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Error propagation: Difference between revisions
→Error estimate (experimental error known)
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:<math>z = f(x, y, ...)\,</math> | :<math>z = f(x, y, ...)\,</math> | ||
:<math>(\Delta z)^2 = \left ( \frac{\partial f}{\partial x}\right )^2 \Delta x^2 + \left ( \frac{\partial f}{\partial y}\right )^2 \Delta y^2 + ... </math> | :<math>(\Delta z)^2 = \left ( \frac{\partial f}{\partial x}\right )^2 \Delta x^2 + \left ( \frac{\partial f}{\partial y}\right )^2 \Delta y^2 + ... </math> | ||
This formula holds exclusively for a Gaussian (normal) distribution of errors (assuming the errors are small and that the independent variables ''x'', ''y'', ... are indeed independent). | This formula holds exclusively for a Gaussian (normal) distribution of errors (assuming the errors are small and that the independent variables ''x'', ''y'', ... are indeed independent). | ||
<ref>http://mathworld.wolfram.com/ErrorPropagation.html|Error Propagation (MathWorld)</ref> | |||
One should be aware that many situations exist where error distributions are not normal (see below). | One should be aware that many situations exist where error distributions are not normal (see below). | ||
One can easily check whether the error distribution is normal by doing repeated experiments under the same conditions and observing the resulting distribution of ''s''. | One can easily check whether the error distribution is normal by doing repeated experiments under the same conditions and observing the resulting distribution of ''s''. | ||