Hi,

Jerry wrote:

Those problems aside, the availability of a Round
function that rounds
in this way is a welcome addition. You wouldn't
know it from MS
documentation (which calls it "Banker's" rounding
despite the fact that
banker's don't seem to use it), but this is type of
rounding is
specified by ASTM, IEEE, and most other standards
bodies that choose to
define rounding. It is usually a better way to handle
data, because it
tends to minimize the impact of accumulated
rounding errors on
subsequent calculations, because it tends to equalize
the number of
times that you round up vs. round down. As such it
is sometimes called
"unbiased" rounding.


I struggle with the explanation that this reduces bias (unless you are
looking at a non random distribution that is already biased to return
values exactly on the 0.5 points).

If you use 'true' rounding, then everything from N to N+4.9999
(recurring) inclusive will be rounded 'down' to N, and everyting from
N+0.5 to N+0.9999 (recurring) will be rounded 'up' to N+1 (where N is
an integer number - consider it positive for the sake of this
discussion).

This is a symmetrical rounding 'function' and as such is unbiased.

If we now redefine to use what was referred to above as Banker's
rounding, and round down approximately half the time when we have a
value of N+0.5, we have made the function non-symmetrical, and hence
biased.

The only excpetion would be if we have a sample that returns discrete
values, that may include N+0.5 more often that we would otherwise
expect, in which situation there may be a case.

Does this make sense?

Alan.



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