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TABLE 3-4 Illustration of the Computations Necessary to Test Whether an Individual 's Usual Intake of Phosphorus Is Below the Tolerable Upper Intake Level (UL) for Different Numbers of Days of Observed Intake for a Woman 40 Years of Age


Using SD from CSFIIa

If SD is 25 Percent Larger

If SD is 50 Percent Larger

Mean intake

3.8 g

3.8 g

3.8 g

SD of intakeb

0.4 g

0.5 g

0.6 g

UL for phosphorusc

4.0 g

4.0 g

4.0 g

z-Values = (mean intake − UL)/(SD/square root [n])

1 d of intake




3 d of intake




7 d of intake




Percentage confidence that the woman's usual intake is below the ULd

1 d of intake




3 d of intake




7 d of intake




NOTE: The confidence with which one can conclude that usual intake is below the UL decreases when the number of days of daily intake records for the individual decreases or when the SD of daily intakes increases.

aSD = standard deviation; CSFII = Continuing Survey of Food Intake by Individuals.

bSD of phosphorus intake for women 19 through 50 years of age taken from CSFII (Appendix Table B-2).

c Tolerable Upper Intake Level for women 31 through 50 years of age.

d Confidence values were taken from a standard z-table (Snedecor and Cochran, 1980). The z-table is used because the SD of daily intake is assumed to be known (e.g., from CSFII), and is not computed from the woman's daily observations.

phorous intakes associated with high energy expenditure). The UL for phosphorus has been determined to be 4.0 g/day, and the SD of phosphorous intake, from CSFII, is 0.41 g. Given that her observed mean intake is below the UL, can we conclude with desired assurance that her usual intake of phosphorus is below the UL and that she is not at potential risk of adverse health effects? Again, situations are shown with 1, 3, and 7 days of intake data.

From the example in Table 3-4, it can be seen that even when observed mean intake is less than the UL, sometimes it cannot be concluded with desired accuracy that usual intake is also below the UL. When only one day of intake data is available for the individual, one would have only between 63 and 69 percent (depending on the SD of daily intake) confidence in concluding that her intake of 3.8 g

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