Changes in src/sas/sasgui/perspectives/fitting/media/residuals_help.rst [84ac3f1:99ded31] in sasview

File:

• src/sas/sasgui/perspectives/fitting/media/residuals_help.rst (modified) (3 diffs)

src/sas/sasgui/perspectives/fitting/media/residuals_help.rst

@@ -27 +27 @@
 
 $\chi^2$ is a statistical parameter that quantifies the differences between
-an observed data set and an expected dataset (or 'theory') calculated as
+an observed data set and an expected dataset (or 'theory').
+
+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
-  =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2]
+  \chi^2_N
+  =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / N_\mathrm{pts}
 
-Fitting typically minimizes the value of $\chi^2$.  For assessing the quality of
-the model and its "fit" however, *SasView* displays the traditional reduced
-$\chi^2_R$ which normalizes this parameter by dividing it by the number of
-degrees of freedom (or DOF). The DOF is the number of data points being
-considered, $N_\mathrm{pts}$, reduced by the number of free (i.e. fitted)
-parameters, $N_\mathrm{par}$. Note that model parameters that are kept fixed do
-*not* contribute to the DOF (they are not "free"). This reduced value is then
-given as
+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
 
 .. math::
@@ -49 +47 @@
   / [N_\mathrm{pts} - N_\mathrm{par}]
 
-Note that this means the displayed value will vary depending on the number of
-parameters used in the fit. In particular, when doing a calculation without a
-fit (e.g. manually changing a parameter) the DOF will now equal $N_\mathrm{pts}$
-and the $\chi^2_R$ will be the smallest possible for that combination of model,
-data set, and set of parameter values.
-
-When $N_\mathrm{pts} \gg N_\mathrm{par}$ as it should for proper fitting, the
-value of the reduced $\chi^2_R$ will not change very much.
+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.
@@ -98 +90 @@
 | 2015-06-08 Steve King
 | 2017-09-28 Paul Kienzle
-| 2018-03-04 Paul Butler