In particle physics we use blinding of variables, which is a bit distinct from what's called blind studies in medicine, to deal with this problem. I'll use my own thesis as an example: I was trying to measure charm mixing parameters, imaginatively denoted x and y. There were some theoretical predictions: they were expected to be less than 1%, x should be smaller in absolute magnitude than y, and they should have opposite sign; in addition there were some prior measurements that we would presumably not conflict with, within the errors.

Now, there was quite a bit of coding to do before I had a result, and a whole bunch of test runs on real data. So to avoid the problem outlined above, whenever I ran a test on actual data (as opposed to simulated data), I would not print out the actual results, but results with an unknown (random) number added. So the code would look like this (much simplified) :

double resultForX = getX();

double errorForX = getXError();

double blindValueX = getRandomUsingSeed(42);

print "Result is " + (resultForX + blindValueX) + " plus-minus " + errorForX;

So if I got, say, x=3%, very unexpected, I would not be tempted to go look for an error in the code; I'd have no idea whether I genuinely had an unexpected result, or a vanilla result with a big blinding factor.

Note that I used the same random seed every time, so I would have comparable results from run to run; if I changed something and suddenly had 1% in place of 3%, I knew something was up. But I still had no idea whether I had a New-Physics-indicating result or just a confirmation of theory.

To end blinding I had to get permission from a review committee (not my thesis committee, but other workers inside the same experiment); then I commented out the blinding lines and printed the true values. Alas, they were quite consistent with expectations.

There is a coda to this: At my thesis defense, one of the committee asked an excellent question, which I had to answer before I could submit the thesis. In the course of answering it, I did in fact find (to my horror!) a sign error in my code. Fortunately it did not change the final result very much, but it was highly embarrassing.

This approach isn't suitable to every problem, but we use it wherever we can.