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 110
APPENDIX A
Adjustment of Intake Distributions
Used in This Report
All original analyses in this report have been based
on data from the 1977-1978 Nationwide Food Consumption
Survey (NFCS), which were provided by the U.S. Department
of Agriculture (USDA) for this purpose. Data were avail-
able for approximately 2,400 women and 1,750 men between
the ages of 23 and 34 years.
AS described in Chapter 4, food intakes estimated on
each of 3 consecutive days were not collected by the
same technique each day. The first method of observa-
tion consisted of an interview and recall of foods eaten
on the day prior to the interview. The respondent was
then instructed to keep a record of food intake for the
remainder of the day of the interview and the following
day. Subsequent statistical analyses have suggested
that either the method or the sequence of observation
days has an effect on reported intake; however, this
effect has not been considered in the analysis presented
herein. The resulting variance has been pooled with
intraindividual variance. Because the data refer to
adjacent days rather than to independent estimates of
intake, there is a potential for loss of statistical
power as a result of the design of data collection,
because of possible correlation of food intake between
days for a given person.
-
Note: The data analyzed in this report are for nutri-
ents ingested in foods. Infonmation about dietary sup-
plements was not included in the 1977-1978 NFCS. As a
result, all analyses presented in the report underesti-
mate intake and overestimate the prevalence of inade-
quate intake. The magnitude of this bias is not known.
110
OCR for page 111
111
The USDA provided data in the fore of fixed fre-
quency interval distributions. The data for individual
subjects were ranked and the mean intake computed for
each interval. Altogether there were 200 intervals,
each consisting of 0.5% of the subject days. me data
were presented in three ways: (1) data for 1 day with-
out grouping data for each person (i.e., as if all data
were independent), (2) mean values for 3 days of intake
data for each person, and (3) mean values of the loga-
rithm of intakes for each of 3 days for each person.
These were the basic working data sets for the analyses
presented in this report.
The USDA also conducted and reported to the subcom-
mittee its analysis of variance (ANOVA) results for the
NFCS data. For this analysis, the 1-day data were loga-
rithmically transformed, and the subcommittee performed
an ANOVA by standard techniques, assigning variance to
model (subjects), to day (sequence), and to residual.
Subsequently, variance was assigned to on' y two
components--model and residual. A typical ANOVA is
displayed in Table A-1, together with an illustration of
the derivation of interindividual and intraindividual
variance estimates. From the data transformation shown
in the table, the variance attributable to subjects is
computed as:
V(subject) = (0.40930366 - 0.16502502)/3 a 0.081427866,
and the standard deviations (SDs) attributable to subjects
(interindividual) and to day-to-day variation within subjects
TABLE A-1. ANOVA: Protein Intake by Adult teen, Shown by
Logarithmically Transformed Data
Degrees
of
Source Freedom Sum of_Squares MeSE 05 aid
Modela 1 ~ 751 716e 69947157 0 ~ 40930866
Errorb 3 ~ 498 577e 257S1426 0 ~ 16502502
TotalC 5'249 1'293 ~ 95698583
-
a3 V( subj ect) ~ V(error).
bV(error).
CCorrected.
OCR for page 112
112
( intrainaividua1 ) are computed as the square roots of
V(subject) and V(error). Thus, SD(~nter) = 0.2853556 and
SD(intra) = 0.4062326. The adjusted SD of 3-day data may be
estimated as the square root of the sum of variances
[V(subject) + V(error)]/3 to yield a 3-day SD of 0.369372.
The results of ANOVAs carried out for the NFCS data sets
are presented in Table A-2. For comparison, the observed
SDs in the original logarithmically transformed data sets
are presented as well as the 3-day SD derived as described
above.
In estimating the distribution of usual intakes, the
obj ective was to remove the effects of the day-to-day
variation in intake, the error term in the ANOVA. This
component of variation includes both real day-to-aay
variation in intake and any random error in methodology
(e.g., day-to-day variation in under- and overreporting of
actual intake attributable to method). Of course, it does
not adjust for any systematic bias in the data sets (consis-
tent under- or overreporting for individual subjects).
TABLE A-2. Estimate" of Interindividual and Intra-
individual Variation in Logarithmically
Transformed Datsa
Nutrient
Estimates of Variation
Nether of SD(inter- SD(intra-
Sub~ects individual) individual)
Males:
Protein 1,752 0.2853 0.4062
Iron 1,752 0.2909 0.3825
Vitamin A 1,752 0.5119 0.8547
Vitamin B 1,752 0.6493 0.8441
Thiamin/day 1, 752 0.3497 0.4415
Thiamin/koal 1, 752 0.1898 0.3421
Females:
Protein 2,394 0.3370 0.4468
Iron 2,394 0.3518 0.3987
Vitamin A 2,394 0.6092 0.8834
Vitamin C 2,394 0.7090 0.8843
. . .
