But imagine that you are the first researcher ever who has researched the jelly beans. And you only did one experiment. And it happened to succeed. Where is the selection here?
That's a different case -- you have no selection bias here, but your conclusions are still uncertain -- if you pick p=0.05 as your threshold, you're clearly accepting that there is a 5% chance of a Type I error: the green jelly beans did nothing, but the noise happened to be such that you interpreted it as conclusive evidence in favor of your hypothesis.
But that all is fine -- the readers of scientific papers are expected to understand that results significant to p=0.05 will be wrong around 5% of the times, more or less (not exactly because the usual test measures P(D|H), the probability of the observed data given the (null) hypothesis while you really want P(H|D), the probability of the hypothesis given the data).
base rate neglect means ignoring the fact that "if you take a random thing, the probability that this specific thing causes acne is very low"
People rarely take entirely random things and test them for causal connection to acne. Notice how you had to do a great deal of handwaving in establishing your prior (aka the base rate).
As an exercise, try to be specific. For example, let's say I want to check if the tincture made from the bark of a certain tree helps with acne. How would I go about calculating my base rate / prior? Can you walk me through an estimation which will end with a specific number?
the readers of scientific papers are expected to understand that results significant to p=0.05 will be wrong around 5% of the times, more or less
And this is the base rate neglect. It's not "results significant to p=0.05 will be wrong about 5% of time". It's "wrong results will be significant to p=0.05 about 5% of time". And most people will confuse these two things.
It's like when people confuse "A => B" with "B => A", only this time it is "A => B (p=0.05)" with "B => A (p=0.05)". It...
A few notes about the site mechanics
A few notes about the community
If English is not your first language, don't let that make you afraid to post or comment. You can get English help on Discussion- or Main-level posts by sending a PM to one of the following users (use the "send message" link on the upper right of their user page). Either put the text of the post in the PM, or just say that you'd like English help and you'll get a response with an email address.
* Normal_Anomaly
* Randaly
* shokwave
* Barry Cotter
A note for theists: you will find the Less Wrong community to be predominantly atheist, though not completely so, and most of us are genuinely respectful of religious people who keep the usual community norms. It's worth saying that we might think religion is off-topic in some places where you think it's on-topic, so be thoughtful about where and how you start explicitly talking about it; some of us are happy to talk about religion, some of us aren't interested. Bear in mind that many of us really, truly have given full consideration to theistic claims and found them to be false, so starting with the most common arguments is pretty likely just to annoy people. Anyhow, it's absolutely OK to mention that you're religious in your welcome post and to invite a discussion there.
A list of some posts that are pretty awesome
I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
More suggestions are welcome! Or just check out the top-rated posts from the history of Less Wrong. Most posts at +50 or more are well worth your time.
Welcome to Less Wrong, and we look forward to hearing from you throughout the site!
Note from orthonormal: MBlume and other contributors wrote the original version of this welcome post, and I've edited it a fair bit. If there's anything I should add or update on this post (especially broken links), please send me a private message—I may not notice a comment on the post. Finally, once this gets past 500 comments, anyone is welcome to copy and edit this intro to start the next welcome thread.