the prevalence estimate is below 50%,
the effects will lead to a slight underestimation of the
prevalence, and if the prevalence is above 50%, the effects
will somewhat overestimate it. Fortunately, as demonstrated
in Chapter 8, the under- or overestimations and the impact
of confidence limits are not so great as to invalidate the
approach to assessment. Nevertheless, it is clear that
Improvement of food composition data bases can improve the
estimate of the prevalence of inadequate intake. True bio-
logical variation between individual samples of food will
limit the improvement that can be gained. Modeling ap-
proaches such as those presented in this appendix together
with those presented in Chapter 8 can be used to ascertain
which types of improvements in the food composition data
base would have the greatest impact on estimations of the
prevalence of inadequate intakes. Analyses of this kind can
provide the basis for establishing priorities for future
analytical work.
True systematic biases in either food composition or food
intake data are not considered in the analyses presented
herein, but are discussed in Chapter 7. As was shown, these
effects, if present, will influence the prevalence estimates.
Elimination of systematic biases due to errors in methods
should receive a high priority for this reason.
REFERENCES
FAO/WHO/UNU (Food and Agriculture Organization/World
Health Organization/United Nations University). In
press. Energy and Protein Requirements. Report of
a Joint FAO/WHO/UNU meeting. World Health
Organization, Geneva.
USDA (U.S. Depart ment of Agriculture) . 1976-1984. Com-
position of Foods: Raw, Processed, Prepared. Agri-
culture Handbook No. 8. Sections 1-12.
Agricultural Research See vice, U. S . Department of
Agriculture, Washington, D.C.
OCR for page 141
141
1
IY
8
E~
~5
-
~ O
P. ~
~n
O
d_
O
O
C~
~ O
O S
t~
S ~
o
oe ~
3 3
o
S
U)
a ~
o
S~
a' ~
0 3
:~:
O
O ~
0 ~r:
r.
X
~ U)
~ U)
~:
1
W
IY
E~
g-~-
°~0
00 f
W Y
3 ti3 _
u-) ~ 1 1 _' ~ r— 0 ~ ~ 0
~ ~ 1 1 ~ ~ ~ ~ ~ ~ ~)
r. 0
U~
o o
· ~
o o
00 1
_I t~ 1
O O ~ ~D ~ O ~ a, ~ 0
1 ~ ~ O ~ C~ 0 1
_~ ~ ~ _~ _1 ~ 1
1 ·~D ~ t~D ~ tD —~ ~ °
o o o o o ~ o
· ~ · ~ e · · ~
O O O O O O O O O
1 ~ C~ ~ ~ t— _I ~ d' 1
~ ~ ~ ~ _t _I ~ q' 1
~ ~ 1
1 ~ 1
1 _' 1 1 ~ ~ ~
t C~ I I ~ _4 q'
a~ 0 _I Ol (g ~ ~)
C~ ~ ~ ~ ~ ~ ~
0 ~ ~ ·n 0 0 0
· · · · · · ~
O O O O O O O
~ ~ 1 U~ tS) _1
_I ~ 1
o o o o o o o ~ o o o o o o o o o o o o o
~ ~ ~ ~ u~ 0 ~ ~ a, ~ 0 co 0
un ~ ~ ~ ~ ~ ~ ~ o ~ ~ ~ ~ cN
u~ ~ ~
un
· ~
o o
~ ~ c
~.
m ~ ~s
U~ ~ CC
· ·
0
0 r~ iD ~ ~ u~
· · · · · ~
0 ~ 0 0 ~ 0
r ~ c~
o,
C~
0 ~ ~ ~ a~
.
