Truncating doesn’t get the respect it deserves.

Like rounding, truncating gets rid of those pesky decimal places that imply a higher degree of accuracy than truly exists. When you’re talking about a ten point scale or 100 percent ranges, 56.85637328 is identical to 56.

Like rounding, truncating makes numbers that are nine places away from each other appear to be equal. 7.5 and 8.4 are 9 points apart but both get rounded to 8. Just as 8.0 and 8.9 are 9 places away from each other but both get truncated to 8.

The only time when rounding has a very slight advantage over truncating is when you’re using scales with a very small range. Where rounding retains the five points in a five point scale, truncating essentially reduces a five point scale to a four point scale. Now that isn’t inherently bad, but when you haven’t got a lot of variability in your results to begin with, every box counts. That is, afterall, why we love decimal places.

Personally, I prefer truncating over rounding. It’s a great sound numerical karate chop. And It just sounds cooler.

Written on the go

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Rewrite: The object is to round to the NEAREST integer, but introduce a bias towards zero (smaller absolute integers). Rounding to the nearest would be done by adding in 32768 before the truncating division. Using a smaller “offset” than 32768 gives the desired bias effect. If the offset is a power of 2 e.g 2**k, it can be done by: shift k bits, add 1, shift 16-k bits.

Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in 1982. It was initially set at 1000.000, and after 22 months had fallen to about 520 — whereas stock prices had generally increased in the period. The problem was caused by the index being recalculated thousands of times daily, and always being rounded down to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating with better rounding gave an index value of 1098.892 at the end of the same period.

Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in 1982. It was initially set at 1000.000 (three decimal places of accuracy), and after 22 months had fallen to about 520 — whereas stock prices had generally increased in the period. The problem was caused by the index being recalculated thousands of times daily, and always being rounded down to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating with better rounding gave an index value of 1098.892 at the end of the same period.

Thought provoking. Truncating would mean that choice lists would typically total less than 100%, where rounding means they can sometimes exceed 100% (which has confused some of my clients in the past). In fact, the total will equal 100% – 0.5%*choices on average.

I think I’m going to have to stick with rounding.