Changeset a7c6f38 in sasview for src/sas/sasgui/perspectives/fitting/media/residuals_help.rst

Timestamp:

Mar 4, 2018 4:07:55 PM (6 years ago)

Author:

butler

Branches:

master, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, unittest-saveload

Children:

84ac3f1

Parents:

943e17a

Message:

Clarify use of chi^{2 in GUI and documentation}

Changed Gui name and tooltip to reflect we are using reduced chi^{2 not
simply Chi}2/Npts. Also edited the documenataion to finish making that
clear and in the process cleaned up a few old (i.e. incorrect)
statements.

File:

• src/sas/sasgui/perspectives/fitting/media/residuals_help.rst (modified) (2 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').
-
-When showing the a model with the data, *SasView* displays this parameter
-normalized to the number of data points, $N_\mathrm{pts}$ such that
+an observed data set and an expected dataset (or 'theory') calculated as
 
 .. math::
 
-  \chi^2_N
-  =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2] / N_\mathrm{pts}
+  \chi^2
+  =  \sum[(Y_i - \mathrm{theory}_i)^2 / \mathrm{error}_i^2]
 
-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
+Fitting typically minimizes the value of $\chi^2$.  However, for assessing the
+quality of the model and its "fit" this parameter is not terribly helpful on its
+own.  Thus *SasView* instead displays a normalized version of this parameter,
+using the traditional reduced $\chi^2_R$.  This is the $\chi^2$ divided by the
+degrees of freedom (or DOF). The DOF is simply the number of data points being
+considered reduced by the number of free (i.e. fitted) parameters. 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
 
 .. math::
@@ -47 +49 @@
   / [N_\mathrm{pts} - N_\mathrm{par}]
 
-The normalized $\chi^2_N$ and the reduced $\chi^2_R$ are very close to each
-other when $N_\mathrm{pts} \gg N_\mathrm{par}$.
+where $N_\mathrm{par}$ is the number of *fitted* parameters. 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.
 
 For a good fit, $\chi^2_R$ tends to 1.