where Yj denotes the intake for the individual observed on the jth day and is the mean of the n days of observed intakes. The within-individual standard deviation SDwithin is computed as the square root of Vwithin. Unless a large number of nonconsecutive days (e.g., more than 10 or 12 days) of intake records are available for the individual, it is recommended that the pooled estimate from Table B-2, Table B-3, Table B-4 through Table B-5 be used instead. Whereas this pooled estimate is likely to be incorrect for the individual, at this time there is no better alternative. More research is needed in this area that will permit estimating an adjustment of the pooled variance estimate to suit a particular individual.
The assumption of normality (or near normality) of the observed intakes Yj is critical, as the proposed approach relies on normality of the difference D. Normality of D will not be satisfied whenever the observed intakes Yj (and consequently, the observed intake mean) are not normally distributed. How does one decide whether the distribution of observed intakes for an individual is approximately normal? Typically there are not enough days of intake data available for an individual to be able to conduct a test of normality of the observed intakes. Therefore, one must rely on the CV of daily intakes that are presented in Table B-2, Table B-3, Table B-4 through Table B-5.
As a rule, any nutrient with a CV above 60 to 70 percent should be considered to have a nonnormal distribution for the following reason: if daily intakes for an individual are normally distributed, then subtracting 2 SD of intake from the individual's mean should still result in a positive value, as intakes are restricted to being positive. Suppose that the CV of intake was 60 percent, then the SD of intake is 0.6 × mean intake. If 2 SDs of intake are now subtracted from the individual 's mean intake a negative value is obtained, indicating that the distribution of observed intakes around the individual's usual intake is not normal.
Mean intake − 2 SD intake = mean intake − 2 × 0.6 × mean intake
= mean intake − 1.2 mean intake
= −0.2 × mean intake.
The value in the last equation is negative, suggesting that the normal model is not reasonable when the CV of intake is above 60 to 70 percent.