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1.. residuals_help.rst
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3.. |chi| unicode:: U+03C7
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6.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
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8.. _Assessing_Fit_Quality:
9
10Assessing Fit Quality
11---------------------
12
13When performing model-fits to some experimental data it is helpful to be able to
14gauge how good an individual fit is, how it compares to a fit of the *same model*
15*to another set of data*, or how it compares to a fit of a *different model to the*
16*same data*.
17
18One way is obviously to just inspect the graph of the experimental data and to
19see how closely (or not!) the 'theory' calculation matches it. But *SasView*
20also provides two other measures of the quality of a fit:
21
22*  |chi|\  :sup:`2` (or 'Chi2'; pronounced 'chi-squared')
23*  *Residuals*
24
25.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
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27Chi2
28^^^^
29
30Chi2 is a statistical parameter that quantifies the differences between an observed
31data set and an expected dataset (or 'theory').
32
33*SasView* actually returns this parameter normalized to the number of data points,
34*Npts* such that
35
36  *Chi2/Npts* = { SUM[(*Y_i* - *Y_theory_i*)^2 / (*Y_error_i*)^2] } / *Npts*
37
38This differs slightly from what is sometimes called the 'reduced chi-squared'
39because it does not take into account the number of fitting parameters (to
40calculate the number of 'degrees of freedom'), but the 'normalized chi-squared'
41and the 'reduced chi-squared' are very close to each other when *Npts* >> number of
42parameters.
43
44For a good fit, *Chi2/Npts* tends to 0.
45
46*Chi2/Npts* is sometimes referred to as the 'goodness-of-fit' parameter.
47
48.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
49
50Residuals
51^^^^^^^^^
52
53A residual is the difference between an observed value and an estimate of that
54value, such as a 'theory' calculation (whereas the difference between an observed
55value and its *true* value is its error).
56
57*SasView* calculates 'normalized residuals', *R_i*, for each data point in the
58fit:
59
60  *R_i* = (*Y_i* - *Y_theory_i*) / (*Y_err_i*)
61
62For a good fit, *R_i* ~ 0.
63
64.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
65
66.. note::  This help document was last changed by Steve King, 08Jun2015
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