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Goodness of Fit

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Definition

A measure of how well a chosen model describes the data. Goodness of fit of a model can be assessed by summary or graphical methods. Most summary measures of fit involve calculating the distance between the observed data and the fitted values obtained from the model. Small values of these summary measures of distance indicate a good fit. A complete assessment of the model also involves an examination of the individual components of the measures (i.e., the residuals). In replicated experiments, the fit of the model is tested using a Lack-of-fit test.

Another application of goodness-of-fit is to test whether or not the data at hand come from a specified distribution. Several parametric and non-parametric goodness-of-fit tests exist to evaluate whether or not the data conform to a specified distribution. Among these, the Anderson Darling test and Bartlett test (parametric) and Chi-Square test and Kolmogorov-Smirnov test (non-parametric) procedures are most commonly used to test the assumption of normality of the data.

External Links

Anderson-Darling and Shapiro-Wilk tests from NIST: - http://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm Kolmogorov-Smirnov Goodness-of-Fit Test from NIST: - http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm Bartlett Test from NIST: - http://www.itl.nist.gov/div898/handbook/eda/section3/eda357.htm Chi-Square Goodness-of-Fit Test from NIST: - http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm