Modified Median Statistics and Type Ia Supernova Data

The median statistic has recently been discussed by Gott \textit{et al.} as amore reliable alternative to the standard $\chi^2$ likelihood analysis, in thesense of requiring fewer assumptions about the data and being almost asconstraining. We apply this statistic to the currently available combineddataset of 92 distant type Ia supernovae, and also to a mock SNAP-classdataset. We find that the performances of the modified median and $\chi^2$statistics are comparable, particularly in the latter case. We further extendthe work of Gott \textit{et al.} by modifying the median statistic to accountfor the number and size of sequences of consecutive points above or below themedian. We also comment on how the performance of the statistic depends on thechoice of free parameters that one is estimating.Comment: A few clarifying comments and references added. Version to appear in The Astrophysical Journa