At this point you'll have to use the last tool in your arsenal, your brain. You're going to have to draw upon the scientific method and begin to develop some experiments or tests to help you test your hypothesis and gather evidence. That evidence will either support your hypothesis or refute it, but in either case there will be something important to learn so be sure to remain objective and unbiased when looking over your results. Remember, you're in this to learn facts, not to be right. The evidence you gather will give you insight about what search engine optimization techniques work and to what degree a particular technique works.
Now people who know about designing experiments will tell you that a proper experiment will strive to have strict control over all but a single variable. Conversely, people who know about search engine optimization will tell you that for most variables of interest to SEOs, you cannot control all but one. But that's ok, we're not trying to get that level of control in our basic testing. Don't get me wrong, if there is an easy way to isolate each variable and test them independently, you should be doing it, but given the current landscape, it's simply not an option for most cases.
The main reason that you will have a very hard time isolating variables is that with most changes, especially when it comes to links, you will be affecting several variables with a single change. To make testing more feasible, we just need to lower our expectations a little. If we were looking to find out exactly how exactly how much a variable was worth, we'd need strict control over other variables to properly quantify the one we're testing. But in most cases, simply knowing that a variable has an effect at all is half the battle. If you need more information than that, you'll have to spend time developing broader testing strategies.
The core principles to grasp are that you want to observe, hypothesize, test and finally rinse and repeat. You need to do all four of these things in order to become a knowledgeable SEO. The game is hard and it's only getting harder. In order to be successful, you're going to have to develop sound testing strategies. It's the only way to stay ahead.