Foods that we eat and their relationship to health

## Week-weighted Averages in CANDAT

When expressing and comparing results of multi-day (3 day commonly) food recalls one tends to use the average daily intake as a measure of a subject’s intake. Of course, 7 day recalls will give more accurate estimates of this daily intake and the accuracy will increase if all the days of a week are used. The assumption here is that subjects will eat differently on different days with the greatest variability been between week days and weekend days.

Rather than simply computing an average daily intake one may get more accurate results by weighting the days of the week and the weekend days differently.

A weight of 5 for each week day and a weight of 2 for weekend days should allow us to calculate week-weighted averages for any number of recalls. Of course, for recalls without weekends this would just be a day of the week average and vice-versa.

The week-weighted average could be calculated as follows:

xw = (∑ wi × xi) ÷ ∑ w

where xw is the weighted average with  xi as the daily intakes, and i is 1 – 5 (codes for days of the week) or 0,6 codes for weekend days corresponding to Sunday and Saturday respectively. w1-5 would then be 5 and w0,6 would be 2.

with a variance of

Var(xw) = Var(x) × ((∑ wi2) ÷ (wi)2)

where Var(x) would be the variance over all the days of the food intakes for the subject.

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