To interpret this difference between observed mean intake () and the median requirement (EAR, the best estimate [r] of the unobservable ρ), one needs a measure of the variability of D. The standard deviation of requirements (SDr) and the standard deviation of intakes (SDwithin or SDi) can be used to estimate the SD of D, the difference between observed mean intake and r for the individual, as
Vr denotes the variance of the distribution of requirements in the group and Vwithin denotes the variance in day-to-day intakes of the nutrient. Both variances are computed as the square of the corresponding standard deviations. As the number (n) of days of intake available on the individual increases, the variance of the observed mean intake should decrease (i.e., the accuracy of the estimate for y increases). This is why Vwithin is divided by n when computing the standard deviation of the difference D.
The SDD increases as the
SDi increases, or
number of intake days (n) available for the individual decreases.
That is, the more uncertainty that exists about the accuracy of the value D, the larger D will need to be before it can be confidently stated that the individual 's usual intake is adequate. The following extreme cases illustrate this approach:
If the intake of an individual could be observed for a very large (infinite) number of days, then the second term (Vwithin/n) in the expression for SDD would tend to zero. The uncertainty about the adequacy of the individual 's intake would result primarily from not knowing where in the distribution of requirements that individual's unobservable requirement ρ is located. The degree of uncertainty about adequacy would then be proportional to the variability of requirements in the group.
If the individual were to consume the same diet day after day, then the second term (Vwithin/n) would again be very small, even with small n, because the variability in intakes from day to day would be very small for that individual. Again, the uncertainty about the