Error propagation: Difference between revisions

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:<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>  
<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''.