An alternative to the goodness of fit

Abstract

An alternative measure to the goodness of fit (GoF) is developed and applied to experimental data. The alternative goodness of fit squared (aGoFs) demonstrates that the GoF regularly fails to provide evidence for the presence of systematic errors, because certain requirements are not met. These requirements are briefly discussed. It is shown that in many experimental data sets a correlation between the squared residuals and the variance of observed intensities exists. These correlations corrupt the GoF and lead to artificially reduced values in the GoF and in the numerical value of thewR(F2). Remaining systematic errors in the data sets are veiled by this mechanism. In data sets where these correlations do not appear for the entire data set, they often appear for the decile of largest variances of observed intensities. Additionally, statistical errors for the squared goodness of fit, GoFs, and the aGoFs are developed and applied to experimental data. This measure shows how significantly the GoFs and aGoFs deviate from the ideal value one.