Imagine a target where archer A and archer B are trying their luck for a good shot. The following figure is the outcome. Now let us try to figure out who has done the best. Again it depends on what you want to see. The common error measurements are as follows:
Constant error measures the deviation from the target. The formula for it is: Σ (xi-T)/N, where T is the target and N is the number of shots. It comes with a positive or negative sign which points out the direction of the error. Absolute constant error will give the absolute value of CE alone without mentioning the direction.
Variable Error :
Variable error measures the consistency of the shots. It calculates the standard deviation of the total shots. Its formula is sq.root (Σ (xi-M)^2/N, where M is the average shot.
Absolute error is the overall deviation without considering the direction. In constant error there is a danger of cancellations of error because of direction. However, the error due to bidirection gets eliminated in absolute error. Its formula is Σ absolute ((xi-T)/N).
So here is a question for you? Among A and B, who is the better archer? Are you bothered about the deviationper se or concerned more about the consistency? I would say bet on archer B than A because he has lesser variablity.
Root Mean Square Error:
This measures both the deviation and the consistency of the shots. Its formula is sq.root (Σ (xi-T)2/N).
Coefficient of Variation:
It is nothing but standard deviation divided by mean. It gives a clear picture about the deviation. If there are lots of tremors, then the standard deviation increases and so the coefficient of variation.
Richard A. Schmidt, Timothy D Lee, (1999. Motor Control and Learning (Third Edition). Human Kinetics.
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The explanations about all the errors are here. Click the link below.
Measurements of Error