A cost estimator can be correct on average while missing every individual case by a substantial amount. Overestimates and underestimates can cancel when signed errors are averaged. That cancellation is useful for measuring direction, but it is not a complete measure of how close the predictions were.

The National Weather Service distinguishes mean error from mean absolute error in its forecast verification explanation. This article borrows only that mathematical distinction. It uses no weather findings, thresholds or institutional cost data. Every study-cost observation and prediction below is fictional and serves as a small, reproducible evaluation exercise.

Calculate error with one stated sign convention

Suppose four comparable monthly study-cost cases each have an observed cost of 1,000 in one currency. Method A forecasts 800, 1,200, 800 and 1,200. Method B forecasts 1,050 for every case. Define error as forecast minus observed cost, so a negative error means an underestimate.

Case Observed A forecast A signed error B forecast B signed error
1 1,000 800 -200 1,050 50
2 1,000 1,200 200 1,050 50
3 1,000 800 -200 1,050 50
4 1,000 1,200 200 1,050 50

A's mean signed error is zero: the four errors sum to zero. B's mean signed error is fifty. Judged only by closeness of average signed error to zero, A might appear better. Yet A misses each case by two hundred, while B misses each by fifty.

Mean absolute error removes the signs before averaging. A's result is 200 and B's is 50. B is closer in every one of these invented cases despite its positive average bias. The two measures answer different questions: direction of error and typical magnitude of error under this averaging rule.

Connect the metric to the decision

If a student funds exactly A's prediction, cases one and three have shortfalls of 200. Overestimates in other cases do not automatically transfer money to those students. A zero aggregate bias therefore does not establish that every individual budget is safe.

This is not an argument for simply adding fifty to every real estimate. The fictional observations are too small and artificial to establish a useful adjustment. A real method needs evaluation on relevant cases, consistent cost definitions and information about how its predictions were produced.

Check whether predictions were genuinely recorded before the outcomes were known. Fitting a model to the same cases and then evaluating its fit is different from testing forecasts on later or held-out cases. Preserve dated predictions and outcomes so the claimed evaluation can be reproduced.

Inspect the distribution, not only another average

An absolute-error mean can itself hide unusual large misses. Record the individual errors or an appropriately documented distribution, along with the number of cases. If some predictions concern very different budget sizes, consider how that scale affects interpretation rather than mixing incompatible amounts.

Missing outcomes and revised observations also matter. State which cases were excluded and which version of the observed cost was used. A method should not appear more accurate merely because its difficult cases disappeared from the evaluation. Compare competing methods on the same appropriate set where possible.

Keep the sign convention visible. Some producers define error in the opposite direction; that reverses the interpretation of positive and negative bias without changing absolute error. Read the methodology before treating a positive number as overprediction.

The budget uncertainty guide concerns planning around unknown costs. This worksheet asks whether a forecasting method has actually demonstrated useful performance. A defensible research note reports the evaluation population, the prediction date, signed and absolute errors, and important exceptions. It does not turn “right on average” into a promise that an individual student's bills will match the forecast.