I'm relatively new to statistics, and understand that my question may be completely misworded. I am testing my own algorithm versus another. While the outputs are not identical, I want to show that the differences are "statistically insignificant." How can I quantify this, to make my point?
If you are comparing two groups and want to show no significant difference, this is called equivalence testing. It essentially reverses the null and alternative hypotheses. The idea is to define an interval of insignificance called the window of equivalence. This is used a lot when trying to show that a generic drug is a suitable replacement for a marketed drug. A good source to read about this is William Blackwelder's paper titled “Proving the null hypothesis” in clinical trials.