tD ~ O
· · · · · ~
O O O _I _~ N
0 ~ ~ a, ~ 0 ~ _I ~
. ~ ~ ~ ~ ~ a~ U~ (D
a) 0 ~ a'
0m
· · · · ~
- - O O ~
~ ~ O
u, ~ 0 a~
· · ~ · ~
O O ~ ~ C
9 ~ tD o
(D ~ un O cr, ~ 0
0 u~ a' ~ ~ ~ 0
a
· · · ~
~ O O ~
· · · ~
· · —
U~
~n 0 CO a) ~ ~ ~ ~ ~ ~ tD
~ ~ ~ ~ ~ ~ ~ ~ c~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
O ~D ~ o ~ U, ~ ~ C~ r. ~ ~ ~ co
{D ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ a' 0
~ ~ ~ ~ ~ ~ un ~
0 ~ u~ ~ 0 0 0 0 0 ~n 0 ~ u~ co 0 0 ~ ~ 0 0
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ a) ~ ~ u~
co un
R
0 ~n
a' 0 ~ ~n
—
~ ~ X ~ 0 ~ X Q) S
O ~ -- ~ ~ 5: ~ ~ ~ ~ Q) `2,
_~ oB X ~ ~ ~ ~ ~ 3 ~ ~ R ~ ~ ~
° ~ ~ ~ ~ ~ ~ ~ O O £ ~ ~ O V
V R O ~ ~ ~ ~ ~ ~ o ~ ~ ~ -
£ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ O ~ ~ ~ ~ ~ X
O ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ O ~ ~ ~ ~ ~ V
o ~ ~ ~ V ~ ~ 0 0 ~ ~ 0 —
~ ~ O ~ - ~ ~ O ~ ~ > - ~ ~ ~ 0 0 ~ ~ ~ ~
3u ~n cJ~ ~ CJE~ v c~ ~:o vm Z: v ~ ~ uv m
0
~5
~n
0
0
v
0
O
0
0
0
x
0
0 0
~ 0
q4 u~
m
1 a,
0
~ 0
0
o~
m s~
OCR for page 142
142
TABLE E-10. Example of the
tion Eat: mates
Application of Random Selection of Food Compo~i-
for Calciuma
. .
Tabulated Hypothetical Calcium Content
Content (mg in food consumed)
Food Item ( mg ) 1 2 3 4 5 6 7 8 9 10
Watermelon 56 16 28 63 51 70 53 63 87 89 31
Cherries 113 185 178 184 134 90 67 191 190 140 77
Soy mi lk
concentrate 38 40 46 53 52 16 37 42 32 52 25
Cereal mix 67 77 64 101 40 62 109 87 54 43 61
Figs 11 11 7 14 6 20 8 15 13 18 11
Lettuce 8 7 12 8 7 9 9 8 8 5 9
Cucumber 18 14 20 22 14 13 16 17 12 17 24
Tomato 10 2 13 12 6 14 10 19 13 15 9
Cabbage 54 75 48 40 62 35 51 74 64 57 44
Green peppers } 1 1 2 2 1 1 1 1 1 1
Avocado 4 6 3 5 3 4 5 6 5 2 3
Olives 29 31 27 35 28 32 28 33 26 27 33
Green onions 8 8 9 8 5 5 11 9 7 10 8
Bread, white 49 49 90 25 35 62 42 81 24 36 49
( nonmilk)
Mayonnaise 14 16 11 10 11 9 13 9 20 14 11
Corn on the cob 4 5 2 5 6 6 4 4 5 3 3
Peanut butter 126 134 143 136 131 142 102 148 166 157 104
Kidney beans 110 73 167 178 127 183 95 87 230 100 274
Celery 2 2 2 2 3 3 2 1 1 3 2
Cantaloupe 24 24 30 34 17 20 38 32 16 24 33
Black currants 6 6 8 6 6 4 5 6 7 8 7
Total 814 784 907 942 746 801 706 933 980 822 820
abased on vegetarian diet described in Table E-9. Overall mean = 844. 5;
SD ~ 91.45; and Cal = 10.83~.
