Processing Speed
Number Line Estimation Task
Also called: number line task, number-to-position task, bounded number line estimation
Measure how people map numbers onto space: participants mark where numbers fall on lines from 0 to 100 and from 0 to 1000, scored by percent absolute error.
4-6 minUntimed
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
- 31
- Evidence grade
- C
- Registered clinical studies
- 3
What it measures
Measures how people place numbers in space. A number appears above a line that runs from 0 to 100 or from 0 to 1000, and the participant marks where the number belongs. The main score is the percent absolute error: how far the marks fall from the true places, as a share of the line.
Constructs
- Numerical magnitude
- Number-space mapping
- Estimation
- Proportional reasoning
Research uses
- Numerical cognition and mathematics learning research
- Developmental studies of children's estimation
- Research on mathematics difficulties
- Within-study group comparison
How the paradigm works
Number line estimation asks where a number belongs on a line. A number appears above a horizontal line whose ends are labeled 0 and 100, or 0 and 1000, and the participant marks where the number falls, as in Siegler and Opfer (2003). A click or tap on the line sets the mark; another click, a drag or the arrow keys move it, and Done confirms it. There is no time limit and no feedback in the test. The standard runs the 0 to 100 line first and then the 0 to 1000 line, 20 numbers each; a study can run either line alone.
More about the paradigm
The numbers were chosen for this test by a rule: on each line, the whole numbers nearest to (k / 21)^1.5 of the line's end, for k = 1 to 20. They cover the whole line and fall closer together near 0, where a linear and a logarithmic pattern of estimates differ most. Each line's numbers come in an order drawn from the session's seed. Two practice numbers on a line from 0 to 10 show where they belong afterwards.
The main score is the percent absolute error (Siegler and Booth, 2004): the distance from each mark to the number's true place, as a percent of the line, averaged over the numbers. Lower is better. For each line, the test also fits the estimates against the numbers (linear) and against their logarithm (logarithmic), as Siegler and Opfer (2003) did: young children's estimates on the longer line are often fitted better by the logarithm, and adults' by a straight line. A later account reads the same curve as proportion judgment (Barth and Paladino, 2011). Across studies, number line estimation is related to mathematical competence (Schneider and colleagues, 2018). Marks set under 100 ms after a number appears count as anticipations and are left out. Scores support research and do not diagnose.
Scores
- Percent Absolute Error%
- Mean distance from each mark to the number's true place, as a percent of the line, over both lines.
- Lower is better
- Percent Absolute Error, 0 to 100%
- The same on the line from 0 to 100.
- Lower is better
- Percent Absolute Error, 0 to 1000%
- The same on the line from 0 to 1000.
- Lower is better
- Linear Fit, 0 to 100score
- R-squared of the estimates on the numbers, on the line from 0 to 100, from at least 8 marks.
- Higher means estimates rise evenly with the numbers
- Logarithmic Fit, 0 to 100score
- R-squared of the estimates on the natural logarithm of the numbers, on the line from 0 to 100.
- Above the linear fit means a compressed pattern
- Linear Fit, 0 to 1000score
- R-squared of the estimates on the numbers, on the line from 0 to 1000, from at least 8 marks.
- Higher means estimates rise evenly with the numbers
- Logarithmic Fit, 0 to 1000score
- R-squared of the estimates on the natural logarithm of the numbers, on the line from 0 to 1000.
- Above the linear fit means a compressed pattern
- Linear Slope, 0 to 100score
- Slope of the estimates on the numbers on the line from 0 to 100.
- 1 when estimates grow with the numbers
- Linear Slope, 0 to 1000score
- Slope of the estimates on the numbers on the line from 0 to 1000.
- 1 when estimates grow with the numbers
- Median Timems
- Median time from a number appearing to Done.
- Informational
- Numbers Scoredcount
- Marks scored, without anticipations.
- Informational
- Anticipationscount
- Marks first set under 100 ms after the number appeared; left out of the other measures.
- Lower is better
- Planned Numberstrials
- Numbers the session's settings ask for: 40 with both lines, 20 with one.
- Informational
Use and evidence
31 papers from 2021 to 2025 name this task in their title or abstract, up 29% compared with 2016 to 2020. That ranks it 296 of 395 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 11 |
| 2023 | 5 |
| 2022 | 4 |
| 2021 | 5 |
| 2020 | 4 |
| 2019 | 5 |
| 2018 | 6 |
| 2017 | 3 |
| 2016 | 6 |
| 2015 | 2 |
| 2014 | 1 |
| 2013 | 2 |
| 2012 | 1 |
| 2011 | 1 |
| 2010 | 0 |
| 2009 | 1 |
| 2008 | 1 |
| 2007 | 2 |
| 2006 | 2 |
| 2005 | 0 |
| 2004 | 0 |
| 2003 | 0 |
| 2002 | 0 |
| 2001 | 0 |
| 2000 | 1 |
Use grade D
30 to 99 papers from 2021 to 2025.
Evidence grade C
At least 2 test-retest papers, 30 reliability or validity papers or 3 registered clinical studies.
- Papers on test-retest reliability
- 0
- Papers on reliability or validity
- 1
- Registered clinical studies using it as an outcome
- 3
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.
