# Approximation error

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In psychophysics the **approximation error** in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because

- the measurement of the data is not precise (due to the instruments), or
- approximations are used instead of the real data (e.g., 3.14 instead of π).

One commonly distinguishes between the **relative error** and the **absolute error**.

The numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.

## DefinitionsEdit

### Absolute errorEdit

In psychmetrics, for example, the absolute error refers to the difference between the judged value of a stimulus, an approximation *b* and its true or consensual value *a*, ignoring the value of the difference. Mathematically the **absolute error** is

### Relative errorEdit

In psychometrics the relative error is the absolute error divided by the true value of the stimulus

### Percent errorEdit

and the **percent error** is

where the vertical bars denote the absolute value, *a* represents the true value, and *b* represents the approximation to *a*.