Attention
Magnitude Estimation Task
Also called: Stevens' power law, power law of sensation, ratio estimation, psychophysical scaling, magnitude estimation of length
Measure how the numbers people give to line lengths grow with length: participants number each line against a reference line called 100, scored as the exponent of a fitted power law.
4-6 minUntimed
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
- 72
- Evidence grade
- C
- Registered clinical studies
- 0
What it measures
Measures how the numbers people give to line lengths grow with the lengths. Each screen shows a reference line called 100 and a second line, and the participant types a number in proportion to how long the second line looks. 9 lengths, from a quarter of the reference line to 4 times it, are shown 3 times each. The main score is the exponent of the power law fitted to the numbers, with the fit's R-squared.
Constructs
- Magnitude estimation
- Psychophysical scaling
- Length perception
- Ratio judgment
Research uses
- Psychophysics research
- Perception research
- Numerical cognition research
- Within-study group comparison
How the paradigm works
The Magnitude Estimation Task measures how the numbers people give to lines grow with the lines' length. In magnitude estimation (Stevens, 1957), people give each stimulus a number in proportion to how large it seems, against a reference stimulus called by a set number. On log scales the numbers fall on a straight line whose slope is the exponent b of a power law, R = k L^b: an exponent of 1 means numbers in proportion to the stimulus, below 1 that they grow more slowly than it, and above 1 faster. Absolute magnitude estimates of line length did not differ between groups with mean ages of 25, 50 and 68 years (Verrillo, 1981).
More about the paradigm
Here each screen shows a reference line 80 pixels long, called 100, above a second line, and the participant types a whole number from 1 to 9999 for the second line. The second line has one of 9 lengths from 20 to 320 pixels, in even steps on a ratio scale from a quarter of the reference line to 4 times it, so numbers in proportion to length run from 25 to 400. The reference line is on every screen, as in Mertens, Mertens and Lerche (2021), and each line starts at a place drawn from the session's seed, so the ends of the two lines do not line up. On a narrow screen both lines shrink by the same factor. A session has 3 blocks (2 to 5 as a setting), each showing every length once in a new order, after 2 practice lines. After a practice line the screen restates the number as a ratio to the reference line; no screen says what a number should have been.
The main score is the exponent: the slope of the least-squares line of log number on log length ratio over the scored lines, reported with that fit's R-squared. Ward and colleagues (2015) fitted each listener's exponent this way and set aside runs with an R-squared below 0.67, the value below which a fit is flagged here. The number the fitted line gives a line as long as the reference, the median number for the task's line that is as long, and the median distance of the numbers from numbers in proportion to length show how the scale was used. A number more than 10 times too large or too small for its line is taken for a slip and left out. Scores support research and do not diagnose.
Scores
- Power-Law Exponentscore
- Slope of the least-squares line of log number on log length ratio over the scored lines: the exponent b of R = k L^b.
- 1: numbers in proportion to length; below 1: numbers grow more slowly than length; above 1: faster
- Fit R-Squared%
- R-squared of that line over the single numbers.
- Below 0.67 is flagged
- Number at the Reference Lengthscore
- The number the fitted line gives a line as long as the reference line.
- 100: the reference line's number was kept
- Number for the Reference-Length Linescore
- Median number given to the task's line that is as long as the reference line.
- 100: the line was seen as long as the reference
- Ratio Error%
- Median distance of the numbers from 100 times each line's length over the reference line's, as a percent of it.
- Lower is closer to numbers in proportion to length
- Median Answer Timems
- Median time from the number box appearing to the number being submitted.
- Informational
- Anticipationscount
- Numbers submitted under 100 ms after the number box appeared, left out of the scores.
- 0 expected
- Slipscount
- Lines whose number was more than 10 times too large or too small for the line; they are left out of the fit.
- More than a quarter of the lines is flagged
- Refused Entriescount
- Entries refused because they were not a whole number from 1 to 9999.
- Informational
- Lines Scoredtrials
- Lines whose number enters the fit.
- Informational
- Lines Answeredtrials
- Lines with a number recorded, out of 27 as standard.
- Informational
Use and evidence
72 papers from 2021 to 2025 name this task in their title or abstract, down 17% compared with 2016 to 2020. That ranks it 256 of 495 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 23 |
| 2024 | 11 |
| 2023 | 9 |
| 2022 | 16 |
| 2021 | 13 |
| 2020 | 16 |
| 2019 | 17 |
| 2018 | 18 |
| 2017 | 24 |
| 2016 | 12 |
| 2015 | 33 |
| 2014 | 16 |
| 2013 | 22 |
| 2012 | 27 |
| 2011 | 16 |
| 2010 | 23 |
| 2009 | 24 |
| 2008 | 20 |
| 2007 | 11 |
| 2006 | 22 |
| 2005 | 16 |
| 2004 | 21 |
| 2003 | 8 |
| 2002 | 6 |
| 2001 | 11 |
| 2000 | 10 |
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
- 6
- Papers on reliability or validity
- 73
- Registered clinical studies using it as an outcome
- 0
Note on the counts: counted with specific phrases, since magnitude estimation is also a rating scale for pain, breathlessness and voice quality.
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 3 November 2026 from OpenAlex and ClinicalTrials.gov.
Task design
The trial sequence as the test runs in ConductCognition.
- Each screen
- A reference line 80 pixels long, called 100, above a second line, each 4 pixels thick in its own field 340 pixels wide. The participant types a whole number from 1 to 9999 for the second line, with no time limit; a number keypad opens on phones.
- Lines
- 9 lengths from 20 to 320 pixels, in even steps on a ratio scale from a quarter of the reference line to 4 times it. Each line starts at a place drawn from the session's seed, so the ends of the two lines do not line up. On a narrower screen both fields shrink by the same factor.
