If there was one element of statistical literacy that you could magically implant in every head, what would it be?

The idea of ALL beliefs being probabilities on a continuum, not just belief vs disbelief.

I think a lot about signal detection theory, and I think that's still the best I can come up with for this question. There are false positives, there are false negatives, they are both important to keep in mind, the cost of reducing one is an increase in the other, humans and human systems will always have both.

So, for example, even the most over-generous public welfare system will have deserving people off the dole and even the most stingy system will have undeserving recipients (by whatever definition), so the question (for a welfare system, say) isn't how do we prevent abuse, but how many abusers are we willing to tolerate for every 100 deserving recipients we reject? Also useful in lots of medical discussions, legal discussions, pop science discussions, etc.

The very basics of probability. I'm talking to the level of "there is about a 1 in 6 chance of a reasonably fair dice coming up 3 on a single roll"

I remember a friend telling me about a game some of his classmates played which was basically about calling high/low on the next card dealt.

He'd made a modest and steady income simply calling based on whether it was greater or less than 7 for the first few cards and he was known as being "lucky". They honestly couldn't comprehend something as simple as that.

That the statement "X causes Y" is almost meaningless without knowing how much.

Bread gives you cancer? Really? OH MY GOD! (small print, only 1 in a [huge number] chance)

But most people seem to only have 3 levels of belief about things.

"X does"," X does not", "X maybe does" and round them to 1,0 and 0.5 respectively.

You'll find yourself having conversations with these people along the lines of

Nutter:"You shouldn't let children do that! it causes cancer!"

You:"there's less than one in a million chance assuming they do this every day of their lives"

Nutter:"SEE! IT CAUSES CANCER! I KNEW IT! YOU MONSTER "

Most people are depressingly thick.

The Law of Truly Large Numbers. And that 1 in a million experiences are actually super common in a world with 7B+ people. I have a background in the sort of Christianity that emphasizes the reality of miracles and apparently unexplained phenomena, so this would likely help sooth that annoyance.

Noise happens. Even if X is predictive of Y, it's rarely perfectly predictive.

For instance, suppose that 1000 students take a math test, then take a different math test that covers the same material with different problems. It is highly likely that their rankings on the two tests will be strongly correlated. It is highly unlikely that their rankings on the two tests will be exactly the same.

And it is quite possible that a few students will do vastly better on one test than the other, due to things that have nothing particularly to do with their mathematical ability. If you give a math test to a sufficiently large student population, then some student's boyfriend will have gotten hit by a car on the morning of the math test. That will probably mess with their scores.

The desire to know error estimates and confidence levels around assertions and figures, or better yet, probability mass curves. And a default attitude of skepticism towards assertions and figures when they are not provided.

That when you've already picked someone/something out from the general population based on a particular property you cannot then use the same criteria to come to conclusions.

If you use a DNA matching technique with a 1 in a million chance of a false positive to pick your suspect out of a large database of people you cannot then use that "1 in a million chance" as part of the evidence against them. Yet courts absolutely would. (doing it the other way round, selecting one person then using the test is perfectly reasonable)

95% of all statistics are made up. It's very easy to make up data or confuse people with bad statistical treatment, but most science reporters / news media don't bother, they just honestly misunderstand the source data instead. If you can't check the statistical technique in detail yourself, and you don't very highly trust the source to do so (hint: news media are almost never trustworthy), you should ignore any statistical claims as being basically uncorrelated with reality.

This may not be strictly statistical, but I would choose the idea that in order to make any meaningful statement with data, you always have to have something to compare it to.

Like someone will always come in some political thread and say , "X will increase/decrease Y by Z%.) And my first thought in response is always, "Is that a lot?"

For a recent example I saw, someone showed a graph of Japanese student suicides as a function of day of the year. There were pretty high spikes (about double the baseline value) on the days corresponding to the first day of each school semester. The poster was attributing this to Japanese school bullying and other problems with Japan's school system.

My first thought was, "wait. Show me that graph for other countries. For the world, if such data has been reliably gathered." If it looks the same, it's not a uniquely Japanese problem. What if it's worse in other countries, even?

Yeah, I'd really like to see people stop using information where it doesn't mean anything in isolation. A lot of people think that controls in science exist to make sure that the effects you see aren't spurious or adventitious. It's not like that's wrong, but it's deeper and even more fundamental than that.

I'm a scientist, so let me give you an example from my research (grossly simiplified and generalized for brevity).

Substance A was designed such that it manifests an as-of-yet unexplored type of structural situation. We then carried out a reaction on substance A to see what some of the effects of this situation are. Something happened.

So, if we were to leave it at that, what would we have learned? Nothing. We need substance B, which does not have that siutation going on but is otherwise as similar to A as we can make it, to see what IT does, to see if it does anything different than A. See, we need to do the experiments on both B and A not to see whether the results of A are 'real'. We need to do it to see what the results even ARE in the first place.

I'd give people the ability to do multiple regressions in their head. Because I want to be able to do multiple regression in my head.

All probabilities are Bayesian, i.e., conditioned on some information I.

I would explain about blocking, how people can be matched up by profession, socio-economic status, smoker or non-smoker, and various other traits, to make comparisons where those factors are assumed to be equal.

Generalized method of moments because "implanting" it in every head would require greatly increasing the intelligence of most of mankind.

I'd like to see people have a clue what a probability actually is. I'm tired of hearing how the weather forecast was "wrong".

Wait a sec.. didn't we have a thread like this some time ago?