You can't ever prove that switching to X doesn't change the result. All you can really hope for is putting smaller limits on the amount by which something could

You can't ever prove that switching to X doesn't change the result. All you can really hope for is putting smaller limits on the amount by which something could be improved. For one dumb example: if you wanted to see if rats can fly, you might observe 100 rats and see that none of them fly away. But this doesn't prove anything: in reality even if 3% of rats could fly you'd get this result about 5% of the time. You've really shown with 95% confidence is that less than 3% of rats fly.