Slight belated self-correction - you’re explicitly wrong about what Occam’s Razor says, and I disagree with you on that point.
Don’t all results come by seeming ‘coincidence’? If you flip 10 coins most of your results will be a lot of 4,5,6 heads up/down, with fewer 3,2,1,0 heads or tails combos, so although you might not see very many combos with 1 heads and nine tails or all heads, having one over thousands of tries would be expected. However if you had many trials that had bizarre outcomes (10H, 9H, 9H, 10H), they arrive by the same coincidence as any other results, but may call your results into question if your hypothesis is “there is an equal chance of heads vs tails.”
It’s easy to do with a coin, we know that a fair coin should be totally random and have 1:2 probability over large numbers.
But again, versus what golden standard? This was your assertion here:
What is meant by coincidence? If I read twenty articles each studying the effects of a certain fruit or veggie on overall health(null hypothesis-eating x every day makes you healthier{defined equally across all studies}), and half accept the null hypothesis with ‘95% confidence’ and half reject it with the same confidence you can’t apply coincidence to any of the results over any others. Does coincidence mean that a healthy fruit just assigned to a random group of sick losers and it’s effect wasn’t noticed? Maybe. Or was a non-healthy fruit given to a random selection of people that were becoming more healthy anyways and wasn’t as useful as shown in the study?
The point is that to claim with ‘95% confidence’ means that there was a substantial change in the average level of the tested group when compared to the control group. Could it have just been a random occurrence? Sure, but you wouldn’t be able to sample 4 people (3 women and 1 Man) and make the claim that with ‘95% confidence the population is 3/4 female’. To be able to claim that you have that level of confidence in your results implies that your sample size was sufficiently large enough to weed out any potential random sampling goofs that do happen.
I don’t “trust authorities”.
I trust the scientific method, properly applied, to arrive at correct conclusions over time and expect that mistakes will be overcome, given that science has built-in self-correcting mechanisms and is continually working to improve itself and expose weaknesses and conflicts of interest.
I do not trust small case series and poorly designed single studies that are interpreted to provide sweeping conclusions about scientific/medical matters.
I am highly skeptical of anecdotes and testimonials offered in lieu of good evidence.
I am prone to outright dismiss claims founded heavily or solely on the proposition that vast segments of our medical/scientific community are on the take/evil/out to deceive us. To paraphrase Pogo, the “authorities” is us. They get sick and die, and their friends/relatives/loved ones get sick and die too. They share the same concerns and fears we all have.
I’m not sure it’s worse now than it used to be, but we are definitely living in a time when a significant portion of the population listens to pseudo-authorities who display the arrogance of ignorance (Jenny McCarthy the antivaxer is a case in point, but I also include the various MDs and scientists who pride themselves on being “mavericks” but display fundamental ignorance either about their fields or unrelated fields about which they pretend to be knowledgeable).
Currently there is a widespread Internet ad proclaiming some wonder method for whitening teeth, dreamed up by a “mom”. Why in hell would anyone in their right mind be interested in trying this? Wouldn’t you at least want a method developed by a dentist, or better yet a treatment devised and tested by qualified researchers in dental science?