  It has recently been pointed out by Kowalski et. al. (arxiv:0804.4142) that
there is `an unexpected brightness of the SnIa data at z>1'. We quantify this
statement by constructing a new statistic which is applicable directly on the
Type Ia Supernova (SnIa) distance moduli. This statistic is designed to pick up
systematic brightness trends of SnIa datapoints with respect to a best fit
cosmological model at high redshifts. It is based on binning the normalized
differences between the SnIa distance moduli and the corresponding best fit
values in the context of a specific cosmological model (eg LCDM). We then focus
on the highest redshift bin and extend its size towards lower redshifts until
the Binned Normalized Difference (BND) changes sign (crosses 0) at a redshift
z_c (bin size N_c). The bin size N_c of this crossing (the statistical
variable) is then compared with the corresponding crossing bin size N_{mc} for
Monte Carlo data realizations based on the best fit model. We find that the
crossing bin size N_c obtained from the Union08 and Gold06 data with respect to
the best fit LCDM model is anomalously large compared to N_{mc} of the
corresponding Monte Carlo datasets obtained from the best fit LCDM in each
case. In particular, only 2.2% of the Monte Carlo LCDM datasets are consistent
with the Gold06 value of N_c while the corresponding probability for the
Union08 value of N_c is 5.3%. Thus, according to this statistic, the
probability that the high redshift brightness bias of the Union08 and Gold06
datasets is realized in the context of a (w_0,w_1)=(-1,0) model (LCDM
cosmology) is less than 6%. The corresponding realization probability in the
context of a (w_0,w_1)=(-1.4,2) model is more than 30% for both the Union08 and
the Gold06 datasets.
