In Figure D-18, again the three curves represent the three different values of the EAR, but now the correlation between intakes and requirements was fixed at 0.7. Referring back to Figure D-14 and Figure D-16, one can see that as the value of SD_r increases, the true prevalence first decreases and then increases. This is a result of the pattern of overlapping the requirements and intake distributions. The biases in the estimates of prevalence shown in Figure D-18 follow the same pattern. It is important to notice that the EAR cut-point estimate of prevalence does not track the changes in true prevalence as the SD_r varies, and thus produces biased estimates.

In summary, violating the assumption requiring that the variance of requirements be smaller than the variance of intakes is likely to have a noticeable impact on the reliability of the prevalence estimate. To date, suggested estimates of the variance of requirements for most nutrients are smaller than those calculated for intakes. In principle, therefore, one need not worry about potential violations of this assumption. A situation in which the variance of intake may become small relative to the variance of requirements is for institutionalized

FIGURE D-18 Effect of the standard deviation of requirement (SD_r) on bias of the estimated prevalence of inadequate intakes using the Estimated Average Requirement (EAR) cut-point method for 10 values of the SD_r. For all values of the SD_r, mean intake = 90, SD of intake = 30, and correlation between intake and requirement = 0.7. The EAR was set at 55 units (solid line with dots), 70 units (dotted line with stars) and 90 units (dashed line with squares).