Error estimation
From GOSIA
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Error estimation in any physics field can sometimes be difficult and is often poorly understood. It is common for errors to be underestimated because of a failure to correlate error contributions from all significant (strongly coupled) fit parameters, and fallacies about error propagation abound. | Error estimation in any physics field can sometimes be difficult and is often poorly understood. It is common for errors to be underestimated because of a failure to correlate error contributions from all significant (strongly coupled) fit parameters, and fallacies about error propagation abound. | ||
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| + | ==Diagonal errors versus correlated errors== | ||
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| + | The ''diagonal'' error is the error one obtains by varying only a single parameter "x" above and below it minimum chi-squared value to find the intersection of the chi-squared vs. with the line defined by chi-squared = minimum chi-squared + 1. The diagonal error is generally much smaller than the full correlated error, and the latter is the error that should be quoted. | ||
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| + | The ''correlated error'' is defined by the lower and upper limits of the parameter being measured of the (ideally elliptical) intersection of the reduced chi-squared surface with the plane defined by reduced-chi-squared + reduced-chi-squared_minimum + (reduced-chi-squared_minimum/N), where "N" is the number of [ degrees of freedom] in the fit. | ||
==Proper treatment of correlated errors in the general case== | ==Proper treatment of correlated errors in the general case== | ||
