We need pedagogical research on τ (tau) versus π (pi)!

After reading a bit of a wikipedia talk page (which I may or may not continue to read), I have a thought:

I'd like to see a relatively-large-scale study done comparing the pedagogical success of "π" (pi) versus "τ" (tau) with students learning the relevant mathematics (trigonometry; perhaps other things?) for the first time.

Because it seems to me there's a hypothesis that's been proposed: that τ is a better pedagogical tool for teaching the relevant trigonometric concepts than π is.  There's a bit of anecdotal evidence for this, but anecdotal evidence is at the very bottom of the hierarchy of evidence, so it seems to me we can do better.

So I'd like to see us go up the hierarchy at least as far as a cohort study (the middle of the hierarchy as listed), with a cohort divided into groups that learn π, and groups that learn τ, and see how they do, both initially and over a more extended period of time, in their skills in the various mathematical concepts.

I can immediately think of 4 main possible outcomes (perhaps there are more?):

1. There is strong support for the hypothesis within the cohort;
2. There is strong evidence _against_ the hypothesis within the cohort;
3. There is strong evidence that it makes little difference; or
4. The evidence is not strong, in any particular direction.

My (admittedly biased) hope and estimation is that #1 would be the outcome, but I'd honestly be happy to learn of #2 or #3, provided I thought the study was well-designed and well-executed.

For any of the first 3 outcomes, though, it strikes me as something that could settle the debate a bit.  And for the 4th outcome, hopefully that would also come with insights into how to improve future research in the area.

Now, I'm not a researcher, and I'm not particularly learned in pedagogy, especially as relates to childhood mathematics instruction, so... I don't feel prepared to do much with this.  But perhaps I could help facilitate it some way?  If someone with more relevant skills wants to collaborate with me, I'd be happy to do some work towards putting together a crowd funding campaign, or some such thing.

Anyway, I hope you all had a nice half-circumference / radius day.  Because pi is (still) wrong, and, while I'm failing to find the source for this at the moment (hopefully I will at some point, and can update this post), so is the notion that π became "3.14..." by being the ratio of circumference divided by the diameter.  My understanding (based on the source I'm failing to find) is that it was actually defined as the ratio of the half-circumference divided by the radius.  So, even Vi Hart's above-linked video is a little bit wrong (though mostly it's just a wonderful work of rant-art).  C/2r isn't C/D, it's (C/2)/r... hopefully I'll find the reference to prove it.  (Not that it's not also C/D, just that that's not how π was defined in the article that popularized π as a symbol referring to that particular constant.)

Let's take a new τurn, shall we?