Mental Rotation Slope
Regress mental-rotation RT on shortest unsigned circular angular disparity, explicitly mapping 270° to 90°; task correctness filtering must precede input.
Description
Mental-rotation slope relates reaction time to angular separation.
Mental-rotation slope relates reaction time to angular separation. Reducing angles to the shorter rotation maps equivalent orientations to a distance from zero through 180 degrees.
The tool returns shortestRotationDegrees (shortest rotation degrees); slopeMsPerDegree (slope ms per degree); interceptMs (intercept ms); fitRSquared (fit r squared). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Mental Rotation Slope
Use Mental Rotation Slope when you already have stimulusAnglesDegrees, reactionTimesMs and want shortestRotationDegrees, slopeMsPerDegree, interceptMs, fitRSquared. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Mental Rotation Slope and understand its results
- Enter stimulusAnglesDegrees, reactionTimesMs using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read shortestRotationDegrees, slopeMsPerDegree, interceptMs, fitRSquared. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| stimulusAnglesDegrees | Stimulus angles degrees | list of number | Required |
| reactionTimesMs | Reaction times ms | list of number | Required |
Wrap positive or negative angles, then regress positive RTs against the shortest angles. Require at least two distinct resulting angles.
angle = min(wrap360(θ),360−wrap360(θ)); RT ≈ intercept+slope×angle The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"stimulusAnglesDegrees": [
0,
90,
270,
180
],
"reactionTimesMs": [
100,
190,
190,
280
]
},
"output": {
"shortestRotationDegrees": [
0,
90,
90,
180
],
"slopeMsPerDegree": 1,
"interceptMs": 100,
"fitRSquared": 1
}
}Limitations and assumptions
The linear fit does not test strategy, accuracy or stimulus comparability; repeated trials are not grouped by angle first.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Visual Search Slope: Aggregate correct-trial visual-search RTs by set size and fit equally weighted condition means; signed slopes are retained and no serial/parallel search diagnosis is asserted. Cognitive Decline Slope: Fit longitudinal cognitive score change after caller-supplied visit-specific practice offsets; score direction and diagnostic interpretation are not assumed.
Methodological background: Least squares estimation.1
References
-
Least squares estimation — NIST/SEMATECH
Similar or alternative tools
- Visual Search Slope
Aggregate correct-trial visual-search RTs by set size and fit equally weighted condition means; signed slopes are retained and no serial/parallel search diagnosis is asserted.
- Cognitive Decline Slope
Fit longitudinal cognitive score change after caller-supplied visit-specific practice offsets; score direction and diagnostic interpretation are not assumed.