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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.

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  • $\begingroup$ This is more of an issue with the quote than your question, but I don't see how the error in that duration case would be cumulative. As I understand it the idea is that the longer a rat is in the box, the more opportunities they have to press the button, and so more time in box = more pellets dispensed. But unless the interval between button presses is always increasing, I don't see why the error is necessarily cumulative. $\endgroup$ – Ian_Fin Jul 19 '16 at 15:01
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The cumulative error (also referred to as system error) - It's a single direction error. e.g, - If you are to measure 10 km run & your stopwatch is running 2 sec faster every minute. So at the end of the experiment to calculate error you will add 2 secs for each minute.

Additive errors (also referred as multiplicative) - Error term which can go either way based on the scenario. Good example is residuals in a linear regression model. The residuals can be both negative or positive based on your observation (unlike 1st scenario)

Hope this helps.

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