by "fail to reject the null hypothesis that there is no audible difference" do you mean that most blind tests are flawed? sorry I'm not english native and got kinda confused
Statistics reasoning and clear English sometimes don’t go together. I’ve found at ASR one has to be careful with one’s claims to avoid being jumped on. So…
Statistics from trials aren’t considered formal proof of anything. We can only *reject* a hypothesis, typically a hypothesis of no relationship (hence “null”) between two variables. In this case, the null hypothesis is “There is no audible distinction between cables (electronics, etc.)”. If someone gets a statistically significant result distinguishing (blind) between cables, for instance, that is a result that rejects the null hypothesis, not *proof* that they can hear a difference. But as we do many experiments and fail to reject the null hypothesis, we become more comfortable with the null hypothesis. Or, if we do many (blind) trials and repeatedly reject the null hypothesis, we become comfortable that there may, in fact, be a relationship between the cable and the audible result.
With medicine, for instance, the null hypothesis would be that the medication under testing makes no significant difference from a placebo in double blind trials. We decide a medicine may work if trials reject that null hypothesis repeatedly, to a statistically significant level (typically only a 5% chance that the result was random).
If expensive cables and electronics were medication for an audibly better listening experience, they would not be approved under accepted methodologies. They would be in the health food aisle with the homeopathic remedies. And yet, there are a few people here who say our belief in the null hypothesis is “flat earth” thinking. quite something.
That is the laborious, sometimes double negative, nature of repeated testing.
I’m sorry if this is pedantic. I can’t imagine reading statistical trials in either of my foreign languages.