OCR for page 143
143
Q
)4
V
0
o
z
JJ
3
V
o
~n
IB
V
V
oo
tY
g
o
V
a'
O
S4
O
Q C)
o~
o
0
N ~
9~P
~ol ~
V) ~
0
~: £
0~m
51-
O
, ~
..c —
~ V —
~ :s
3 03 _
~V
~ ~o
E~ ~0
0 ~ ~ ~ 0 ~ ~ u, 0 ~ ~ a'
· ~ e . e ~ e ~ e e e ~ e e e
a, ~ ~ ~ un r" ~ ~ ~ ~ ~ ~ a,
r~ ~ ~ ~ ~ ~ ~ ~ u~ ~ uO ~ r~
r~
~n 0 ~ 0 0 ~ ~ ~ ~ ~r ~ ~ (D 0~ 0
0 - 0 ~ ~ O ~ ~ ~ ~ ~ O ~ O ~
· e e e e e e e e e ~ e e e e
0 ~ ~ ~ 0 0 0 ~ ~ 0 0 0 r~ 0 0
U~
e e e
~ {D
U~
r~
~r
UO O
O
CO
O ~ 0`
e e e
~ ~ O
0`
~r ~r ~ ~ ~r ~ ~ -4
e e e e e e e e
~ ~ ~o 0 r~ ~ ~ ~ r.
a~ ~ ~ 0 0
1 u~ ¢' 1` ~ ~1
1
~ ~ ~ o ~ tD ~ tD ~ ~ ~ ~ CO O
e e ~ e e | e e e e e e e e e
_l a~ In t~ 1 _~ C~ a~ t~ ~ ~ ~ ~ t~
~ ~ ~ ~ ~ ~ r~ ~ ~ ~4
O ~ ~ ~ ~ 1 ~ O ~D 1` ~ 1` 0 t~ _'
1 ~ _1 1 _~ O4
41
- m ~ r m~ ~ ~ ~ ma~ " - ~ ~4
e · · · · ~ e · · · · e ~ e e
eF a' U, ~ ~ ~ ~ ~ ~ ~ ~ a' ~ 0 a'
~D ~ ~ ~ ~ r~ ~ r~ c~ a
r~
o~ ~ ~ u~ ~ ~ ~ (D ~ O ~ ~ ~ ~
r~ {D r~ 0
e · · e e e e e e · · · · e e
O ~ ~ ~ O O O ~ O O O O O O O
_1
e e
1
_~ _~ 1
Ch ~ 1
1` 1
tD ~ ~ ~n
e e
0"
e e ~
U'
a,
· e
U~ ~
~ o ~ ~ tD CD {D O ~
e · e ~ ~ e e e e
'? ~ a, ~ ~ ~r
r~
~r ~ ~ un ~ ~ ~ u~ ~q
c~ ~ iD ~ r~
r"
c~ ~ r~ 0 0 {D ~ ~r ~
e e · · · · · e e
~ ~ ~ 0 a, 0 ~ ~ ~
a) ~ 0 0 ~ 0 ~9 a~ 0 0 tD ~ r~ r~
r~ a'
~ ~ e e e ~ ~ e e · e · ~ e e
0m ~ ~ ~ ~ ~ ~ ~ O ~ ~ ~ O
~ ~ ~ ~ r~
.
d tD CD ~ tn ~ o 0 1` ~ 0
tD ~ r~ ~ _d ~ ~ ~ CD - 1 ~ ~ ~ ~
r~ O4 ~ ~ e4
0 0 ~
0 ~ ~ ~ V
S~ ~ 0 ~ ~ ~ X
= O ~ O ~ Y O
, - ~ ~ ~ _ ~ ~ 0 ~ ~ O O
~ 0 0 V 3 0 ~ ~ ~ S
0~ ~ ~ ~ ~ V O ~ ~ ~ o, O
mE m~ ~ ~ ~ 0 ~ ~ Y ~ ~ ~ ~ V
- ~ mm 0S Y ~ S ~ ~ ~ S OX
h 0 ~ ~ 3 ~ ~ 3
~ ~ ~ S ~ O ~ ~ S ~ - O O ~ ~
0 cn v~ u~ ~ C) P ~ ~) ~ 5: P4 Pd pd U]
X
o
o
0
~a
E~
OCR for page 144
144
-
o
-
E~
e1- ~
CD
o
o o
~ 5~*
~ 3
oo S~ E
O ~ U. ~
~ ~ a)
~ ~ ; -m
S —
0 0 ~
5 03 _
O
· -
=" ~ 1
~ _1 1 1
o o
· ~
Ct) ~ 1 1
~ a, 1 1
o o
· · ~
Ct) CD 1 ~)
_~ t~i 1 _~
o ~ ~ U~
~ o
o o ~ U~
o o
· ~
r~
r~
CO 1
~ 1
o
U.
