Number Sense Test

What the test asks

Two skills that need no counting. Can you tell which of two sets is larger when there is no time to count? And how many things can you take in at a glance, before counting has to start? Task A measures the first and gives your Weber fraction w; task B measures the second and gives your subitizing range. Either can be run alone, and each is saved as soon as it ends.

Task A: which colour has more

• A cross for 500 ms, then an empty field for 250 ms.
• Blue and yellow dots, mixed, for 200 ms: 12 frames at 60 Hz.
• The field empties and you answer Blue or Yellow, with no time limit. You can answer while the dots are still there.

The two counts are in one of five ratios, 1:2, 3:4, 5:6, 7:8 or 9:10, with 5 to 20 dots per colour. In half of the trials both colours have the same mean dot size, so the colour with more dots also covers more of the field. In the other half both cover the same total area, so the colour with more dots has smaller dots. Each dot differs from the average of its colour by up to 35%. Blue and yellow are used because the common red-green types of colour blindness do not confuse them.

Short is 160 trials and Long is 400, split equally among ratios and size rules, with a break every 80 or 100 trials. Your first run starts with 10 easy practice trials that tell you whether you were right; they do not count.

The design follows Halberda, Mazzocco and Feigenson (2008), who tested 14-year-olds with four ratios and 5 to 16 dots per colour, and the web version of Halberda et al. (2012) with 5 to 20. The ratio 9:10 is added here, so that a sharp observer still makes mistakes to measure.

How w is calculated

The model of Halberda et al. (2008) treats each set as a noisy inner estimate whose spread grows with the number: w = 0.2 means that 10 dots feel like anything around 8 to 12. A smaller w is a finer number sense. Comparing two such estimates gives the chance of a right answer:

Φ is the standard normal distribution; n₁ and n₂ are the two counts. With 10 against 20 dots and w = 0.2 the second part is Φ(2.236) = 98.73%. Only the ratio matters, so all pairs with one ratio share one point on the curve.

The original model has only w. This page adds a lapse rate l from 0 to 10%: the share of trials where you blinked or looked away and could only guess. Without it those trials are blamed on w: in a simulation with 4% lapses and w = 0.2 at 400 trials, a model without the lapse rate overstated w by about 12%.

The page finds the w and l under which your answers were most probable. The 95% interval holds every w under which they stay nearly as probable: twice the difference in log likelihood is below 3.84, with l refitted for each w. w is searched from 0.02 to 2; a result at either end means the test did not settle, and the page says so.

The effect of area is w (equal area) − w (equal size), with its own interval from the likelihood. It comes from one fit with a shared lapse rate, so it can differ a little from the two separate values on screen. If you lean on how much of the field a colour covers, the equal-area trials are harder and the difference is positive. When the interval includes 0, the run shows no clear effect.

How far to trust w

The page's calculation was run on simulated people (November 2026, 2,000 runs per case). They answer exactly by the model, so tiredness or a bad day are not in these figures:

• w = 0.2, no lapses, 400 trials: median estimate 0.192, and the 95% interval held the true value in 95.4% of runs.
• The interval is typically 45% of w wide at 400 trials and 67% at 160.
• Neither length reliably tells w = 0.15 from w = 0.25. For one run of each, the two 95% intervals overlapped in 91% of pairs at 160 trials and in 61% at 400.

Real people add more noise. Halberda et al. (2012) report a split-half reliability of w of 0.72 for 300 trials in 10,548 people and 0.56 for 200 trials in another 3,006.

Task B: how many dots

• The same cross and empty field.
• 1 to 9 dark dots at random places for 350 ms, then a patterned mask for 100 ms that wipes out the after-image.
• You answer with a number as fast as you can without mistakes. The time runs from the moment the dots appear.

There are 8 trials for each number, 72 in all, in about 4 minutes, plus 9 practice trials on your first run. The timing follows experiment 1 of Leibovich-Raveh et al. (2018): 1 to 9 pictures for 350 ms and a 100 ms mask, with spoken answers.

How the subitizing range is calculated

Small numbers are named almost at once and large ones take longer, with a bend between them. The method of Leibovich-Raveh et al. (2018) finds that bend in the mean time of your correct answers for each number:

The curve is an S rising from a to a + b, steepest at x₀. The range is where the tangent at that steepest point crosses the flat line through f(0), which comes before the steepest point. With x₀ = 4.5 and k = 2 it is 3.50. The chart shows both lines.

