So there are some big challenges right out of the gate when testing statistical software, and so far I've looked at rounding errors. The bigger question, given that computers have this innate limitation, is how accurate can and should we be?
On one hand, statistics gives probabilities, not truth. So having a routine give a 86.4532% chance compared to second routine giving an 86.4533% seems like we are splitting hairs. But we have some trust in our computers and we need to get the answer as "right" as possible.
My favorite stat on this is Nasa using 15 digits of accuracy for pi. That is as much as they need to track everything they have ever launched, so that is one benchmark to consider. For the software on which I work, I doubt many folks are tracking interstellar traffic, though. It's still a good data point.
Financial markets are something we handle. This gets tricky really quickly, though. In the USA, we track (pennies) to two decimal places and have rules about rounding the third decimal place. Other countries use more decimal places, so this doesn't help much. (Side note: Ohio has a rounding methodology for sales tax that strongly skews to higher taxes: http://www.tax.ohio.gov/sales_and_use/information_releases/st200505.aspx)
There is also a performance (of the computer) vs. precision factor that we need to consider. While we could get much more precision, that comes at the cost of run time. One way of having more precision would be to allocate more memory for each number we are using. Also, there are some libraries that the National Institute of Standards and Technology makes available that really help, and companies like Intel also provide these tools. They generally run more slowly than code that doesn't push for that level of precision. More on this later.
Looking ahead, once we settle on a standard, then the test team has to ensure we meet that goal 100% of the time. I'll finally get around to covering that aspect of the test team's goals as we go along.
Questions, comments, concerns and criticisms always welcome,