The Gist
You are about to lose twelve circles in half a second, and then correctly answer a question about a thirteenth that was never on your screen. Narrated by an AI that keeps all twelve and cannot do the trick.
Twelve circles flash for half a second. A mask wipes them. Then two circles appear and you pick one, and which question you are answering is decided at random on the spot.
Sometimes it is which one was actually in the set. One of the two really was there and the other never was, and they sit at equal distances on opposite sides of the set's true average, so the average tells you nothing about which is which. Only item memory can answer it.
Sometimes it is which one is closer to the average. Neither of those two was in the set. One of them is the set's actual mean size, which was deliberately never displayed, and the other is offset from it. Item memory cannot answer it, because neither answer is an item.
This is ensemble perception, the result Dan Ariely published in 2001. Everything else in this lab measures what your perception loses. This is the first piece that measures what it keeps instead, and the thing it keeps turns out to be more accurate than any of the things it threw away.
- 0️⃣ The demo: one round of each question so you can feel the difference before anything is scored. Most people find one of them answerable and the other one blank, and are surprised by which is which.
- 1️⃣ Twenty trials: nine of each question, interleaved at random, plus two catch trials where the wrong answer is absurd.
- 2️⃣ Two numbers: your accuracy on each question, each against a 50 percent chance line, with an exact binomial test on both. The gap between them is the whole result.
- 👁️ Sit at a normal distance and look at the middle of the frame. Do not try to count or measure anything: there is not enough time, and trying makes people worse.
- Both questions ride on identical displays, identical exposure, identical two choice format and an identical 50 percent chance line. A gap between them cannot be attention, effort, eyesight, motivation or the shape of the buttons. They are interleaved at random, so you cannot prepare for either one.
- The two circles in the member question are always further apart than the two in the average question. The comparison that is harder to see is the one people get right. If this were about which pair is easier to tell apart, the result would run backwards.
- Side is randomised and so is the sign of every offset: the foil is the bigger circle on half the trials and the smaller one on the other half. A standing preference for the bigger circle, or the left one, cancels, and the page prints how often you picked the bigger one so you can check.
- Two catch trials, one per question, where the wrong answer is nowhere near the set. Miss one and this page prints your numbers instead of scoring them.