~r
o
0 1
1
o
1
~ 1
r~
o 1
~D
1
1
tD ~ O
· · —
U~
U~
a' ~
o ~ o
· · —
o o o
.
O 1
u, 1
a'
· —
0 1 ~ ~D 1
1 ~ ~ 1
u~ CD O
o~
a, Dd s~ ~
~ ~ :, ~ C) ~ oe
_ _ O ~ O ~ ~ O
r' ~ ~ S ~ ~ ~ ~ ~ ~ o
~ ~ ~ ~ 3 0 ~ ~ ~ S s
Q) ~ t~ ~ ~ Q) V O q~ ~ ~ ~ O
=~ ~ ~ ~ ~ ~ == ~ ~ S
- ~ ~ ~ ~ s x~ ~ ~ ~ ~S ~ ~ ~ X
) ~ ~ 3 ~ ~ 3 E ~ o ~ ~ ~ v 54
~ ~ ~ s ~ O o ~ ~ ~ ~ O O
O u' u' tQ £ C) E~ ~ o Pe ~ ~ P4
·`
U~
¢:
3
2 t)
t) N
O '
0 ~
a'
o
00
~:
JJ ·-
. -
~n
's
0
~ I
:D 0
0 O'
U
£
~ ·~
U~ ·-
o ~
-
O
~ o
0 ' -
P~ ~
tD
c) m
~ F
:~ _ ~
1 ~ JJ
~a
~ '
.Y
c0
O '
E $4
U5 O.
·
5: ·. ~
_ ·`
:>
V '
q5
O ~ ~
3 -
= -
F O
—
:~
:r S
_ ~
~ ·`
u2 3 ~
s~ ~ ~
o £
~ ~ -
Q,
~4 ~
~4 S
O ~
h ·'
a'
R
~5
3 V
~ Z
o
· F
o~ 0 ~
~ ~ .~
m~ ~
OCR for page 145
145
rat
o
o
o
~4
o
a
s
3
o
A
07
JJ
at
-
o
JJ
~n
o
C,
~o
r~
E~
o ~-
o
aC ~
3 ~ _
~o
|R
u ~
91-
cn £
a'
F:
o ~
C)
O ~ c~ a) ~ ~ ~ ~ 0 ~ ~ ~ ~
e ~ · ~ ~ ~ e
cn ~ ~ ~ ~ ~ ~ ~ ~ ~ r~
~ ~ ~? ~ tD ~ ~ ~q ~ tD
U~ ~ ~ ~ U~
O O U~ ~ O
· ~
O O O ~ O
a~ a~ ~ ~ ~ un
~ ~ O ~ O O ~ O
· ~ ~ ~ · ~ ~ —
O O O O ~ O O ~
~r ~ r~
· · ~ · · e ~ · e
_~ 1 1` _~ OD Ct) a~ ~ ~ CD t~ ln
1 _I tD ~) ~ _1 1~ C~
O ~ ~ ~ O ~ ~ O ~ ~ U~
_' ~ ~ _I ~) ~ 1
~r u~ ~ ~ CD a~ ~ ~ ~D u
U~ ~ ~ ~ ~ ~ O O ~ O ~ ~
O ~ O ~ ~ ~ ~ u~ ~ ~ ~ ~ ~r
* * * * * *
~r ~ ~ ~ 0 ~ ~ ~ 0
. . . · · . . . . · . . .
