We need to know what IQ level is necessary to grasp which statistical ideas.

I haven't used calculus since I left the university. The geometry I've used is very basic. I've used algebra maybe a few dozen times - and I work in a supposedly technical profession (software engineer). But I use basic statistics all the time in my day-to-day decisionmaking, not to mention my understanding of "important" issues, such as the casualty rate in Iraq, or the poverty rate in Africa. At the level which I use it, it is not more difficult than mandatory high-school math - and it's much more important.

But the raison d'etre of the intellectual discussion is basically signaling and cuing; in other words, social display

I agree that statistically sophisticated reasoning introduces a "chilling effect" into casual intellectual conversation. This is the essential point. But it simplifies too much to say that this is because the purpose of intellectual conversation is social display.

For one thing, most participants don't think that's its purpose. They don't know enough about statistics to realize that there exists a higher standard of conversation which they are failing to meet. So they are doing their best with the tools they have, not compromising their conversation for the sake of display.

And if we suppose that social display is a subconscious motive, then it seems just as likely that it is also the subconscious motive for statistically sophisticated argumentation within those social circles that do have some mathematical culture. So social display, as such, need not corrupt conversation's truth-discovery properties.

Instead, I would argue the fundamental problem is that conversation must be amusing. It needs to have certain entertainment properties. Those properties are spoiled by statistical argument, just as they are spoiled by arguments that require masses of evidence or diagrams (unwieldy to manage while you're holding a cocktail), by arguments that involve very long chains of reasoning (exhausting, compared to the easy surprise of an apercus), or by arguments that appeal to the authority of one of the interlocutors (possibly valid, but certainly rude to everyone else).

The systemic problem here is that many people educated only in the humanities are unaware of the difference between converation-as-social-entertainment and conversation-as-truth-discovery-procedure. But this is not too surprising. The humanities have their origin as a curriculum in rhetoric, as a training in persuading others. And as long as men live in society, persuading other men will usually be more valuable than discerning the objective truth.

a "chilling effect" indeed: once I was asked "Must you relentlessly intellectualise everything?" My crime was to have asked for evidence.

Linking it to "social display" is right on. While talking about more scholarly subjects may often seem to be on a higher level - I think often it serves the same purpose as talking about LeBron James wearing a Yankees Hat or whether or not Journeyman is Quantum Leap 2.0. All usually are good indicators not only of effectiveness of forming an argument, being concise yet complete, and listening skills.