Estimate the Difference Game
Two groups, one flash. By how many does the first one win?
About How Much More?
How Much More? flashes two groups of small pictures next to each other, such as apples and lemons or fish and octopuses. The question names one of them and asks how many more of that kind there are than of the other. You slide to the difference, from 0 to 40.
Asking for a difference is harder than asking which group is bigger. You have to estimate both counts and subtract, or compare the two directly. The smaller group has between 8 and 44 items, and the bigger one exceeds it by between about 15 and 90 percent. The flash lasts 3.8 seconds on level 1 and 2.2 seconds on level 10.
How to play
- Read the question: it names the kind of item that has more.
- Look at the two groups while they are shown. Their order on the screen is random.
- Move the slider to the difference when the groups have disappeared.
- The note after your answer gives the real counts of both groups.
Two groups of items appear for a moment. Slide to how many more of the first kind there are than of the second kind.
How scoring works
The score depends on the distance between your answer and the real difference. You get 100 for an exact answer, and the score falls to 0 at a distance of 70 percent of the real difference on level 1 and 40 percent on level 10, with a minimum of 4. For a difference of 20 on level 10 an error of 4 still earns about 50 points.
The difference is always at least 2. The time to answer is 10 seconds after the flash. The slider runs from 0 to 40 on every level, so its range gives no hint of the answer.
What it trains
It trains comparing amounts and the subtraction of two estimates. This is how we judge whether one queue is much longer than another, how many more votes a candidate had, or how large the gap is between two bars in a chart.
The game also teaches that errors in the two estimates add up. A small error in each count can lead to a large relative error in the difference, which is a fact worth knowing when you read statistics.
Tips for a higher score
- Compare the groups by pairing them in your mind: match one apple with one lemon and see how many apples have no partner.
- Estimate the sizes of both groups in rows of five, and subtract the row counts.
- Use the shape. If one group fills a column more than the other, estimate how many columns of 5 or 10 the extra part is.
- Do not bother about perfect counts. An estimated difference within a few items is already a good result.
- Check which kind the question asks about. The group with more items can appear on the left or on the right.
The idea behind it
In numerical cognition research, comparing and combining approximate numbers is part of the normal operation of the approximate number system. Studies by Elizabeth Spelke and others show that even young children can add and subtract approximate amounts without symbols, long before formal teaching.
A statistical fact is behind the difficulty: when you subtract two noisy estimates, their errors do not cancel but add up in variance. A group of 40 estimated to within 10 percent and a group of 30 estimated to within 10 percent gives a difference of 10, with an uncertainty of about 5, which is as large as 50 percent of the answer.
Frequently asked questions
Why not ask which group is bigger?
That question is covered by Dot Compare. How Much More? asks for a quantity, which is more demanding.
Do the pictures matter?
No. They are different on every round for variety, but only the number of pictures counts.
Which games train a related skill?
Dot Compare compares two swarms, and Fair Share reads shares of a total.
Related games
Free, no account. Your best scores are saved on your device.