Power Law of Practice Calculator

Explicit caller-calibrated practice-power model T(n)=A+B*n^-c; no coefficients fabricated or fitted automatically. Assumes model applicability, not universal learning rate, ability or clinical improvement.

Description

A power-law learning curve relates practice-trial number to a calibrated task-time scenario.

A power-law learning curve relates practice-trial number to a calibrated task-time scenario.^[1]

The supplied asymptote, excess and exponent are model parameters rather than fitted results.

When to use Power Law of Practice Calculator

Use this tool to calculate or review the supplied observations under the stated rules. Establish the assessment or recording protocol, units, instrument version and independently applicable reference or calibration.

How to use Power Law of Practice Calculator and understand its results

Establish the assessment or recording protocol, units, instrument version and independently applicable reference or calibration.
Enter callerCalibratedAsymptoticTimeSeconds, callerCalibratedExcessTimeSeconds, callerCalibratedPracticeExponent, actualPositivePracticeTrialNumber, using the field meanings and rules below, then run the tool.
Read result.conditionalPredictedTaskTimeSeconds. Use the units and sign conventions below.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
callerCalibratedAsymptoticTimeSeconds	Caller calibrated asymptotic time seconds	number	Required
callerCalibratedExcessTimeSeconds	Caller calibrated excess time seconds	number	Required
callerCalibratedPracticeExponent	Caller calibrated practice exponent	number	Required
actualPositivePracticeTrialNumber	Actual positive practice trial number	number	Required

Require nonnegative asymptote time, excess time and exponent, plus integer practice trial 1–1000000000. Return asymptote+excess×trial^(−exponent). A zero exponent is allowed and leaves the excess constant. The tool does not fit parameters.

predictedSeconds=asymptoteSeconds+excessSeconds×trialNumber^(−exponent)

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Structured result; its nested fields below contain the actual calculation or selected reference	object
result.conditionalPredictedTaskTimeSeconds	Conditional Predicted Task Time Seconds	number

json

{
  "input": {
    "callerCalibratedAsymptoticTimeSeconds": 1,
    "callerCalibratedExcessTimeSeconds": 8,
    "callerCalibratedPracticeExponent": 1,
    "actualPositivePracticeTrialNumber": 2
  },
  "output": {
    "result": {
      "conditionalPredictedTaskTimeSeconds": 5
    }
  }
}

Limitations and assumptions

Actual acquisition, assessment protocol, instrument version and calibration determine applicability. The tool does not examine a person, classify images, administer a questionnaire or choose diagnostic cutoffs.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use Mixing Cost Calculator: Mixing cost compares matched repeat-trial performance in mixed and pure task blocks. For a complementary comparison, use Fechner Law Calculator: Fechner's logarithmic model relates stimulus intensity to a calibrated threshold and slope.

References

Power Law of Practice Calculator — tool.io

Similar or alternative tools

Mixing Cost Calculator
Mixing cost compares matched repeat-trial performance in mixed and pure task blocks.
Fechner Law Calculator
Fechner's logarithmic model relates stimulus intensity to a calibrated threshold and slope.