# 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

1. the measurement of the data is not precise (due to the instruments), or
2. 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.

## Definitions

### Absolute error

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

$\epsilon = |a - b|\,$

### Relative error

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

$\eta = \frac{|a - b|}{|a|}$

### Percent error

and the percent error is

$\delta = \frac{|a-b|}{|a|}\times{}100\%$

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