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distribution is skewed (such as iron requirements of menstru- ating women, or dietary intakes of vitamin A, vitamin B 12 , vitamin C, and vita- min E), a different methodology needs to be developed. For these nutrients, individual assessment should continue to place emphasis on other types of information available. NUTRIENTS WITH AN EAR For nutrients with an EAR, a z-score is calculated using the following equation: z - score = mean observed intake \u2013 EAR (SD of requirement) +(within - person SD) / number of days of intake records]2 2[ Copyright © National Academy of Sciences. All rights reserved. Dietary Reference Intakes: The Essential Guide to Nutrient Requirements http://www.nap.edu/catalog/11537.html PART I: APPLYING THE DIETARY REFERENCE INTAKES 29 The use of this equation requires the following information: \u2022 Mean observed intake: The mean nutrient intake of an individual is the best estimate of an individual\u2019s usual intake. \u2022 EAR: The EAR is the best estimate of an individual\u2019s requirement for a nutrient. \u2022 SD (standard deviation) of requirement: This is the variation in require- ments between individuals. It is calculated as the coefficient of variation (CV) times the EAR (see Appendix H). \u2022 Within-person SD of intake: The variation in day-to-day nutrient intake within the individual is an indicator of how much observed intake may deviate from usual intake. (This has been estimated in the original DRI reports by using CSFII data; see Appendix I.) \u2022 The number of days of intake records or recalls. As illustrated in Box 2, the equation solves for a z-score on the normal distribu- tion curve. Some z-scores and their associated probabilities are listed in Table 1. The larger the z-score, the larger the probability associated with that value. The numerator of the equation is the difference between the estimated intake and the estimated requirement. It can intuitively be seen that the higher an intake is compared to the requirement, the larger the numerator will be. The denomina- tor of the equation is the term that incorporates all the variability. Thus, as the variability gets smaller, the z-score will get larger. Note that an increase in the number of days of records will lead to a decrease in the amount of variability. NUTRIENTS WITH AN AI For nutrients with an AI it is not possible to estimate the requirement of indi- viduals. The AI represents an intake (not a requirement) that is likely to exceed the actual requirements of almost all individuals in a life stage and gender group. In fact, the AI may even be higher than an RDA (if it was possible to calculate one). When trying to compare an individual\u2019s intake to his or her requirement, the AI is not very useful because it is in excess of the median requirement, perhaps by a very large margin. Therefore, when intakes are compared to the AI, all that can be concluded is whether the intake is above the AI or not. It is possible to determine the confidence with which one can conclude that usual intake exceeds the AI using the following equation: Copyright © National Academy of Sciences. All rights reserved. Dietary Reference Intakes: The Essential Guide to Nutrient Requirements http://www.nap.edu/catalog/11537.html 30 DRIs: THE ESSENTIAL GUIDE TO NUTRIENT REQUIREMENTS z - score = mean observed intake \u2013 AI within - person SD / number of days of intake records The use of this equation requires the following information: \u2022 Mean Observed Intake: The individual\u2019s mean observed intake \u2022 AI: The AI for a similar life stage and gender group BOX 2 Example: Using the Quantitative Approach for Individual Assessment for a Nutrient with an EAR Suppose a 40-year-old woman had a magnesium intake of 320 mg/day, based on 3 days of dietary records. The question is whether this observed mean intake of 320 mg/ day indicates that her usual magnesium intake is adequate. To determine the probability that her usual intake meets her requirement, the following data are used: \u2022 The mean observed intake for this woman is 320 mg/day. \u2022 The EAR for magnesium for women 31\u201350 years is 265 mg/day \u2022 The SD of the requirement distribution for magnesium is 10 percent of the EAR (Appendix H), therefore 26.5 mg/day. \u2022 The within-person SD (day-to-day variability) in magnesium intake for women this age is estimated to be 86 mg/day (Appendix I). \u2022 There are 3 days of dietary records. Solving for the z-score yields: z - score = 320 \u2013 265 [(26.5) + (86) 3]2 2 / = = ª 55 56 0 98 1 0. . Table 1 lists a selection of and their associated probabilities. Looking up a z-score of 1.0, it can be seen that 85% probability of correctly concluding that this intake is ad- equate for a woman in this age category. Copyright © National Academy of Sciences. All rights reserved. Dietary Reference Intakes: The Essential Guide to Nutrient Requirements http://www.nap.edu/catalog/11537.html PART I: APPLYING THE DIETARY REFERENCE INTAKES 31 \u2022 Within-person SD of intake: The variation in day-to-day nutrient intake within the individual is an indicator of how much observed intake may deviate from usual intake (see Appendix I) \u2022 The number of days of intake records or recalls Solving for the equation gives the confidence with which one can conclude that usual intake is greater than the AI. If an individual\u2019s intake equals or ex- ceeds the AI, it can be concluded that the diet is almost certainly adequate. However, if the calculation does not result in the conclusion that there is a high probability that the usual intake is larger than the AI, it cannot be inferred that intake is inadequate. Professional judgment, based on additional types of information about the individual, should be exercised when interpreting in- takes below the AI. NUTRIENTS WITH A UL The UL can be used to assess the likelihood that an individual may be at risk of adverse effects from high intakes of that nutrient. An equation has been deter- mined to assess the probability that usual intake is below the UL given the mean observed intake. This equation is useful because even when mean ob- served intake is less than the UL, it cannot always be concluded with the de- sired amount of accuracy that usual intake is also below the UL (due to the variability associated with observed intake). This is particularly the case when the observed mean intake is a value close to that of the UL (as could be the case when considering intake from food plus supplements). When using a UL to assess a person\u2019s nutrient intake, it is important to know whether the UL applies to intake from all sources or just from specific sources, such as supplements, fortified foods, or pharmacological preparations. The equation is as follows: z - score = mean observed intake \u2013 UL within - person SD / number of days of intake records The use of this equation requires the following information: \u2022 Mean Observed Intake: The individual\u2019s mean observed intake (from applicable sources) \u2022 UL: The UL for a similar life stage and gender group \u2022 The within-person SD of intake: The variation in day-to-day nutrient intake within the individual is an indicator of how much observed in- take may deviate from usual intake (see Appendix I) \u2022 The number of days of intake records or recalls Copyright © National Academy of Sciences. All rights reserved. Dietary Reference Intakes: The Essential Guide to Nutrient Requirements http://www.nap.edu/catalog/11537.html 32 DRIs: THE ESSENTIAL GUIDE TO NUTRIENT REQUIREMENTS Solving for the equation yields the confidence with which one can conclude that usual intake is less than the UL. Intakes less than the UL are likely to be safe; and intakes equal to or greater than the UL may indicate a potential risk of adverse effects. The higher the intake in comparison