Biological organisms cannot repeat a movement exactly the same way across practice trials or attempts. In other words, there is an inherent amount of imprecision in the motor systems of animals, including humans. This variability can be considered a source of error. Second, in any attempt to solve a new motor problem, whether a young athlete pole vaulting or a dog attempting to catch a tennis ball for the first time, there is inaccuracy— in other words, error—as the organism figures out how to solve these motor problems.
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:
ei = Xi – 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.
The trajectory RMSE measure can be slightly altered to ask an important theoretical question in motor control. Are trajectories scalable in space and time? In other words, does the production of a skilled action show evidence for an ideal template that might exhibit spatial variability and temporal variability, while the movement appears to be derived from a common invariant trajectory? In speech motor control, Anne Smith, Lisa Goffman, Howard Zelaznik, Goangshiuan Ying, and Clare McGillem developed a measure known as the spatial–temporal index (STI). First, the trajectory time base is changed to a percentage. Therefore, all movements have a temporal scale from 0 to 100. Second, the displacement values are placed on a normal scale (they usually range from –1.5 to +1.5). At each 2-percentage interval, the standard deviation of the normalized displacements is computed. The 50 standard deviations are either summed or averaged. The STI captures how closely a set of trajectories follows the average spatial–temporal trajectory. The average normalized trajectory purportedly represents the invariant template. The STI measure does not make any theoretical statements about the cause of any spatial– temporal invariance. The measure has been shown to capture development of speech motor patterns and the effects of practice on speech learning. Although the assumptions of linear scaling might not be fully justified, the measure appears to be fairly robust in spite of these issues.
The Value of Errors
The previous section presented the descriptive aspects of error. Now, attention is focused on whether errors are good, bad, or indifferent. Obviously, at high levels of performance errors generally are considered bad. Missing the putt to lose the championship is not a good thing. In competition, errors might seem to always be bad. But, that clearly does not have to be the case. A good baseball pitcher deliberately may throw a bad pitch so that the batter might swing and miss, or the batter might be expecting a pitch in the future series of pitches. Is home plate the target on every pitch? No! Thus, errors in pitching are difficult to measure. However, errors in pitching can be measured in practice. The target changes, but during the game, error in pitching can only be measured if we know the goal of the pitcher.
What about errors during practice? For high-level performers errors might be necessary for an expert to figure out the nuances of a difficult task. For example, when concert pianists need to learn a new fingering sequence, they experiment with the best method to get it done. In other words, they are making deliberate errors to help them search for the solution to this new problem. New learners need and use errors to guide the learning process. James A. Adams, one of the first, if not the first, to propose a major role of errors in learning, believed that errors provided motivation and information that learners use to change their attempt on the next trial. Ann Gentile, although not explicit on this matter, believes that learning is a search process. The learner is attempting to find a reasonable solution to the motor learning problem. She calls this getting the idea of the movement. After this approximate solution, the learning then works at refining the solution. One can define getting the idea when the learner is consistently producing an acceptable level of error and then moves to a deliberate attempt to reduce error. What would be the consequences of a performer not being able to control and produce error? One would be an inflexible robot. Errors provide the flexibility for individuals to respond to their environment.
Human beings would not be functional if they only possessed fixed action patterns, such as stereotypical reflexes.
Errors also are organized. Robert Sessions Woodworth in 1899, Paul M. Fitts in 1954, and more recently Richard A. Schmidt, Howard Zelaznik, Brian Hawkins, James S. Frank, and John T. Quinn in 1979 described this organization. The organization is called the speed-accuracy trade-off. With some exceptions the cost of increasing movement speed (decreasing duration, increasing distance, or the combination of the two) is a decrease in movement accuracy in the spatial dimension. Home run hitters tend to strike out more often than singles hitters. Why? A home run in baseball requires increased bat speed. The cost of that increase is paid in the currency of an increase in spatial variability. There is a clear exception to this speed–accuracy trade-off in the temporal domain. Temporal variability decreases as the timed interval decreases (in other words, doing the task faster). Therefore, in tasks that require both spatial as well as temporal accuracy performers need to learn the optimal movement speed to minimize spatial error but maximize temporal accuracy.
What is the source of error and variability? One way to view errors and variability in performance is via the classic view of test theory. A performance score is composed of two components, the true score and a source of random variations called an error. The true score represents the mean of an infinite number of trials. In other words, the true score is a construct, and thus it represents the individual’s level of performance.
Recently, scholars in motor behavior have begun to discover that error over a series of trials does have a random component. However, error also has a predictive component. In other words, a performance score in series predicts a performance score in later in the time series. These relations are called long-term correlations, and are thought to be the results of the underlying nonlinear dynamics of human performance. These long-term correlations are shown in fluctuations of step–cycle duration, reaction time, and cycle duration in repetitive timing tasks. There are some very exciting hints that these long-term fluctuations are crucial to healthy behavior, and the lack of these correlations might be the signature of diseased states. Fluctuations, which are not random, but structured, are a reliable signature of normal biological function.
The observation that errors have a nonrandom component might be the reason for the success of sport psychologists working with high-level performers. Obviously if errors in performance were solely random, the only way to improve performance would be to dramatically increase the amount of deliberate practice. However, most high-level performers already practice many hours per day. If performers acquire techniques to control the nonrandom component of performance fluctuations, performance will improve.
- Adams, J. A. (1971). A closed loop theory of motor learning. Journal of Motor Behavior, 3, 111–150.
- Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381–391.
- Gentile, A. (1972). A working model of skill acquisition with application to teaching. Quest, 17, 3–23.
- Schmidt, R. A., Zelaznik, H. N., Hawkins, B., Frank, J. S., & Quinn, J. T. J. (1979). Motor-output variability: A theory for the accuracy of rapid motor acts. Psychological Review, 86, 415–451.
- Schutz, R. W., & Roy, E. A. (1973). Absolute error—devil in disguise. Journal of Motor Behavior, 5, 141–153.
- Smith, A., Goffman, L., Zelaznik, H. N., Ying, G. S., & McGillem, C. (1995). Spatiotemporal stability and patterning of speech movement sequences. Experimental Brain Research, 104, 493–501.
- Woodworth, R. S. (1899). The accuracy of voluntary movement. Psychological Review, 3, 1–114.