Lesson plan
Mean absolute error
In statistics, mean absolute error (MAE) is a measure of errors between paired observations expressing the same phenomenon. Examples of Y versus X include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. MAE is calculated as the sum of absolute errors (i.e., the Manhattan distance) divided by the sample size: \mathrm{MAE} = \frac{\sum_{i=1}^n\left| y_i - x_i\right|}{n} =\frac{\sum_{i=1}^n\left| e_i \right|}{n}. It is thus the arithmetic mean of the absolute errors |e_i| = |y_i - x_i| , where y_i is the prediction and x_i the true value. Alternative formulations may include relative frequencies as weight factors. The mean absolute error uses the same scale as the data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between predicted values that use different scales. The mean absolute error is a common measure of forecast error in time series analysis, sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists more generally in technical literature.
Article summary
In statistics, mean absolute error (MAE) is a measure of errors between paired observations expressing the same phenomenon. Examples of Y versus X include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. MAE is calculated as the sum of absolute errors (i.e., the Manhattan distance) divided by the sample size: \mathrm{MAE} = \frac{\sum_{i=1}^n\left| y_i - x_i\right|}{n} =\frac{\sum_{i=1}^n\left| e_i \right|}{n}. It is thus the arithmetic mean of the absolute errors |e_i| = |y_i - x_i| , where y_i is the prediction and x_i the true value. Alternative formulations may include relative frequencies as weight factors. The mean absolute error uses the same scale as the data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between predicted values that use different scales. The mean absolute error is a common measure of forecast error in time series analysis, sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists more generally in technical literature.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.