Processing Speed
Dot Comparison Task
Also called: approximate number system task, ANS acuity task, nonsymbolic number comparison, numerosity comparison, numerosity discrimination, Weber fraction task
Measure the approximate number sense: how precisely people judge which of two briefly shown dot clouds has more, without counting.
5-7 minTimed: desktop or laptop with a mouse or trackpad
Free to start: 10 free participants per account, then $0.99 per participant for academic research, or any yearly plan. Preview any test free after you sign up.
- Papers, 2021 to 2025
- 34
- Evidence grade
- D
- Registered clinical studies
- 0
What it measures
A measure of the approximate number system: how precisely people judge which of two groups of dots has more, without counting. Two clouds of 6 to 24 dots flash side by side for 750 ms, and participants press the key for the side that had more. The main score is the Weber fraction fitted to the answers at four fixed ratios; lower means finer judgments of number.
Constructs
- Approximate number system
- Numerical magnitude
- Quantity estimation
Research uses
- Math learning and dyscalculia research
- Numerical cognition research
- Development and aging research
How the paradigm works
The Dot Comparison Task measures the approximate number system: the sense of quantity that lets people tell which of two groups has more without counting. Its precision is described by the Weber fraction, the noise in a person's sense of number as a share of the number itself; the lower it is, the closer two numbers can be and still be told apart. Individual differences in it have been linked to mathematics achievement (Halberda, Mazzocco and Feigenson, 2008).
More about the paradigm
On each trial a cross shows between two empty circles for 500 ms, then a cloud of white dots appears in each circle for 750 ms, the display time Halberda and Feigenson (2008) used with adults. Participants then press F if the left circle had more dots and J if the right one had more, with no time limit. The two counts differ by one of four fixed ratios, 1:2, 3:4, 5:6 and 7:8, with 6 to 24 dots per circle. On half the trials the dots have the same mean size on both sides, so the larger number also covers more area; on the other half the total dot area is the same, so the larger number has smaller dots. Neither size nor area can stand in for number across the session. Each round has 48 trials, every pair of counts with the larger number on each side under each control; the standard session has 3 rounds (2 to 4), 144 trials in a seeded order, after 6 practice trials with feedback, about 6 minutes. Every display time and dot layout is fixed before the session. Displays switch on screen frames, the measured times are saved on every trial, and trials whose dots ran more than one frame off plan leave the score. Desktop and laptop only.
The main score is the Weber fraction, fitted by maximum likelihood to the answers at the four ratios with a guess rate, as in Halberda and Feigenson (2008); lower means finer judgments of number. Accuracy overall, at each ratio and under each control are also reported, with the size, area and spread of the dots on every trial. Inglis and Gilmore (2014) found plain accuracy more reliable than the Weber fraction from one session, so studies may prefer it. Scores support research and do not diagnose.
Scores
- Weber Fractionscore
- The spread of the sense of number as a share of the number, fitted with a guess rate by maximum likelihood to the answers at the four ratios (Halberda and Feigenson 2008, equation 1), searched from 0.02 to 2.
- Lower is better; finer judgments of number
- Weber Fraction at Lowest Valueflag
- 1 when the fit sits at 0.02, the bottom of its range: answers were right at nearly every ratio, so the score is an upper bound.
- 1 is noted for review
- Weber Fraction at Highest Valueflag
- 1 when the fit sits at 2, the top of its range: answers barely followed the number of dots.
- 1 is flagged for review
- Guess Rate%
- Fitted share of trials answered by guessing, from 0 to 0.2.
- Informational
- Accuracy%
- Share of scored trials answered with the side that had more dots.
- Higher is better
- Accuracy by Ratio%
- Share right at each ratio, keyed 1:2, 3:4, 5:6 and 7:8.
- Falls as the ratio nears 1
- Same-Size Accuracy%
- Share right when the dots had the same mean size on both sides, so the larger number also covered more area.
- Higher is better
- Same-Area Accuracy%
- Share right when the total dot area was the same on both sides, so the larger number had smaller dots.
- Higher is better
- Control Effect%
- Same-size accuracy minus same-area accuracy.
- Positive values mean answers leaned on the area or size of the dots
- Median Answer Timems
- Median time from the question to the answer.
- Informational; the answer has no time limit
- Anticipationscount
- Answers under 100 ms from the question, which are not scored.
