Comparing low and high-z slope distributions

From: Alexander Conley (AJConley@lbl.gov)
Date: Sun Nov 07 2004 - 01:06:32 PST

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    There was definitely something wrong with the values given in the paper
    for the mean slopes and the error in that mean.

    In any case, the new values are:

    Low-z: beta = 1.9854 +- 0.0299
    High-z: beta = 1.9654 +- 0.1130

    There are 47 low-z and 5 high-z, so you expect a sqrt(10) = 3
    improvement,
    but for some reason there is a factor of 4. With only 5 SNe involved,
    this probably
    doesn't mean much -- I suppose one could estimate the error in the rms
    or something.

    The addition of a few extra low-z SNe has dragged the mean slope up
    slightly for
    the low z sample (by maybe 0.02).

    I thought for a while about using the weighted mean for this, but I
    don't
    think it's valid. The weighted mean seems to require that all of the
    measurements
    are of the same quantity, and since I believe that there is some
    intrinsic dispersion
    in the slopes, this doesn't apply. The raw mean, on the other hand, has
    it's own life. In any case, using a weighted mean decreases the error
    in the low-z
    sample by about a factor of two, but doesn't really do anything for the
    high-z sample.

    They are consistent -- but the high-z error is pretty big.

    Alex



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