~ 0 u~ ~ ~ 0 a, ~ 0 ~ ~ ~ a,
U~ ~ ~ ~ _1 N 11~ 1D ~ ~I t~ U,
O 1` _I ~ a) In ~ ~ ~ t~4 CD a,
O O O O ~ ~ ~ ~ ~ ~ O
. . . · . . . . · · · · ~
0 0 0 r~ 0 0 0 0 0 ~ o 0 0
* * * * *
tD r~ ~ a~ ~ ~ r~ ~9 r~
· . · · . . · · · . · · .
~ u~ ~ ~ a~ ~ ~ a' 0
a~ r~ U~ tD ~ ~ a~ ~ ~ 0 ~r
O u~ a'
* ~ * ~ *
r~ ~ a' ~ ~ ~ r~ tD ~ ~ ~ ~ CD
· . . . . . · . . . . . .
u~ O ~q CD ~ ~ ~ r~ u~
~ ~D a~ u~ ~ ~ ~ O ~ ~
un ~? a~ ~ ~ ~ a~ ~ ~ tD ~ ~ ~D
· · · . · · · . · . . · .
O ~ r~ ~ 0 ~ 0 0 ~ ~ 0
U~
.
O O ~ O ~
U~ ~ ~9 U~ {q
~4 r~ ~ r~
O
~ a1 ' ~ ~ ~ ~
s a, ~ o, ~ 0
O
O
- ~ r~ D
m~ a~ ~ o.=s s
Q) ~ ' ~ ~ JJ ~ C~ ' s~ s~
0
£' 54 3 ~ r~
~ ~ o ~ o ~ ~ ~ ~ ~ ~Y: ~ ~ ~
s ~ ~ m~ ~ ~ ~ ~ o ~ ~ ~ ~ ~ V
h ~ O ~ ~ S
~d ~ ~ 3 E~ O C
V
X
e0
~a
C
~C
O
V
E~
OCR for page 146
o
c)
-
~3
!4a
8 ¢,
s ~
8`
0
3 t~ _
JJ
O
O ~ O ~ ~
~ a, 0 CD tD ~ 0\ 0 ~ ~n
· · · · · · · · · ~
O O O O U~ O O O O O ~ O O
~r
U~
.
tD r~ ~ tD ~ ~ ~ ~ o o 0\ 0
N _I N ~ C~ ~~ {~~ U-~ [' ~D tr'} tq
_l _d _1 ~ ~ _~ O4 _~ N _
%4 ~ 0
O JJ
0 ~ ' ~ V ~ ~
~ ~ ~ ~ ~ ~ O
0 0 ~ ~ ~ O ~ ~ ~ ~
~ O ~ ~ ~ ~ ~ ~ O U
_' ~ ~ m~ ~ ~ ~ ~ O
' (S) ~ ' %4 h ~ ~ O '
~ - - ~ ~ 0 ~ ~ X
0U ~ ~ ~ ~ ~ ~ ~ V ~ ~ ~ ~ ~ ~ R
~d~ ~ ~ 0 0 ~ ~ 0 0 ~ ~ ~ ~ X
S~ ~ ~ ~ ~ m~ ~ ~ ~ ~ O
~ ~1 kl 51 ~ O ~ ~ S: ~ h
C~ 1~ C) ~ ~ 14 ~ p
N
-
~ 0`
U~
' ~:
-4
~0 ~
IB JJ
_'
0
~ '
V
O
~D
~ O
O ~
tD
m
_
0£
4J
u~ '
o
54 ~
r.
·.
- ~
. — 0
t~
~a
JJ
s ~
v ~
s
0 ~
~ co
q4 c,
o ~
l4
~ £
i~
Z ~
Representative terms from entire chapter:
food item
