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OCR for page 127

APPENDIX D
Algorithm for Computing the
Probability of Intake Inadequacy
The probability approach described in this report
depends on placement of the observed intake within a
normalized distribution of requirements and calculation
of the area under the normal distribution to the right
of the observed intake. This is done by computing the Z
value of the observed intake as:
Z = Observed Intake — Mean Rea~Ir~m~nt,
Standard Deviation of Requirement
The statistical tables of the standard normal distri-
bution are then consulted to determine the area to the
right of Z. This represents the probability that the
intake in inadequate for the randomly selected person.
An algorithm for use on a computer gives very good
agreement with published values of the area under the
normal distribution (Abramowitz and Stegun, 1965). The
following segment of a computer program illustrates the
use of this algorithm. (The program segment is written
in Applesoft Basic.)
1510 Z = (A(X)—~)J(~ * Cat
1515 IFZ

128
In this program, the following variables have been
generated before reaching the above program segment:
A(X) is the intake report for nutrient X; NR is the aver-
age requirement for nutrient X; and CV is the coeffi-
cient of variation of requirement for nutrient X,
expressed as a decimal rather than as a percentage. The
variables R and R(X) represent the calculated proba-
bility that the intake of nutrient X is inadequate to
meet the requirement for a person.
In the computations in this report, this algorithm
has been used with A(X) and R(X) representing the intakes
and risks for equal intervals of the population ranked by
level of intake (see Appendix A). The values of R(X)
have been summed across the population. This yields an
estimate of the prevalence of inadequate intakes within
the population, which is then divided by the population
size.
Computer routines are used to estimate requirements
on the basis of subject characteristics, to adjust require-
ment estimates for the additional needs of pregnancy or
lactation, and at the same tome, to adjust variance esti-
mates for the new requirement estimate. The program also
imputes weight or Energy intake if not provided as input
(used in conjunction with derivation of a requirement
estimate for some nutrients) and again adjusts the vari-
ance of the derived requirement estimate to take into
account the variance associated with the imputed value.
This program was written for application to a particular
person. There are also algorithms for making equivalent
adjustments in the analysis of population data rather than
individual data if needed.
REFERENCE
Abramowitz, M., and I. A. Stegun, eds. 1965. Handbook
of Mathematical Functions with Fo. =ulas, Graphs, and
Mathematical Tables. Applied Mathematics Series No.
55. National Bureau of Standards. U.S. Department of
Commerce, Gaithersburg, Maryland.