The mean of n days of intake of the nutrient by the individual, , is the best estimate for y, the individual's usual intake. The day-to-day variation in intake for a given individual, also referred to as the within-person standard deviation of daily intakes, SDwithin, is proportional to the uncertainty about the accuracy of as an estimate of y. The mean () will be a reliable estimate of the usual intake y when the number of intake days n from which the mean was computed is large or when the SDwithin is low. If an individual eats the same diet day after day, then the day-to-day variability in intakes for that individual would be very low, and one or two days of intake information might be sufficient to precisely estimate that individual's usual intake of the nutrient. Conversely, a large number n of dietary intake observations is needed to estimate the usual intake of a nutrient for an individual whose diet is variable from one day to the next.
It is implicitly assumed that food intake can be measured accurately in terms of quantity of food and food composition. Therefore, results from individual assessments should be interpreted with caution and where possible, should be combined with other interpretive data.
Thus the following statements can be made:
If y > ρ, then the individual's usual intake of the nutrient is adequate.
If y < ρ, then the individual's usual intake of the nutrient is inadequate.
Because neither y nor ρ is observed, and r must be used instead. Inferences about the adequacy of the individual 's diet can be made by looking at the observed difference (D), where
D = − r.
Intuitively, if D is large and positive, it is likely that the true difference y − ρ is also large and that the individual's diet is adequate. Conversely, if D is a large negative number, then it is likely that ρ is larger than y and that the individual's intake is not adequate. The obvious question to be posed is, How large would D have to be before it can be concluded, with some degree of assurance, that the unobservable usual intake is larger than the unobservable requirement?