I was reading a brief theory of measurement from ftp://ftp.sas.com/pub/neural/measurement.html when a passage got me stuck. It says that
Consider a rat in a Skinner box who pushes a lever to get food pellets. The number of pellets dispensed in the course of an experiment is obviously an absolute-level measurement of the number of pellets dispensed. If number of pellets is considered as a measure of some other attribute, the measurement level may differ. As a measure of amount of food dispensed, the number of pellets is at the ratio level under the assumption that the pellets are of equal size; if the pellets are not of equal size, a more elaborate measurement model is required, perhaps one involving random measurement error if the pellets are dispensed in random order. As a measure of duration during the experiment, the number of pellets is at an ordinal level. [...] In the example above with number of pellets as a measure of duration, the errors would be cumulative, not additive, and the error variance would increase over time.
From reading about the classical model of error, I gather that an additive error is one that can be factored out by averaging many measurements. How does the cumulative error work? I nearly thought they are the same, but this passage makes it clear they are not.