- Lower is better
- Early Key Pressescount
- F or J pressed before the question appeared, which are not taken as answers.
- Informational
- Frame Intervalms
- Median time between screen frames during the trials.
- About 16.7 on a 60 Hz screen
- Refresh RateHz
- Screen refresh rate from the frame interval.
- Informational
- Displays on Time%
- Share of answered trials whose dots showed within one frame of 750 ms; only these are scored.
- Under 0.9 is flagged for review
- Completed Trialstrials
- Trials answered in the scored run.
- Fewer than planned is flagged for review
- Planned Trialstrials
- Trials the run set out to show.
- Informational
Use and evidence
34 papers from 2021 to 2025 name this task in their title or abstract, up 55% compared with 2016 to 2020. That ranks it 282 of 395 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 9 |
| 2024 | 2 |
| 2023 | 9 |
| 2022 | 9 |
| 2021 | 5 |
| 2020 | 4 |
| 2019 | 8 |
| 2018 | 5 |
| 2017 | 2 |
| 2016 | 3 |
| 2015 | 4 |
| 2014 | 1 |
| 2013 | 2 |
| 2012 | 2 |
| 2011 | 1 |
| 2010 | 0 |
| 2009 | 3 |
| 2008 | 1 |
| 2007 | 0 |
| 2006 | 0 |
| 2005 | 0 |
| 2004 | 0 |
| 2003 | 0 |
| 2002 | 0 |
| 2001 | 0 |
| 2000 | 0 |
Use grade D
30 to 99 papers from 2021 to 2025.
Evidence grade D
Little published measurement evidence found.
- Papers on test-retest reliability
- 0
- Papers on reliability or validity
- 1
- Registered clinical studies using it as an outcome
- 0
How the grades work
Use: A is 1,000 or more papers from 2021 to 2025, B 300 to 999, C 100 to 299, D 30 to 99 and E fewer than 30. Evidence: A means at least 25 papers report its test-retest reliability and at least 25 registered clinical studies use it as an outcome; B, at least 8 test-retest papers, and either 5 registered clinical studies or 150 reliability or validity papers; C, at least 2 test-retest papers, 30 reliability or validity papers or 3 registered clinical studies; D, little published measurement evidence found. The counts measure use. They include every paper that names the task in its title or abstract. Grades describe the published research on this task, not ConductCognition's version of it.
Source: ConductCognition test census 0.14.0, counted 31 October 2026 from OpenAlex and ClinicalTrials.gov.
Task design
The trial sequence as the test runs in ConductCognition.
- Display
- On a dark panel, two circles 120 px in radius: a cross between them for 500 ms, then a cloud of white dots in each for 750 ms, then the empty circles and the question.
- Answer
- F when the left side had more dots and J when the right side had more, with no time limit. Keys pressed while the dots show are counted and not taken as answers.
- Ratios
- 1:2, 3:4, 5:6 or 7:8, with 3 pairs of counts at each, from 6 to 24 dots per circle.
- Controls
- On half the trials the dots have the same mean size on both sides, so the larger number covers more area; on the other half the total dot area is the same, so the larger number has smaller dots. Each dot's diameter varies by up to 20% around its side's mean.
- Trials
- 3 rounds of 48 (standard; 2 to 4): 144 trials, every pair with the larger number on each side under each control once per round, in a seeded order.
- Practice
- 6 trials at 1:2 and 3:4, with pairs not in the test and feedback for 1,000 ms.
- Fixed times
- Every display time and dot layout is set before the session, and no answer changes it: there is no staircase.
- Score
- The Weber fraction, fitted by maximum likelihood with a guess rate to the answers at the four ratios. Trials whose dots ran more than one frame off plan, and answers under 100 ms, leave the score.
The dot arrays are drawn by our code, and each display's mean dot size, total area, convex hull and total circumference are saved, so studies can check how much these cues mattered. Accuracy is reported beside the Weber fraction; from one session it was the more reliable of the two in Inglis and Gilmore (2014).
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: dot_comparison_test from the scored run, F or J after the dots, with no time limit (chance 50%; the larger array is on each side in half the trials), graded from the saved counts. Below chance invalidates and not above chance is flagged; one key on 90% of answers invalidates when accuracy is not above chance. Answer times run from the question. Responses under 100 ms follow the timed-test rule. No fitted Weber fraction, a fit at the top of its range, a run short of its planned trials, or fewer than 90% of dot displays within one frame of plan is flagged for review.