- Order
- 3 blocks (standard; 2 to 5), each showing the 9 lines once in an order drawn from the session's seed. A block never starts with the line that ended the one before.
- Practice
- 2 lines (50 and 200 pixels), each followed by the number restated as a ratio to the reference line. No screen says what a number should have been.
- Scores
- The exponent: the slope of the least-squares line of log number on log length ratio, the exponent b of the power law R = k L^b, with that fit's R-squared. Also the number the fit gives a line as long as the reference line, the median number for the task's line that is as long, and the median distance of the numbers from numbers in proportion to length.
- Checks
- A number more than 10 times too large or too small for its line is a slip and is left out of the fit. Fewer than half the lines answered, or numbers that do not rise with length, is invalid. Slips on more than a quarter of the lines, a fit below R-squared 0.67 and no fit are flagged and never exclude.
Magnitude estimation is also a way of rating pain, breathlessness or how acceptable a sentence sounds; this test is the psychophysical task on lines, with the reference line on every screen as in Mertens, Mertens and Lerche (2021). An exponent depends on the range of lengths, the reference and how people use numbers, so compare groups or conditions. These are research measures of how numbers follow length, and they do not diagnose.
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: magnitude_estimation_trial from the scored run, one typed number per line, with no correct answer, so accuracy is not judged against chance. Fewer than half the planned lines answered is invalid, and any other incomplete run is flagged. A number more than 10 times too large or too small for the line's ratio to the reference line is a slip and is left out of the fit; slips on more than a quarter of the lines are flagged. Numbers that do not rise with the length of the lines (an exponent of 0 or less) invalidate. A log-log fit below R-squared 0.67, or no fit at all, is flagged. Numbers submitted within 200 ms of the number box appearing on at least half the lines invalidate.
Why these rules
There is no correct option to compare with chance, so accuracy is not judged against chance. Any positive exponent is a result, so its size is never judged; but a longer line is plainly longer, so numbers that do not rise with length did not follow the task. A number far outside the line's ratio is most often a typing slip, as in the anchoring task, so it is left out of the fit, and many slips flag the session because they can also be a misread task. Ward and colleagues (2015) set aside runs whose log-log fit fell below R-squared 0.67; here such a fit is flagged and never excluded. 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.
No percentile. Scores and quality flags only.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Blocks | 3 | 2 to 5 |
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, tablets and phones. Participant devices
- Languages: English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese.
- Available on: Every plan, including the free plan.
- No percentile. Scores and quality flags only. How norms work
- Recruiting online? See the setup guides for Prolific, Sona Systems, CloudResearch Connect and Qualtrics.
Cite and describe
Participants completed the Magnitude Estimation Task in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Stevens SS, 1957), with the standard settings (blocks: 3). The main score was power-law exponent (slope of the least-squares line of log number on log length ratio over the scored lines: the exponent b of R = k L^b).
ConductCognition versions: task version 1.0.0, scoring version 1.0.0. Every export records the versions each session used, for a methods section.
- Stevens, S. S. (1957). On the psychophysical law. Psychological Review, 64(3), 153-181. https://doi.org/10.1037/h0046162Magnitude estimation and the power law of sensation.
- Verrillo, R. T. (1981). Absolute estimation of line length in three age groups. Journal of Gerontology, 36(5), 625-627. https://doi.org/10.1093/geronj/36.5.625Line-length estimates across adult ages.
- Ward, L. M., Baumann, M., Moffat, G., Roberts, L. E., Mori, S., Rutledge-Taylor, M., & West, R. L. (2015). Achieving across-laboratory replicability in psychophysical scaling. Frontiers in Psychology, 6, 903. https://doi.org/10.3389/fpsyg.2015.00903Each person's exponent from a log-log fit, and the R-squared below which a run was set aside.
- Mertens, A., Mertens, U. K., & Lerche, V. (2021). On the difficulty to think in ratios: A methodological bias in Stevens' magnitude estimation procedure. Attention, Perception, & Psychophysics, 83(5), 2347-2365. https://doi.org/10.3758/s13414-021-02266-5The reference on every screen, and how the way of giving numbers moves the exponent.
- Bard, E. G., Robertson, D., & Sorace, A. (1996). Magnitude estimation of linguistic acceptability. Language, 72(1), 32-68. https://doi.org/10.2307/416793Magnitude estimation used as a rating method, which this test is not.
Source papers
- Verrillo (1981): absolute magnitude estimates of line length did not differ between groups with mean ages of 25, 50 and 68 years. Ward and colleagues (2015): each listener's loudness exponent came from a log-log fit of their own numbers, and with 17 numbers in a run some runs did not give a reliable exponent.Paradigm source, Adults
Questions
How long does the Magnitude 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, tablets and phones. The browser must be Chrome, Edge, Firefox or Safari.
What scores does it produce?
Power-Law Exponent, Fit R-Squared, Number at the Reference Length, Number for the Reference-Length Line, Ratio Error, Median Answer Time, Anticipations, Slips, Refused Entries, Lines Scored and Lines Answered. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Magnitude Estimation Task used in research?
72 papers from 2021 to 2025 name it in their title or abstract, down 17% compared with 2016 to 2020. That ranks it 256 of 495 test families in the ConductCognition test census (use grade D). Source: ConductCognition test census 0.22.0, counted 3 November 2026 from OpenAlex and ClinicalTrials.gov.
How much reliability evidence does the Magnitude Estimation Task have?
In the published research, 6 papers report its test-retest reliability and 0 registered clinical studies use it as an outcome (evidence grade C in the ConductCognition test census).
Does it report a percentile?
No. Scores and quality flags only.
Which settings can a researcher change?
Blocks (2 to 5). 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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