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We propose a new statistic that has been designed to be used in situationswhere the intrinsic dispersion of a data set is not well known: The CrossingStatistic. This statistic is in general less sensitive than `chi^2' to theintrinsic dispersion of the data, and hence allows us to make progress indistinguishing between different models using goodness of fit to the data evenwhen the errors involved are poorly understood. The proposed statistic makesuse of the shape and trends of a model's predictions in a quantifiable manner.It is applicable to a variety of circumstances, although we consider it to beespecially well suited to the task of distinguishing between differentcosmological models using type Ia supernovae. We show that this statistic caneasily distinguish between different models in cases where the `chi^2'statistic fails. We also show that the last mode of the Crossing Statistic isidentical to `chi^2', so that it can be considered as a generalization of`chi^2'.

The Crossing Statistic: Dealing with Unknown Errors in the Dispersion of Type Ia Supernovae