Processing Speed
Number Midpoint Task
Also called: number bisection task, numerical bisection, arithmetic mean verification
Measure arithmetic midpoint judgments: participants decide whether the middle number is exactly halfway between two others. Compare accuracy and speed across number ranges and multiplication patterns.
3-8 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. Try it here first, with no account.
- Papers, 2021 to 2025
- 2
- Evidence grade
- D
- Registered clinical studies
- 0
What it measures
Measures how accurately and quickly people judge arithmetic midpoints. Three numbers appear in increasing order: decide whether the middle number is exactly halfway between the other two. Scores compare number ranges, multiplication patterns and distances from the true midpoint.
Constructs
- Arithmetic mean judgments
- Number magnitude
- Arithmetic fact knowledge
Research uses
- Mathematics education research
- Numerical cognition research
How the paradigm works
Number bisection asks whether the middle of three increasing integers equals the arithmetic mean of the outside numbers. Nuerk and colleagues (2002) used this judgment to study number representations. The task distinguishes the size of the interval, multiplication patterns, and how far an incorrect middle number lies from the true mean.
More about the paradigm
Our code generates increasing triplets of two-digit integers. Each round has 64 trials, half true midpoints and half false. True midpoints cross small or large number ranges with the presence or absence of a multiplication pattern. False midpoints cross close or far deviations with integer or half-integer endpoint means. Eight separate triplets provide practice.
The standard is one round, with a setting for one to three. A cross appears for 500 ms, followed by the numbers for up to 6,000 ms. Participants answer with F or J on a desktop or laptop keyboard. Practice gives feedback for 800 ms; test trials give none. Accuracy is the main measure, with correct response times and condition summaries alongside it. Responses under 100 ms are counted as anticipations. Scores support research; the generated items do not use published norms or diagnostic cutoffs.
Scores
- Accuracy%
- Share of all test trials answered correctly from 100 to 6,000 ms, including missed and premature responses in the denominator.
- Higher is better
- Median Correct Response Timems
- Median time for correct answers from 100 to 6,000 ms.
- Lower is faster
- Range Effectms
- Median correct time for true midpoints with large ranges minus small ranges, with five correct responses per group.
- Positive means wider ranges took longer
- Multiplication Pattern Effectms
- Median correct time for nonmultiplicative minus multiplicative true midpoints, with five correct responses per group.
- Positive means multiplication patterns were faster
- Distance to Midpoint Effectms
- Median correct time for false midpoints close to the true mean minus far from it, with five correct responses per group.
- Positive means close misses took longer
- True Midpoint Accuracy%
- Share of true midpoint trials answered correctly.
- Higher is better
- False Midpoint Accuracy%
- Share of false midpoint trials answered correctly.
- Higher is better
- Accuracy by Number Condition%
- Accuracy by range and multiplication pattern for true midpoints, or distance and integer mean for false midpoints.
- Compare conditions
- Response Time by Number Conditionms
- Median correct response time in each number condition.
- Compare conditions
- Anticipationscount
- Responses under 100 ms; excluded from correct responses and response-time summaries.
- Lower is better
- Missed Responsescount
- Trials with no usable key press within 6,000 ms.
- Lower is better
- Completed Trialstrials
- Test trials shown in the selected run.
- Compare with planned trials
- Planned Trialstrials
- Number of test trials planned for the run.
- Informational
Use and evidence
2 papers from 2021 to 2025 name this task in their title or abstract. That ranks it 486 of 495 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 0 |
| 2024 | 1 |
| 2023 | 0 |
| 2022 | 1 |
| 2021 | 0 |
| 2020 | 1 |
| 2019 | 0 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 0 |
| 2015 | 4 |
| 2014 | 3 |
| 2013 | 1 |
| 2012 | 1 |
| 2011 | 5 |
| 2010 | 2 |
| 2009 | 2 |
| 2008 | 1 |
| 2007 | 3 |
| 2006 | 3 |
| 2005 | 2 |
| 2004 | 1 |
| 2003 | 0 |
| 2002 | 0 |
| 2001 | 1 |
| 2000 | 0 |
Use grade E
Fewer than 30 papers from 2021 to 2025.
