Errors

Definition and Measurement

Error is defined as the difference between an observable behavior and a desired behavior. More formally, error is the difference between an observed score and a desired score, called a target:

$$e_i=X_i–T$$

where e is the error, X is the score on trial i, and T is the target score. Traditionally error has been classified as bias, precision, and accuracy.

Bias means that a set of scores tends to produce either a negative or a positive error. Bias is also called algebraic error, as it has a magnitude and a direction (positive or negative) on each and every trial. The average algebraic error, or bias, over a series of trials has been called constant error.

Precision is a measure of response consistency. In other words, does the individual perform identically every time? Variability is the usual measure of imprecision. Variability is considered the average distance a set of scores is from the mean score. Typically, the measure of precision is just the standard deviation of the set of scores. Thus, a smaller standard deviation means an increase in consistency (precision) compared to a larger standard deviation. Historically, variable error is the name of this error score.

Accuracy, the most commonly used and important measure of error, is defined as the average distance a set of scores is from a target value. Traditionally, absolute error, defined as the average absolute difference (computed on a trial by trial basis, and then averaged) between a score and a target, was the accuracy measure of choice. Absolute error has several statistical issues that have resulted in researchers abandoning this measure. A much better measure of accuracy is root mean squared error (RMSE). This measure uses the one-dimensional distance formula and then takes the average of the set of distances. RMSE is a combination of bias and variability.

So far in this discussion of error, we have focused on measuring performance as the outcome of a single trial and then describing the average of a set of trials. In other words, these measures are outcome scores. Error also can be used to capture the process of movement. The movement of the effector over time (a trajectory) provides a rich source of information concerning the underlying movement control processes. For example, a movement trajectory can be compared to an ideal movement trajectory and deviations from the ideal would be considered an error. The standard measure of error for a continuous trajectory is RMSE. The error is summed up across samples across a single trajectory. The larger the RMSE, the less accurate the trajectory is to the template or standard.

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