# Changeset 99ded31 in sasview

Ignore:
Timestamp:
Sep 28, 2017 3:29:35 PM (6 years ago)
Branches:
master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
Children:
64cdb0d
Parents:
5005ae0
Message:

improve description of 'fitting quality' and clean up latex formatting

File:
1 edited

### Legend:

Unmodified
 r940d034 ^^^^ Chi2 is a statistical parameter that quantifies the differences between an observed data set and an expected dataset (or 'theory'). $\chi^2$ is a statistical parameter that quantifies the differences between an observed data set and an expected dataset (or 'theory'). *SasView* actually returns this parameter normalized to the number of data points, *Npts* such that When showing the a model with the data, *SasView* displays this parameter normalized to the number of data points, $N_\mathrm{pts}$ such that .. math:: \chi^2/N_{pts} =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / N_{pts} \chi^2_N =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / N_\mathrm{pts} This differs slightly from what is sometimes called the 'reduced $\chi^2$' because it does not take into account the number of fitting parameters (to calculate the number of 'degrees of freedom'), but the 'normalized $\chi^2$ and the 'reduced $\chi^2$ are very close to each other when $N_{pts} \gg \text{number of parameters}. When performing a fit, *SasView* instead displays the reduced$\chi^2_R$, which takes into account the number of fitting parameters$N_\mathrm{par}$(to calculate the number of 'degrees of freedom'). This is computed as For a good fit,$\chi^2/N_{pts}$tends to 1. .. math::$\chi^2/N_{pts}$is sometimes referred to as the 'goodness-of-fit' parameter. \chi^2_R = \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / [N_\mathrm{pts} - N_\mathrm{par}] The normalized$\chi^2_N$and the reduced$\chi^2_R$are very close to each other when$N_\mathrm{pts} \gg N_\mathrm{par}$. For a good fit,$\chi^2_R$tends to 1.$\chi^2_R$is sometimes referred to as the 'goodness-of-fit' parameter. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ A residual is the difference between an observed value and an estimate of that value, such as a 'theory' calculation (whereas the difference between an observed value and its *true* value is its error). value, such as a 'theory' calculation (whereas the difference between an observed value and its *true* value is its error). *SasView* calculates 'normalized residuals',$R_i$, for each data point in the .. math:: R_i = (Y_i - Y_theory_i) / (Y_err_i) R_i = (Y_i - \mathrm{theory}_i) / \mathrm{error}_i For a good fit,$R_i \sim 0$. Think of each normalized residual as the number of standard deviations between the measured value and the theory. For a good fit, 68% of$R_i$will be within one standard deviation, which will show up in the Residuals plot as$R_i$values between$-1$and$+1$. Almost all the values should be between$-3$and$+3$. Residuals values larger than$\pm 3\$ indicate that the model is not fit correctly, the wrong model was chosen (e.g., because there is more than one phase in your system), or there are problems in the data reduction.  Since the goodness of fit is calculated from the sum-squared residuals, these extreme values will drive the choice of fit parameters.  Any uncertainties calculated for the fitting parameters will be meaningless. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. note::  This help document was last changed by Steve King, 08Jun2015 *Document History* | 2015-06-08 Steve King | 2017-09-28 Paul Kienzle