My advice:
(i) Read and understand the Rules of Procedure for Professional Conduct (the “Rules”). They are these silly little quasi-judicial rules that the CFAI puts out to define their proceudres. They kinda look like an amatuer version of the Federal Code of Civil Procedure, but throw out little things like, I dunno, rules of evidence. However, they do institute standards on themselves in regard to processing a disiplinary infraction. YOU CAN USE THESE TO YOUR ADVANTAGE. Understand every single one of their obligations, including timing requirements, notice obligations, quorums, responses, etc. You are due certain documents in a certain order followed by procedural steps in between. Make sure they fulfill every single one of their oblgiations to you. If they screw up any of the steps, you can and should cite it.
https://www.cfainstitute.org/ethics/Documents/Professional%20Conduct%20Program%20Documents/rules_of_procedure.pdf
(ii) Make sure what you have is a Notice of Investigation. There are requirements to a Notice of Investigation set forth in Rule 6.2, so be sure they are included. If not, the paper you are holding in your hand is a nullity in regard to the Rules.
(iii) If what you are holding is, in fact, a valid Notice of Investigation, the next thing that will ensue is… surprise… an investigation. You are not required to respond at all at this stage and, most likely, should plead the Fifth so to speak. Remember that anything you say is going to be parsed to find the nuggets that can be used against you or that they can find evidence to contradict, so let the CFAI go forward with their investigation without formal response. Again, a Notice of Investigation does not require a response.
Here is where it will get tricky for them if the only basis for their investigation is the statistical analysis. The investigation stage allows them to go out to interview people and collect evidence. If there is no factual basis for their investigation, no people to interview to evidence their allegation, and no independent physical evidence to collect, it will be very hard for them to get over the standard of “sufficient evidence of a violation”.
(iv) If they make a preliminary determination that a violation occured, they will most likely send you an Early Resolution Agreement. At this point, they do not have to provide any evidence or even an argument that you have committed a violation. I have read through the Rules a couple times and can’t find any benifit to signing it (other than the fact that a hearing takes time in which the CFAI will withhold your exam result).
(v) If they do get to the next step of a Statement of Charges. Here they have to present to you their preliminary findings of fact and their conclusions (basically, their legal discovery). Here is where you get to start finding holes in their reasoning… Figure out the math and the method used to flag your test (more about that below). Find out if they got a proctor to talk (and presumably what was alleged). Figure out if your physical testbook was examined. This should include the basis of their findings, so if it is just that your test was statistically flagged as similar to someone else’s, this is where you start to poke holes.
(vi) You should respond in writing to the Statement of Charges. Poke at every piece of evidence that they presented agaisnt you. If a proctor provided incriminating testimony, why didn’t s/he report a violation at the time? Was the proctor prompted by the investigator? Did the investigators check the work in your testbook to see how your answers were derived? How about the person with the similar responses? Why not? Isn’t that important evidence? Was the other test-taker interviewed? Why not? Has his testbook been reviewed? Which answers are considered similar? How far away was he from your desk? Why doesn’t the investigator know this? Did they bother to ask these simple questions? No? Why not? Is the case perhaps that the questions were asked, but the answers didn’t fit the allegations so they weren’t recorded? No? What safeguards were put in place to prevent that kind of bias? How were they enforced? Has the investigator ever been subject to violation of these safeguards? Have any investigators been? If not, are they really effective safeguards?
(vii) I did want to say one thing about the math. As you know from your Quantitative Methods studies, a similarity analysis is similar to a statistical test. They will throw all the tests into a data mining algorithm to figure out the significance of similarity between tests and will send out letters to recipients above a certain threshold (e.g., anyone with less than a .1% chance of similarlities appearing randomly). Take that number and apply the number of test-takers. For example, if there were 100,000 test-takers where no one has cheated, this method would result in 100 totally innocent false positives. (e.g., they are cherry-picking results and using the inherent statistical bias against their candidates). Again this is totally predictable due to faults in their methods. Which is to say, whatever their method, figure it out and challenge it. Don’t be intimidated by their math; as you should know, there are always statistical and operational errors to go after.
(viii) Go get a lawyer. CFAI shouldn’t be pulling this crap and getting smacked down once in a while may get them to reconsider sending out garbage like this.
Hope this helps.