They are not randomized, controlled studies that can show causality or show magnitude of effect by controlling for inherent bias.
Nobody has claimed that they are.
Once again, retrospective, uncontrolled cohort assembled from anecdotal events is one of the lowest levels of scientific investigation. It can generate but not prove a hypothesis.
That's only true if proving the hypothesis involves precisely quantifying the probabilities of the various outcomes, among other things.
They can certainly prove some hypotheses, it just depends on what the hypothesis is, how precisely the outcomes must be quantified to prove the hypothesis, the uncertainty in the predicted outcome, the magnitude of the difference of the predicted outcome probabilities, etc.
In this case, the difference in the various outcome probabilities is significant enough that there's no real need for precise quanitification. In addition, multiple surveys have been conducted and they all agree, not only in terms of reasonable agreement of the various quantifications but also in terms of the overall conclusions.
Taking these studies to a higher level in my opinion is not justified.
Fortunately, it's not necessary to rely on opinion to determine the validity of the surveys. While they certainly do not precisely predict the probability of success of the various tactics, they certainly do provide a accurate insight into which tactics were superior in the sample set.
Even with the uncertainty inherent in surveys like this one, there's no real doubt about the overall conclusion given the wide divide in effectiveness between the two tactics.
First of all, the surveys in question contain incidents involving pepper spray failures. No one is suggesting that pepper spray never fails, only that it fails less often than other tactics.
Second, your initial claim was that the surveys were invalid because of numerous unreported pepper spray failures. You're proving that pepper spray failures are actually very commonly reported which doesn't help your position at all.
Third, if you really believe that surveys involving "retrospective, uncontrolled and anecdotal studies" can't ever prove anything then what could you possibly hope to achieve by providing the results of your own informal survey involving retrospective, uncontrolled and anecdotal incidents?
...bear did not stop UNTIL the 3rd attempt to deter it?...The first two attempts are failures.
So if a person shoots a bear 5 times and it only stops after the fifth shot we should count that as 4 failed attemps to deter and one success? That's ridiculous. If a tactic is used to successfully prevent injury in a bear attack, it's successful even if multiple shots or multiple sprays are required. The overall outcome (injured/uninjured defender) determines the success of the encounter, not how many sprays or shots are required to accomplish it.
Unfortunately, pepper spray now has a true cultish following and rational discussion is hard to accomplish on the pepper spray vs gun data.
In an earlier post, I provided a recipe that would provide a rational basis for calling the survey results into question (assuming the existence of the necessary data to do so). I would be very interested to see anyone take that approach or provide the data required to get the ball rolling.
Your position would be much stronger if you could provide data to support it, or even if you tried to make a reasonable case for its existence instead of basing your position on allegations that surveys can never prove anything and the implication that those who disagree with your opinion are cultish and irrational.