# Mean absolute error

In statistics, the mean absolute error (MAE) is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by

$\mathrm{MAE} = \frac{1}{n}\sum_{i=1}^n \left| f_i-y_i\right| =\frac{1}{n}\sum_{i=1}^n \left| e_i \right|.$

As the name suggests, the mean absolute error is an average of the absolute errors ei = fiyi, where fi is the prediction and yi the true value. Note that alternative formulations may include relative frequencies as weight factors.

T

The mean absolute error is one of a number of ways of comparing forecasts with their eventual outcomes. Well-established alternatives are the mean absolute scaled error (MASE) and the mean squared error.[1] These all summarize performance in ways that disregard the direction of over- or under- prediction; a measure that does place emphasis on this is the mean signed difference.

Where a prediction model is to be fitted using a selected performance measure, in the sense that the least squares approach is related to the mean squared error, the equivalent for mean absolute error is least absolute deviations.

## References

1. ^ Hyndman, R. and Koehler A. (2005). "Another look at measures of forecast accuracy" [1]

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Mean squared error — In statistics, the mean squared error (MSE) of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function,… …   Wikipedia

• Mean absolute percentage error — (MAPE) is measure of accuracy in a fitted time series value in statistics, specifically trending. It usually expresses accuracy as a percentage, and is defined by the formula: where At is the actual value and Ft is the forecast value. The… …   Wikipedia

• Mean absolute scaled error — In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts . It was proposed in 2006 by Australian statistician Rob Hyndman, who described it as a generally applicable measurement of forecast accuracy without… …   Wikipedia

• mean absolute deviation — MAD A measure of forecast error, for example when carrying out adaptive exponential smoothing of time series data. MAD is the average forecast error, either positive or negative, calculated as the sum of the absolute value of forecast error for… …   Big dictionary of business and management

• Mean signed difference — In statistics, the mean signed difference (MSD), also known as mean signed error (MSE), is a sample statistic that summarises how well an estimator matches the quantity θ that it is supposed to estimate. It is one of a number of statistics that… …   Wikipedia

• Absolute deviation — In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the point from which the deviation is measured is a measure of central tendency, most often the median… …   Wikipedia

• Absolute probability judgement — is a technique used in the field of human reliability assessment (HRA), for the purposes of evaluating the probability of a human error occurring throughout the completion of a specific task. From such analyses measures can then be taken to… …   Wikipedia

• Absolute molar mass — is a process to determine the characteristics of molecules. TOC History The first absolute measurements (i.e. made without reference to standards) were based on fundamental physical characteristics and their relation to the molar mass. The most… …   Wikipedia

• Mean difference — The mean difference is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn from a probability distribution. A related statistic is the relative mean difference, which is the mean difference …   Wikipedia

• Mean — This article is about the statistical concept. For other uses, see Mean (disambiguation). In statistics, mean has two related meanings: the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). the expected value of a… …   Wikipedia