All medicine started out as alternative medicine.
Those that have been proved to work were given a new name: we call them medicine.
Those that either weren't proved to work, or were proved to not work moved into the shadows of superstition and became "alternative medicine".
The statistics work like this- if someone wants to test something- they grab a bunch of people to try it on.
1/3 of the bunch are given the medicine, 1/3 are given something that looks and feels like the medicine but does absolutely nothing (this is caused the placaebo) while the third "control" group are given the normal medicine (that's also indistingishable from the new medicine).
Crucially- the people who are testing the treatment don't know what they're having, they're picked randomly and, ideally whoever's handing out the treatment don't know what they're giving either.
The larger the groups; the more valid the results (sometimes a flipped coin comes up heads 10 times in a row, but 100 times in a row is a lot less frequent)
If the treatment's better than the placaebo group and the control group, then that's good news for the new treatment!
But it's not the end- the test has to be reproducable, because that's how science works; other people will try to disprove the test results by scrutinising the way the tests were carried out and carrying out their own tests.