SMTL policy for rounding data is to "*Round to Nearest*" for non-tied values (i.e. those values which do not end in a '5'), and to follow the IEEE "*Round half to Even*" rule for *tied* or *mid-point* values. The principles of the procedure are as follows:
- If rounding to 3 significant figures, using the *Round to Nearest* rule, a value of 3.967 on the balance would be rounded to 3.97. Similarly, 3.943 would be rounded to 3.94.
- For any tied values such as 3.965 or 3.955, the *Round half to Even* rule is used. Thus 3.965 is rounded to 3.96 and 3.955 is also rounded to 3.96 (to the nearest even number of the last significant place).
- If rounding to integers, 127.5 would be rounded to 128, 126.5 would be rounded to 126 and 125.5 would be rounded to 126.
- The *Round half to Even* rule prevents a slight bias which would otherwise occur if the figures were always rounded up or always down. However, it is well known that many numbers cannot be represented accurately internally in computers <http://floating-point-gui.de/basic/>. Although most computers follow the IEEE rules for rounding, they store floating point numbers inaccurately. For example, the floating point number 2.15 as stored internally by many computers as 2.14999999999999991118 (this is true for the 'R' statistical language). Therefore when rounding this number, the ‘round half to even’ rule doesn’t trigger because the number it is operating on is not 2.15, but rather 2.14999999999999991118, which is less than 2.15 and thus the *round to nearest* rule is triggered, which rounds it to 2.1. If the computer had stored it accurately as 2.15, then that would trigger the *round half to even* rule, which would have rounded to 2.2.
The effect that this has on compliance testing depends on the test data under consideration. For example, for FAB testing to EN 455-2:
1. Samples are tested and the force at break (FAB) results are *recorded* and *corrected* as per 455-2;
2. The final set of corrected FAB figures are rounded to 1 decimal place by computer (using the IEEE rounding method in 'R') to give the *reported* raw data (i.e., the individual FAB results recorded in the test report);
3. The median of the *reported* data is calculated and used to assess compliance against the EN 455 standard requirement;
4. If the requirement is for greater than or equal to 9N, then if the non-rounded *corrected* median value was originally 8.95, this would have been rounded by the computer to 8.9, and the glove would fail (as it is less than 9N, assuming shared risk on uncertainty of measurement).
SMTL acknowledges that for certain marginal results (such as 8.95N) the effect of computer rounding will be to fail a glove (8.9N) which would otherwise pass if IEEE "*Round half to even" *rounding by hand had been undertaken (9.0N). This is a consequence of using computers to handle data.