Evidence grade D
Little published measurement evidence found.
- Papers on test-retest reliability
- 0
- Papers on reliability or validity
- 0
- Registered clinical studies using it as an outcome
- 0
Note on the counts: Original generated items; research scores; no published norms..
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 0.22.0, counted 2 November 2026 from OpenAlex and ClinicalTrials.gov.
Task design
The trial sequence as the test runs in ConductCognition.
- Display
- A cross for 500 ms, then the numbers until F or J or a 6,000 ms limit. Response time starts on the frame that draws the numbers.
- Keys
- F for Yes, the middle number is exactly halfway; J for No.
- Trials
- 1 round of 64 test trials as standard; 1 to 3 rounds. Trial order is seeded and recorded.
- Practice
- 8 separate items with 800 ms feedback, one from each design cell. Practice items never enter the test in that run.
- Items
- Increasing integers from 10 to 99. True midpoints: small (4 to 8) or large (12 to 18) endpoint ranges, crossed with consecutive multiples of the step or no such pattern. False midpoints: near (0.5 to 1.5) or far (2 to 5) deviations, crossed with integer or half-integer endpoint means.
- Balance
- 32 Yes and 32 No trials per round. Each of eight cells has eight items; false midpoints fall above and below the mean equally often.
- Score
- Accuracy over all test trials. Correct response times use 100 to 6,000 ms; time contrasts need five usable correct answers in each group.
The items, trial counts and six-second limit were set for this version. Condition contrasts describe these generated items; they do not identify a unique strategy or carry the published tasks’ norms.
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: number_bisection_test from the most complete run, with the last run winning ties. Two balanced keys, chance 50%, graded again from the saved numbers. Below chance invalidates; not above chance is flagged. One key on 90% of answers invalidates when accuracy is not above chance. An incomplete run is flagged. Missed responses and responses under 100 ms follow the timed-test rule.
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). Missed responses and responses under 100 ms keep the platform's timed-test rule: more than max(3, 25%) missed responses or more than max(2, 20%) responses under 100 ms invalidate, and any is flagged. A response under 100 ms cannot be a reaction to the stimulus.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Rounds of 64 judgments | 1 | 1 to 3 |
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 Number Midpoint Task in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Nuerk, Geppert, van Herten and Willmes, 2002; Blume et al., 2021), with the standard settings (rounds of 64 judgments: 1). The main score was accuracy (share of all test trials answered correctly from 100 to 6,000 ms, including missed and premature responses in the denominator).
ConductCognition versions: task version 1.0.0, scoring version 1.0.0. Every export records the versions each session used, for a methods section.
- Nuerk, H.-C., Geppert, B. E., van Herten, M., & Willmes, K. (2002). On the impact of different number representations in the number bisection task. Cortex, 38(5), 691-715. https://doi.org/10.1016/S0010-9452(08)70038-8Verification of arithmetic midpoints and number-representation effects.
- Blume, F., Dresler, T., Gawrilow, C., Ehlis, A.-C., Goellner, R., & Moeller, K. (2021). Examining the relevance of basic numerical skills for mathematical achievement in secondary school using a within-task assessment approach. Acta Psychologica, 215, 103289. https://doi.org/10.1016/j.actpsy.2021.103289Range, multiplication, bisection possibility and distance manipulations.
Source papers
Questions
How long does the Number Midpoint Task take?
About 3 to 8 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?
Accuracy, Median Correct Response Time, Range Effect, Multiplication Pattern Effect, Distance to Midpoint Effect, True Midpoint Accuracy, False Midpoint Accuracy, Accuracy by Number Condition, Response Time by Number Condition, Anticipations, Missed Responses, Completed Trials and Planned Trials. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Number Midpoint Task used in research?
2 papers from 2021 to 2025 name it in their title or abstract. That ranks it 486 of 495 test families in the ConductCognition test census (use grade E). Source: ConductCognition test census 0.22.0, counted 2 November 2026 from OpenAlex and ClinicalTrials.gov.
How much reliability evidence does the Number Midpoint 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 64 judgments (1 to 3). 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.
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