## Personalized Nutrition: Chance of Adequacy

With all of our modern gadgets and gizmos, it’s easier than ever to record how much we’re eating and how often. But does our nutrient consumption meet our needs? In this post, I’m going to teach you how to use some basic statistics to calculate the chance that your consumption for a particular nutrient meets your needs.

But first, as always, it’s important to note that nutrient needs are different between individuals. The needs of one person more than likely do not match the needs of another. Just because someone is eating a low amount of a particular nutrient, and their chance of adequacy calculation may come out low, does not necessarily mean they are deficient. Rather, they may indeed just need less of the nutrient! If you think you are in-fact deficient in a particular nutrient, it is always a good idea to consult with a medical professional.

Now then… Let’s do some nutritional science! We can use information from a publication called the Dietary Reference Intakes to find information about mean requirements and recommendations for nutrient intakes. In particular, two pieces of information for a given nutrient will be important for our chance of adequacy calculation.

1. The EAR – This is the Estimated Average Requirement for a particular group of people. The EAR says how much nutrient intake is sufficient to meet the needs of 50% of the group.
2. The RDA – This is the Recommended Dietary Allowance for a particular group of people. By definition, this number is calculated as two standard deviations above the mean need (EAR). Therefore, a nutrient intake at this level will meet the needs of 97.5% of the group’s population.

The EAR values for many common nutrients can be found here (note this table also contains AI values which are unbolded), and the RDAs can be found here. These values are separated by age and sex. (Some nutrients do not have an EAR/RDA and instead have an AI which is marked by unbolded font in the EAR table, see my note at the bottom of the post for more information about this)

Determining our chance of adequacy is as simple as calculating the Z-score for our nutrient intake. For this calculation we will need the mean and the standard deviation. The mean by definition is the same value as the EAR, and using the RDA we can find the standard deviation.

Standard Deviation = (RDA – EAR) / 2

Putting this information together, the Z-score can be calculated as the following:

Z = (Nutrient Intake – EAR) / (Standard Deviation)

The very last thing we need to do is to consult a Z-score table to determine what percent on the normal distribution the Z-score falls at. A simple table of Z-scores can be found here. Multiplying the decimal number given in the table by 100% yields our chance of adequacy percentage!

Let’s Do An Example

Theory is great, now let’s do an example problem! Suppose John, a 20 year old male eats an average of 83 mg/day of Vitamin C. He wants to know how likely it is that his Vitamin C intake meets his needs.

Using the EAR and RDA tables supplied above, we find that 20 year olds have an EAR of 75 mg/day and an RDA of 90 mg/day. Using this information we can calculate the standard deviation of Vitamin C needs for John’s age group.

Standard Deviation = (90 – 75)/2 = 7.5 mg/day

Now we can find John’s Z-score using the following calculation:

Z = (83 – 75) / 7.5 = 1.06

Looking up a Z-score of 1.06 in a Z-score table gives us .8554 as the area under a standard bell curve. Therefore, John’s chance of adequacy is the following:

Chance of Adequacy = .8554 * 100% = 85.54%

Sometimes there is no EAR/RDA

Yep, some nutrient don’t have an EAR or RDA. This is the case for nutrients where there is not enough research to find establish this information. In the case of these nutrients, another value called the Adequate Intake (AI) is recorded. This is a value of a nutrient at which it is likely that needs are met for healthy individuals. We cannot use this value to calculate our chance of adequacy, however, if you compare your intake to the AI, if you are above the AI your needs are likely met. If you are below the AI, there is not enough information to say anything about your nutritional status for the given nutrient. Adequate intake values are listed on the same table as EAR values, however, they are in unbolded font.