This page differs from the paper in two places, both because a run has only 8 trials per number. The paper rescales the times to run from 0 to 1 and fits only x₀ and k; in simulations with so few trials that pulled the range down by about 0.3, so here a and b are fitted too. The paper drops answers more than 2.5 standard deviations from the mean, which one slow answer among 8 can never reach, so here the limit is 2.5 robust standard deviations (from the median and the median absolute deviation).

For the 95% interval the page draws your answers for each number again at random with replacement 1,000 times, refits the curve and keeps the narrowest range that holds 95% of the results. On simulated people with a true range of 3.5 and noise of 20% of the mean time (November 2026), the median estimate was 3.54, the interval held the true value in 96.9% of 1,000 runs, and it was typically 1.7 wide.

What to look for

• In the first chart the points fall from the easy ratio on the right towards 50% on the left. Points far from the curve, like a low point at 1:2, are worth a second run.
• In the time chart look for the flat start and where it bends. If it rises evenly, the fit says little; the page warns you when the curve explains under 70% of the differences, the limit the paper uses.

Things to try

• Run task A twice in one day and compare the intervals. When they overlap, the difference may be chance.
• Judge only how much blue and yellow there is, then only how many dots, and compare the effect of area.

Comparing your result

History compares runs on the same input whose refresh rates are within 10% (or both below 50 Hz). The page gives no percentile: one run is too short for it, and the published figures come from other procedures. It only shows these next to your result:

• 64 children aged 14: group w = 0.265, individuals from 0.119 to 0.567, with 4 ratios and no lapse rate (Halberda et al., 2008).
• Halberda et al. (2012) find that w gets better until about age 30 and then worsens, with large differences at any age. In 10,548 people aged 11 to 85 it correlated with self-rated school maths at r = −0.19, which is small and predicts nothing about one person.
• Subitizing range: 3.38 for random arrangements (38 students, mean age 18), 4.73 for familiar patterns like dice, and 56% of people between 3 and 4 for random arrangements (Leibovich-Raveh et al., 2018; spoken answers, a fit on 1 to 8). In their experiment 3, with 204 trials, the split-half reliability was 0.69.

Limits

• Pressing a key takes longer than speaking, so your times are not the times in the paper. A fixed delay of the device moves the curve up and leaves the range as it is; an uneven delay does not.
• Brightness and size of the screen change the task. In the 2008 study a typical dot was about 1 degree of visual angle at 50 cm. Here the size follows the field: about that on a large monitor, smaller on a phone.
• A screen draws whole frames: 200 ms is 29 frames = 201 ms at 144 Hz and 15 frames at 75 Hz. Below 50 Hz, or with uneven frames, which remote desktop and power-saving modes often cause, the page offers Run anyway. Below 50 Hz it rounds down so that the flash never gets longer: 6 frames = 184 ms at 32.6 Hz. The run is marked less precise and kept apart in History.
• This is not a test for dyscalculia or a measure of maths ability.

Controls

• Keyboard: task A: F = blue, J = yellow. Task B: keys 1 to 9 on the top row (with a Slovak or other layout too, no Shift needed) or the number pad. Esc = pause; Enter or Space presses the focused button. Only the first key in a trial counts.
• Mouse and touch: the Blue and Yellow buttons, or the buttons 1 to 9. After a pause, break or result, buttons react only after 0.7 s, so a double press cannot skip a step.
• Settings: what to run, the length of task A and optional practice. They are locked during a run.
• Language: the small link at the end of History switches between English and Slovak.

FAQ

Should I try to count in task A?

You can't: 200 ms is too short for 20 dots. Go by your first impression and guess when you are not sure; near 9:10 the model expects a lot of guessing.

Sources

• Halberda J., Mazzocco M. M. M. & Feigenson L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455:665–668. doi:10.1038/nature07246
• Halberda J., Ly R., Wilmer J. B., Naiman D. Q. & Germine L. (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences 109(28):11116–11120. PMC3396479
• Leibovich-Raveh T., Lewis D. J., Al-Rubaiey Kadhim S. & Ansari D. (2018). A new method for calculating individual subitizing ranges. Journal of Numerical Cognition 4(2):429–447. doi:10.5964/jnc.v4i2.74