Changeset 99ded31 in sasview
 Timestamp:
 Sep 28, 2017 5:29:35 PM (7 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, release4.2.2, ticket1009, ticket1094headless, ticket12422dresolution, ticket1243, ticket1249, ticket885, unittestsaveload
 Children:
 64cdb0d
 Parents:
 5005ae0
 File:

 1 edited
Legend:
 Unmodified
 Added
 Removed

src/sas/sasgui/perspectives/fitting/media/residuals_help.rst
r940d034 r99ded31 26 26 ^^^^ 27 27 28 Chi2 is a statistical parameter that quantifies the differences between an observed 29 data set and an expected dataset (or 'theory').28 $\chi^2$ is a statistical parameter that quantifies the differences between 29 an observed data set and an expected dataset (or 'theory'). 30 30 31 *SasView* actually returns this parameter normalized to the number of data points, 32 *Npts*such that31 When showing the a model with the data, *SasView* displays this parameter 32 normalized to the number of data points, $N_\mathrm{pts}$ such that 33 33 34 34 .. math:: 35 35 36 \chi^2/N_{pts} = \sum[(Y_i  \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / N_{pts} 36 \chi^2_N 37 = \sum[(Y_i  \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / N_\mathrm{pts} 37 38 38 This differs slightly from what is sometimes called the 'reduced $\chi^2$' 39 because it does not take into account the number of fitting parameters (to 40 calculate the number of 'degrees of freedom'), but the 'normalized $\chi^2$ 41 and the 'reduced $\chi^2$ are very close to each other when $N_{pts} \gg 42 \text{number of parameters}. 39 When performing a fit, *SasView* instead displays the reduced $\chi^2_R$, 40 which takes into account the number of fitting parameters $N_\mathrm{par}$ 41 (to calculate the number of 'degrees of freedom'). This is computed as 43 42 44 For a good fit, $\chi^2/N_{pts}$ tends to 1. 43 .. math:: 45 44 46 $\chi^2/N_{pts}$ is sometimes referred to as the 'goodnessoffit' parameter. 45 \chi^2_R 46 = \sum[(Y_i  \mathrm{theory}_i)^2 / \mathrm{error}_i^2] 47 / [N_\mathrm{pts}  N_\mathrm{par}] 48 49 The normalized $\chi^2_N$ and the reduced $\chi^2_R$ are very close to each 50 other when $N_\mathrm{pts} \gg N_\mathrm{par}$. 51 52 For a good fit, $\chi^2_R$ tends to 1. 53 54 $\chi^2_R$ is sometimes referred to as the 'goodnessoffit' parameter. 47 55 48 56 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 52 60 53 61 A residual is the difference between an observed value and an estimate of that 54 value, such as a 'theory' calculation (whereas the difference between an observed55 value and its *true* value is its error).62 value, such as a 'theory' calculation (whereas the difference between an 63 observed value and its *true* value is its error). 56 64 57 65 *SasView* calculates 'normalized residuals', $R_i$, for each data point in the … … 60 68 .. math:: 61 69 62 R_i = (Y_i  Y_theory_i) / (Y_err_i)70 R_i = (Y_i  \mathrm{theory}_i) / \mathrm{error}_i 63 71 64 For a good fit, $R_i \sim 0$. 72 Think of each normalized residual as the number of standard deviations 73 between the measured value and the theory. For a good fit, 68% of $R_i$ 74 will be within one standard deviation, which will show up in the Residuals 75 plot as $R_i$ values between $1$ and $+1$. Almost all the values should 76 be between $3$ and $+3$. 77 78 Residuals values larger than $\pm 3$ indicate that the model 79 is not fit correctly, the wrong model was chosen (e.g., because there is 80 more than one phase in your system), or there are problems in 81 the data reduction. Since the goodness of fit is calculated from the 82 sumsquared residuals, these extreme values will drive the choice of fit 83 parameters. Any uncertainties calculated for the fitting parameters will 84 be meaningless. 65 85 66 86 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 67 87 68 .. note:: This help document was last changed by Steve King, 08Jun2015 88 *Document History* 89 90  20150608 Steve King 91  20170928 Paul Kienzle
Note: See TracChangeset
for help on using the changeset viewer.