Numerosity Estimation
Which side has more?
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What is the Numerosity Estimation?
Numerosity Estimation tasks ask people to judge which of two sets contains more items, usually too quickly to count. They are the standard way researchers study the approximate number system, the intuitive sense of quantity that lets us see that one group is larger than another at a glance. This ability has been found in human infants and in many animal species.
A key finding is that these comparisons follow Weber's law: the closer the ratio between two quantities is to one, the harder and slower the judgement becomes. Researchers also control for dot size and total area, so that the answer depends on number rather than how much colour is on the screen. The Neuroptimize game uses the same ideas in a fast left-or-right choice.
How to play the Numerosity Estimation
- Two panels appear side by side, each filled with dots. A prompt at the top tells you what to look for, such as "More dots?", and you tap the side that has more.
- On a keyboard you can use the left and right arrow keys (or A and D) instead of tapping.
- A correct answer moves straight to the next pair. A wrong answer is highlighted in red and the correct side is shown before play continues. You have 45 seconds in total.
- As the level rises, the two quantities get closer together and the number of dots increases. From level 8 the dots come in mixed sizes, and from level 16 the side with fewer dots can have as much colour or more, so you must judge number, not area.
- From level 12 some rounds show two numbers instead, with the prompt "Bigger number?". The font sizes are often mismatched, so the larger-looking number is not always the bigger one. From level 22 these become three-digit numbers.
- From level 18 a third prompt, "More colour?", appears. Here you judge the total coloured area rather than the count, and the side with more area usually has fewer shapes.
Strategies and tips
Read the prompt every round
From level 12 the question can change from one pair to the next. A quick glance at the prompt before looking at the panels prevents answering the wrong question, especially when switching between "More dots?" and "More colour?".
Judge the count, not the ink
At higher levels the side with fewer dots is often given bigger dots so that it looks fuller. Focus on how many separate items there are and treat the overall amount of colour as a trap.
Trust your first impression
The dots are not meant to be counted, and trying to count wastes time on a 45-second clock. Take in both panels as a whole and go with the side that feels more numerous.
Compare digits, not font size
In number rounds the bigger value is often printed smaller. Read the digits from left to right, and with three-digit numbers remember that the first digit is usually the same, so the decision rests on the second or third digit.
Flip your rule for colour rounds
In "More colour?" rounds the answer is the side with more total area, which is usually the side with fewer, larger shapes. Look at the size of the shapes rather than how many there are.
The science behind the Numerosity Estimation
The approximate number system is the ability to estimate and compare quantities without counting. It is present in human infants and in many animal species. Comparisons become harder as the ratio between the two quantities approaches one, in line with Weber's law.
Frequently asked questions
What is the approximate number system?
The approximate number system is the ability to estimate and compare quantities without counting. It lets you tell at a glance that one group is larger than another. Researchers study it with quick dot-comparison tasks like this one.
Why are some comparisons so much harder than others?
Comparisons get harder as the ratio between the two quantities approaches one, in line with Weber's law. Telling 10 dots from 20 is easy, while telling 20 from 22 is much harder, even though the difference is the same. In the Neuroptimize game the ratio gets closer as the level rises.
Is numerosity estimation the same as subitizing?
No. Subitizing is the fast, accurate recognition of very small numbers of items, usually up to about four, without counting. Numerosity estimation covers larger sets, where judgements are approximate and depend on the ratio between the two quantities.
Can I play Numerosity Estimation with a keyboard?
Yes. On a computer you can press the left or right arrow key, or A and D, to choose a side. Tapping or clicking the panels works too.