The Scoop Is Not a Scale: Concentration Errors in Home-Mixed Milk Formula from Kitchen Measurement Alone

Powdered infant formula is dosed at home with a scoop and a bottle marking, and it is widely assumed that the errors of such kitchen measurement are small and therefore harmless. This paper states that claim plainly — small mixing errors are harmless — and tests it arithmetically with a Monte Carlo error budget. For a nominal feed of 120 mL of water plus two scoops, stated variabilities are propagated for level-scoop packing (SD 0.6 g on an 8.8 g scoop), heaped scoops (25% of scoops, about 30% over nominal), water reading error (SD 4 mL), and powder displacement under the habit of filling to the mark after adding powder (half of preparations). Across 200,000 modelled preparations, the concentration factor relative to the intended dilution has mean 1.1258 and SD 0.1308: 52.91% of preparations fall outside a ±10% concentration band, 26.22% fall outside ±20%, and the errors are almost entirely in one direction — 51.76% are more than 10% over-concentrated against 1.15% more than 10% under. Modelled osmolality exceeds 400 mOsm/kg in 7.40% of preparations, reaching a 97.5th percentile of 426.4 mOsm/kg. The claim as stated therefore fails: the individual errors are small, but they are biased, and biased small errors do not cancel. Heaped, unlevelled scoops are the dominant source, contributing 63.7% of the single-source variance. An originated protocol — one 500 mL batch, water measured first, every scoop levelled with a straight edge, powder added to the water and never filled to a mark afterwards — reduces the SD of concentration to 0.0284, a 4.61-fold reduction, leaves 0.04% of preparations outside ±10%, and none above 400 mOsm/kg in the model.