Mental Rotation Accuracy by Angle

Mental rotation asks a two-answer question. The right-hand figure is the left one turned, or it is the mirror image of it, and a coin gets half of them right.

That puts a floor under any accuracy score at fifty per cent. There is no matching ceiling far above it, because nothing on the screen is on a clock.

Somebody who cannot yet see the answer keeps looking rather than guesses. So nearly everybody finishes near the top of the scale, whatever the angle was.

Shepard and Metzler reported one error figure for their whole study rather than a column of them. Their eight participants were wrong on about three answers in a hundred.

A measure squeezed between a floor of fifty and a ceiling near ninety-seven cannot separate anybody. So the paper made its case with the times, and so does this page.

Two numbers here come out of the paper. The first is the time an upright pair took, which was about one second. The second is the rate at which the answers slowed, which was about sixty degrees a second.

Every row between those is the straight line the two constants define. At sixty degrees a second, a quarter turn adds a second and a half, and a half turn adds three.

That is the honest description of the table. It is not five measured cell means, and the paper does not publish it as one. It is what the published line says at five angles, worked out so you can check it.

CognitiveDrill has published no figure of its own for this task, and no cell goes up until it holds at least 1,000 anonymous results. Results stay in your browser, so that day may be a long way off.

One more caution about the level of the line. Those times were collected in a laboratory with a hand switch. A browser adds display and input lag on top, so the whole line sits a little higher on a screen than it did on paper.

The slope is the part of this result that lasted. It says the answers slowed by a fixed amount for each extra degree, with no bumps and no shortcuts.

That evenness is hard to explain by comparing features. Checking whether two arms match should get harder in fits and starts, not in a straight line.

A steady turn does produce a straight line. Turning a shape twice as far takes twice as long, in the head as on a table, and that is what the data looked like.

The same experiment ran pairs turned in the flat of the picture and pairs tipped away into depth. Both gave a line, and the depth pairs gave a slightly slower one.

It is worth being clear about what the rate is not. Sixty degrees a second is a group average from eight practised people on one set of block figures. It is not a constant of the human mind.

Accuracy comes back to life the moment somebody puts a clock on the task. Then a hard pair cannot be paid for with more seconds, so it gets paid for with a wrong answer instead.

The group test built from this task in 1978 works exactly that way. It is a paper test with a short time limit, and marks on it land far below the ceiling a self-paced run produces.

So a quoted mental rotation accuracy means very little on its own. The same person scores near a hundred per cent with no clock and much lower against a three-minute limit.

Ask two things of any accuracy figure before comparing yourself to it. How long did people get, and how many answers were there to choose between.

• Self-paced, two answers: nearly everybody scores in the high eighties or better, and the angle shows up in the time.
• Timed, two answers: the angle shows up in both, and the split between them depends on how each person traded one for the other.
• Timed, five answers on paper: guessing pays, so marks are usually corrected for it and are not comparable with a screen score.

A shallow line is not proof of fast turning. Because both figures are drawings of the same object, one arm can sometimes be matched against another without turning anything.

People do that in a laboratory too. It shows up as a flat line with high accuracy, which is worth knowing about yourself rather than treating as a record.

Practice moves the slope, and moves it quickly. Most of the first few runs are spent learning what the figures look like rather than getting better at rotation.

None of this reaches beyond the task. A quick line here is not a sense of direction, and it is not a claim about anybody's brain. The evidence on how far such gains travel is in what the research on brain training says.

This page also holds no cohort, so it cannot answer the question people ask most about mental rotation. It has nothing to say about how any group scores, because it counted nobody.

The mental rotation test sets the angle itself and fits a line through your correct answers. Its headline is the slope, converted into the extra seconds a quarter turn costs you.

Compare that slope with your own earlier runs on the same machine first. A gradient from twenty pairs is a rough one, and two rough gradients from the same person differ more than most people expect.

Your accuracy is on the card as well, and it is there as a check rather than as a score. If it drops under about eight in ten, you were guessing, and the line through those trials means less.

Times on a screen also carry the machine they were made on. The figures in how processing speed changes with age have to live with exactly the same problem.