Accuracy vs Precision

Accuracy and precision are two distinct properties of a measurement system. A measurement is accurate to the degree it approaches the true (reference) value of the quantity being measured. It is precise to the degree that repeated measurements cluster tightly together, regardless of whether that cluster is centred on the truth. Consumer nutrition discourse routinely collapses the two concepts, to the benefit of marketing and the detriment of clarity.

The archery analogy that actually works

The canonical illustration is an archery target. Five arrows clustered tightly in the top-left corner, well away from the bullseye, are precise but inaccurate — the archer's aim is consistent but wrong. Five arrows scattered around the bullseye, some too high, some too low, some left, some right, but averaging to the bull, are accurate but imprecise. Five arrows tight on the bull are both. Five arrows in a pattern that is both widely scattered and centred far from the bull are neither.

How each is improved

Accuracy is improved by calibration. A kitchen scale that consistently reads 5 grams high on every weighing is inaccurate but may be precise; applying a calibration constant (−5 g) restores accuracy without changing precision. Precision is improved either by using a better instrument (a 0.1-gram scale instead of a 2-gram scale) or, more commonly in statistics, by averaging: the mean of n independent measurements has a standard error that scales as 1/√n. A method with high precision and known systematic bias can be corrected to be accurate; a method with low precision and no systematic bias cannot, practically, be calibrated at the per-measurement level.

Where consumer nutrition muddles the terms

Two classes of claim routinely misuse the terms:

• "Our scale is accurate to 0.1 g." This claim typically describes precision — the scale's repeatability is ±0.1 g — without any statement about whether it reads against a calibrated reference mass. A scale that reads exactly +2 g high on every weighing, consistently, can advertise "accurate to 0.1 g" while being 2 g off the truth.
• "Our app is 95 per cent accurate." This is typically a classification-accuracy claim about food identification — in 95 per cent of photos the top-1 predicted food was correct. That is not a statement about calorie estimation accuracy. A correctly identified apple with a badly estimated portion can produce a calorie figure that is 50 per cent off.

Why the distinction matters in tracking

A calorie-tracking method can fail on either dimension. A method may be precise (logs the same meal at consistent kcal across repeated loggings) but inaccurate (the calorie figure is systematically 15 per cent off). Another method may be accurate on average (calibrated against USDA reference values) but imprecise (the per-meal error is high even if the mean error across many meals is near zero). From the user's point of view, the two failure modes have different consequences — systematic inaccuracy produces directional weight drift over weeks, while imprecision produces daily noise that averages out over weeks but makes per-day targeting difficult. Methodological reports should quote both: MAE or MAPE for accuracy, and the standard deviation of errors (or a coefficient of variation) for precision.