This behaviour is explained in the help file of the ?round function:
Note that for rounding off a 5, the IEC 60559 standard is expected to
be used, ‘go to the even digit’. Therefore round(0.5) is 0 and
round(-1.5) is -2. However, this is dependent on OS services and on
representation error (since e.g. 0.15 is not represented exactly, the
rounding rule applies to the represented number and not to the printed
number, and so round(0.15, 1) could be either 0.1 or 0.2).
round( .5 + 0:10 )
#### [1] 0 2 2 4 4 6 6 8 8 10 10
Another relevant email exchange by Greg Snow: R: round(1.5) = round(2.5) = 2?:
The logic behind the round to even rule is that we are trying to
represent an underlying continuous value and if x comes from a truly
continuous distribution, then the probability that x==2.5 is 0 and the
2.5 was probably already rounded once from any values between 2.45 and 2.54999999999999..., if we use the round up on 0.5 rule that we learned in grade school, then the double rounding means that values
between 2.45 and 2.50 will all round to 3 (having been rounded first
to 2.5). This will tend to bias estimates upwards. To remove the
bias we need to either go back to before the rounding to 2.5 (which is
often impossible to impractical), or just round up half the time and
round down half the time (or better would be to round proportional to
how likely we are to see values below or above 2.5 rounded to 2.5, but
that will be close to 50/50 for most underlying distributions). The
stochastic approach would be to have the round function randomly
choose which way to round, but deterministic types are not
comforatable with that, so "round to even" was chosen (round to odd
should work about the same) as a consistent rule that rounds up and
down about 50/50.
If you are dealing with data where 2.5 is likely to represent an exact
value (money for example), then you may do better by multiplying all
values by 10 or 100 and working in integers, then converting back only
for the final printing. Note that 2.50000001 rounds to 3, so if you
keep more digits of accuracy until the final printing, then rounding
will go in the expected direction, or you can add 0.000000001 (or
other small number) to your values just before rounding, but that can
bias your estimates upwards.