- Lines
- A horizontal line with its ends labeled 0 and 100, then one labeled 0 and 1000 (standard; either line alone as a setting). The number to place appears above the line in digits.
- Numbers
- 20 per line: the whole numbers nearest to (k / 21)^1.5 of the line's end, for k = 1 to 20, so 1 to 93 on the first line and 10 to 929 on the second. They cover the whole line and fall closer together near 0, where linear and logarithmic patterns differ most. Each line's numbers come in an order drawn from the session's seed.
- Answer
- A click or tap on the line sets a mark; another click, a drag or the arrow keys move it, and Done confirms it. No time limit and no feedback.
- Practice
- The numbers 3 and 8 on a line from 0 to 10, each followed by a dashed line where it belongs.
- Error
- Percent absolute error: the distance from the mark to the number's true place, as a percent of the line, averaged over the numbers.
- Fits
- On each line with at least 8 marks, the R-squared of the estimates against the numbers (linear) and against their natural logarithm (logarithmic), and the linear slope.
Siegler and Opfer (2003) had children and adults mark numbers on paper lines from 0 to 100 and from 0 to 1000. This version shows the lines on screen and uses its own numbers, chosen by the rule above, so its errors are best compared with other sessions of this test. The scores support research and do not diagnose.
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: number_line_test from the scored run, one per number. A mark has no correct option to compare with chance, so accuracy is not judged against chance. Marks first set within 200 ms of the number appearing on at least half the numbers invalidate. On a line with at least 8 marks, a linear fit below R-squared 0.2 is flagged, and so is a run with fewer marks than planned; both withhold the percentile.
Why these rules
There is no correct option to compare with chance, so accuracy is not judged against chance. An answer under 200 ms is faster than a simple visual reaction, so it cannot reflect the item. Following response-time effort screening for untimed tests (Wise and Kong 2005), the session is invalid only when at least half the answers are that fast. Even young children's estimates rise with the numbers, so marks whose linear fit falls below R-squared 0.2 barely follow them and may not reflect the task; they are flagged rather than excluded, because a compressed pattern is a real result. A run cut short leaves out numbers and changes the mix the error is averaged over.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Lines | 0 to 100, then 0 to 1000 (standard) | 0 to 100, then 0 to 1000 (standard), 0 to 100 only, 0 to 1000 only |
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
- Untimed test: runs on desktops, laptops and tablets. 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 Line Estimation task in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Siegler RS, Opfer JE, 2003; Siegler RS, Booth JL, 2004), with the standard settings (lines: 0 to 100, then 0 to 1000). The main score was percent absolute error (mean distance from each mark to the number's true place, as a percent of the line, over both lines).
ConductCognition versions: task version 1.0.0, scoring version 1.0.0. Every export records the versions each session used, for a methods section.
- Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237-250. https://doi.org/10.1111/1467-9280.02438
- Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444. https://doi.org/10.1111/j.1467-8624.2004.00684.xPercent absolute error and the link with mathematics achievement.
- Schneider, M., Merz, S., Stricker, J., De Smedt, B., Torbeyns, J., Verschaffel, L., & Luwel, K. (2018). Associations of number line estimation with mathematical competence: A meta-analysis. Child Development, 89(5), 1467-1484. https://doi.org/10.1111/cdev.13068Meta-analysis of the link with mathematical competence.
- Barth, H. C., & Paladino, A. M. (2011). The development of numerical estimation: Evidence against a representational shift. Developmental Science, 14(1), 125-135. https://doi.org/10.1111/j.1467-7687.2010.00962.xProportion judgment as another account of curved estimates.
Source papers
- Siegler RS, Opfer JE (2003). The development of numerical estimation: evidence for multiple representations of numerical quantity. Psychological Science, 14(3):237-250.Paradigm source, Children and adults
- Siegler RS, Booth JL (2004). Development of numerical estimation in young children. Child Development, 75(2):428-444.Paradigm source, Children
Questions
How long does the Number Line Estimation Task take?
About 4 to 6 minutes, as listed in the test library.
What device does a participant need?
Untimed test: runs on desktops, laptops and tablets. The browser must be Chrome, Edge, Firefox or Safari.
What scores does it produce?
Percent Absolute Error, Percent Absolute Error, 0 to 100, Percent Absolute Error, 0 to 1000, Linear Fit, 0 to 100, Logarithmic Fit, 0 to 100, Linear Fit, 0 to 1000, Logarithmic Fit, 0 to 1000, Linear Slope, 0 to 100, Linear Slope, 0 to 1000, Median Time, Numbers Scored, Anticipations and Planned Numbers. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Number Line Estimation Task used in research?
31 papers from 2021 to 2025 name it in their title or abstract, up 29% compared with 2016 to 2020. That ranks it 296 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 Number Line Estimation Task have?
In the published research, 0 papers report its test-retest reliability and 3 registered clinical studies use it as an outcome (evidence grade C in the ConductCognition test census).
Which settings can a researcher change?
Lines (0 to 100, then 0 to 1000 (standard), 0 to 100 only, 0 to 1000 only). 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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