unobservable actual requirement. To answer this question, it is necessary to know the standard deviation of D (SD_D). The SD_D depends on the number of days of intake available for the individual, the standard deviation of the requirement (estimated as 10 to 15 percent of the EAR for most nutrients), and the within-person standard deviation of intake. The latter can be estimated from large surveys of similar groups of people (such as the Continuing Survey of Food Intakes by Individuals [CSFII] data presented in Appendix Table B-2, Table B-3, Table B-4 through Table B-5). Once D and SD_D have been estimated, the probability that intake is above (or below) the requirement can be determined by examining the ratio of D to SD_D.

To illustrate this approach, suppose a 40-year-old woman had a magnesium intake of 320 mg/day, based on three days of dietary records. The question is whether this observed mean intake of 320 mg/day of magnesium over three days indicates that her usual magnesium intake is adequate. The following information is used in conducting this assessment:

• The EAR for magnesium for women 31 to 50 years of age is 265 mg/day, with an SD of requirement of 26.5 mg/day.

• The day-to-day SD in magnesium intake for women this age is 85.9 mg/day based on data from the CSFII (see Appendix Table B-2).

The following steps can now be used to determine whether an intake of 320 mg/day is likely to be adequate for this woman.

1. Calculate the difference D between intake and the EAR as 320 − 265 = 55 mg.

2. Use the formula for the SD_D¹ and determine that the SD_D is 56 mg. The value of SD_D is computed as follows: (a) from Appendix Table B-2, the pooled SD of daily intake for magnesium in women aged 19 to 50 years is 86 mg/day, and therefore the variance of daily intake is the square of the SD or 7,379 mg; (b) divide 7,379 by the number of days of observed intake data (3) to obtain 2,460;

   1

   , where Vr denotes the variance of the distribution of requirements in the group, and Vwithin denotes the average variance in day-to-day intakes of the nutrient. Both variances are computed as the square of the corresponding standard deviations. Intuitively, as the number n of intake days available on the individual increases, the variance of the observed mean intake should decrease (i.e., the accuracy of the estimate for y increases). Thus, the dividing Vwithin by n when computing the standard deviation of the difference D.