Why these rules
Accuracy significantly below chance (one-sided exact test, p < .05) cannot come from guessing; it means the response mapping was reversed or the task was not followed (Slick, Sherman and Iverson 1999 treat below-chance forced-choice performance as definite response bias). Chance-level accuracy can be a real result in impaired participants, so it is only flagged. One option on at least 90% of answered trials, when the correct options are balanced and accuracy is not above chance, means the answers did not depend on the items (the task counterpart of long-string responding in surveys; Curran 2016). An answer under 100 ms from the question was pressed before the question could be read. The display time is part of the design, so trials whose dots ran late leave the score.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Rounds of the 48 trials | 3 | 2 to 4 |
Yearly plans can change settings within these limits. Free and pay-as-you-go studies use the standard settings.
Need a setting this test does not have?
Devices and languages
- Timed test: participants need a desktop or laptop with a mouse or trackpad. Participant devices
- Languages: English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese.
- Available on: Every plan, including the free plan.
- Recruiting online? See the setup guides for Prolific, Sona Systems, CloudResearch Connect and Qualtrics.
Cite and describe
Participants completed the Dot Comparison Task in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Halberda and Feigenson, 2008; Halberda, Mazzocco and Feigenson, 2008), with the standard settings (rounds of the 48 trials: 3). The main score was weber fraction (the spread of the sense of number as a share of the number, fitted with a guess rate by maximum likelihood to the answers at the four ratios (Halberda and Feigenson 2008, equation 1), searched from 0.02 to 2).
ConductCognition versions: task version 1.0.0, scoring version 1.0.0. Every export records the versions each session used, for a methods section.
- Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the "number sense": The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457-1465. https://doi.org/10.1037/a0012682Two arrays side by side for 750 ms with adults, the size and area controls, and the Weber fraction model with a guess rate.
- Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665-668. https://doi.org/10.1038/nature07246The four ratios, and the Weber fraction of each person as a measure.
- Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499-503. https://doi.org/10.1126/science.1102085
- Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43(4), 981-986. https://doi.org/10.3758/s13428-011-0097-5Saving the visual properties that change with number on every display.
- Inglis, M., & Gilmore, C. (2014). Indexing the approximate number system. Acta Psychologica, 145, 147-155. https://doi.org/10.1016/j.actpsy.2013.11.009Accuracy and the Weber fraction as measures of one person.
Source papers
- Halberda J, Feigenson L (2008). Developmental change in the acuity of the "number sense": the approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5):1457-1465.Paradigm source, Children 3 to 6 years and adults
Questions
How long does the Dot Comparison Task take?
About 5 to 7 minutes, as listed in the test library.
What device does a participant need?
Timed test: participants need a desktop or laptop with a mouse or trackpad. The browser must be Chrome, Edge, Firefox or Safari.
What scores does it produce?
Weber Fraction, Weber Fraction at Lowest Value, Weber Fraction at Highest Value, Guess Rate, Accuracy, Accuracy by Ratio, Same-Size Accuracy, Same-Area Accuracy, Control Effect, Median Answer Time, Anticipations, Early Key Presses, Frame Interval, Refresh Rate, Displays on Time, Completed Trials and Planned Trials. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Dot Comparison Task used in research?
34 papers from 2021 to 2025 name it in their title or abstract, up 55% compared with 2016 to 2020. That ranks it 282 of 395 test families in the ConductCognition test census (use grade D). Source: ConductCognition test census 0.14.0, counted 31 October 2026 from OpenAlex and ClinicalTrials.gov.
How much reliability evidence does the Dot Comparison Task have?
In the published research, 0 papers report its test-retest reliability and 0 registered clinical studies use it as an outcome (evidence grade D in the ConductCognition test census).
Which settings can a researcher change?
Rounds of the 48 trials (2 to 4). Settings can be changed on yearly plans; free and pay-as-you-go studies use the standard settings.
Which languages can participants use?
Participants can take this test in English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese. English is on every plan, and the other languages come with yearly plans. Have a native speaker read the machine-translated text before launch.
Is this a clinical test?
No. ConductCognition is for research use only. It runs, scores and exports the test; clinical interpretation is outside the platform.
Every test: the full test list.
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