"Derived from the subcommittee's analysis of the 1977-
1978 NFCS.
OCR for page 113
113
If all data sets fit perfectly to the normal distribution,
it would be possible to use the mean and interindividual SD
to completely describe the new distribution. However, ex~m;-
nation of the distributions revealed a number of departures
from normality. An approach that was adopted might preserve
some of the uniqueness of the original distribution while
removing the effect of intraindividual variation. This
approach is described by the following algorithm, which was
applied to each interval of intake in the original trans-
f ormed data set:
Adjusted intake = (observed intake - mean intake)
x SD(interindividual) + mean intake.
SD(observed)
This adjustment created a new distribution with 200 inter-
vals, still in logarithmically transformed form. By com-
puting the exponential of the values, the distribution was
converted back to the original units and could then be used
in subsequent computations as an estimate of the distribu-
tion of usual intakes.
Descriptive information on some of the distributions used
in this report is presented in Table A-3. The 1-day intake
distribution consists of all single-day measurements analyzed
as if they were independent observations. The 3-day intake
distribution represents the means, calculated at the level
of individuals, for three replicates of intake. The loga-
rithmically transformed 3-day distribution represents the
mean log of each day calculated at the level of the individ-
ual. The transformed distribution, in original units, is as
described above. The most critical measure in the data pre-
sented is the degree to which the transformed data fit the
normal assumption. It would have been preferable to develop
a transformation algorithm appropriate to the individual data
set before conducting the ANOVA (Box and Cox, 1964). How-
ever, this exercise was not conducted for the present report
REFERENCES
Box, G. E. P., and D. R. Cox. 1964. An analysis of
transformations. J. R. Stat. Soc. B26: 211-252.
Cochran, W. G., and G. W. Snedecor. 1980. Statistical
Methods, Seventh edition. Iowa State University Press,
Ames.
.
OCR for page 114
114
TABLE A-3. Characteristics of the Distributions of Nutrient Intake in
This Report
Nutrient and Observed i, b
Data Set Mean Median SD Skew Kurtosis
MALES:
Protein ( g/day )
1-day data 97.8 91.4 45.0 1.185 3.021
3-day data 97.8 93.9 33.9 1.038 2.639
Tran~fonned data 4.4744 4.503 0.3695 -0. S71 1.273
Adjusted data 91.2 89.6 25.0 0.578 1.308
Iron ( mg/day )
1-day data 15.9 14.7 7.4 1.369 3.820
3-day data 15.9 15.} S.7 1.302 3.880
Transformed data 2.6570 2.676 0.3655 -0.335 0.849
Adjusted data 14.9 14.5 4.3 0.849 2. 046
Vitamin A ( IU/day )
lordly data 5,S70 3,37S 9,12S 7.939 82.743
3-day data 5,600 4,155 5,800 4.645 30.160
Transformed data 8.1160 8.150 0.7194 -0. S2S 1.1S2
Ad jutted data 3,780 3.420 1.890 1.411 3.594
Vitami n C (m/day)
1-day data 85.2 57.0 84.6 2.279 7.869
3-day data 85.3 66.7 67.5 2.072 6.630
Transformed data 3.939' 3.980 0.8770 -0.372 0.118
Adjusted data 62.4 52.8 39.4 1.476 3.297
Thiamin ( mg/day )
1-day data 1. 53 1.36 0.87 1. 596 4.012
3-day data 1.54 1.44 0.67 1.494 4.422
Transformed data 0.2197 0.310 0.4334 -0.234 0.516
Adjusted data 1.40 1.35 0.49 1.135 2.903
l~hiamin (mg/1, 000 kcal )
1-day data 0. 64 0 . 59 0 . 2 7 1. 570 3 . 862
3-day data 0.64 0.62 0.18 1.095 2.837
Transformed data -0. 5175 -0. 521 0.2738 -0.179 1.232
Adjusted data 0.61 0.60 0.12 0.697 1.914
FEMALES:
Protein ( g/day )
1-day data 65.5 61.6 31.1 0. 918 1.605
3-day data 65.6 63.0 24.1 0.78? 1.264
Transformed data 4.0527 4.097 0.4377 -1.277 4.469
Adjusted data 61.3 S9.5 18.3 0.346 0.682
Iron (mg/day)
1-day data 10.8 10.0 5.3 1.367 3.800
3-day data 10.8 10.2 4.2 1.318 3.962
Transformed data 2.2567 2.290 0.4195 -0.848 2.796
Ad3 usted data 10. 2 9. 8 3 .3 0. 812 2. 0 88
Vitamin A ( IU/day)
1-day data
3-day data
Transf orbed data
Adjusted data
Vitamin C ( mg/dav )
1-day data
3-day data
Transf orbed data
Adjusted data
4,620
4, 690
7.8647
3, 160
73.1
72.6
3.7219
52.8
2,740
3, 340
7.916
2, 700
48.0
57.3
3.785
43.1 _
7, 360
5, 065
0.8488
1,800
72.9
56.8
0.9789
34.8
6.60S 58.298
3.911 20.675
-G . 853 2.472
1.519 3.891
1.933 S. 440
1.509 2.872
-0.528 0.438
1.316 2.312
71~-79 .
aAlgorithms for skew calculations f ran Cochran and Snedecor, 1980, pp.
bEran Cochran and Snedecor, 1980, pp. 79-81.
Representative terms from entire chapter:
adjusted data
