Given five individuals, each with three days of intake records and observed mean intakes of 1,050, 1,150, 1,200, and 1,250 mg/day, respectively, what can be determined about the adequacy of their usual intakes? Assume that, to determine if the usual intake is higher than the AI, a minimum confidence level of 85 percent is desired.

To calculate the z-values for each of the five individuals, first divide the SD of daily intake by the (as 3 daily records are available for each). In this example, 325/ equals 188. The z-values are now computed as (observed mean intake − AI)/188. For the five individuals, the corresponding z-values are 0.27, 0.53, 0.80, 1.07, and 1.33, respectively. From a standard z-table the probabilities of correctly concluding that the usual intake is larger than the AI for each of the five individuals are 61, 70, 79, 86, and 91 percent, respectively. Only for the last two individuals, with observed mean intakes of 1,200 and 1,250 mg /day, would there be an 85 percent confidence level when stating that usual intakes are greater than 1,000 mg/day.

The value of the z-statistic will increase whenever

• the difference between the observed mean intake and the AI increases;

• the SD of daily intake for the nutrient is low; and

• the number of days of intake data available for the individual increases.

This z-test relies on the assumption of normality of daily intakes. For nutrients such as vitamin A, vitamin B₁₂, and others with a CV of daily intake larger than 60 to 70 percent, this test is likely to perform poorly. While the calculations are still possible, the level of assurance resulting from the test will be incorrect. The performance of the test also depends on accurately estimating the day-to-day variability in intakes for the individual. It is suggested that the pooled SD of daily intake obtained, for example, from Table B-2, Table B-3, Table B-4 through Table B-5 be used in the calculations even though it is likely to be a poor estimate of the individual's true day-to-day variability in intakes. As stated earlier, a more justifiable alternative cannot be offered at this time, as no extensive studies on the dependence of individual SD of intake and individual mean intake have been published. More research is needed in this area.