Which metric is a measure of average magnitude of errors without regard to direction, commonly used in model validation?

• A. R^2
• B. RMSE
• C. MAE
• D. NSE

Answer: (C)

Average magnitude of errors ignoring direction is captured by the mean absolute error. It sums the absolute differences between predicted and observed values and divides by the number of observations, so it reflects the typical size of mistakes without caring whether predictions are high or low. This makes MAE easy to interpret in the same units as the data and robust to sign, unlike metrics that emphasize direction. RMSE also measures error magnitude but squares errors first, giving more weight to larger mistakes; it can overemphasize outliers. R^2 and NSE focus on explained variance or efficiency rather than the average size of prediction errors, so they don’t directly quantify how far off predictions are on average. Therefore MAE is the best choice for assessing average error magnitude without regard to direction.