Thurstone Case V Scale Value Calculator

Restricted ThurstoneCaseVcolumnmeanprobit scale value from actual identified item pair preference fractions interior0–1, symmetric equal variance difference convention. No full model fit, missing comparison imputation or scale origin identified. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.

Description

Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.

Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.^[1]

A column-mean summary requires the equal-variance convention and independently qualified comparisons. The calculation and input requirements are explained below.

When to use Thurstone Case V Scale Value Calculator

Enter nonempty independently qualified pairwise preference fractions strictly between 0 and 1.

How to use Thurstone Case V Scale Value Calculator and how it works

Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
Enter the required fields and run Thurstone Case V Scale Value Calculator.
Read the result fields using the formula, output units, signs and ordering explained below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
actualPairwisePreferenceProbabilities	Actual Pairwise Preference Probabilities. Use the units and matching context stated in the calculation below.	array of number	Required; other constraints below

Enter nonempty independently qualified pairwise preference fractions strictly between 0 and 1. Apply the helper's inverse standard-normal approximation to each and return their mean. Zero and one cannot yield finite probits; no complete paired-comparison fit or scale-origin estimation occurs.

scaleValue=mean(normalQuantile(preferenceProbabilities))

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.value	Numeric result under the formula and output units explained above.	number

json

{
  "input": {
    "actualPairwisePreferenceProbabilities": [
      0.25,
      0.75
    ]
  },
  "output": {
    "result": {
      "value": 0
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Prospect Value Function Alpha/Beta Estimator for a complementary operation: A power-value model becomes a straight line after logarithmic transformation.

Use Prelec Probability Weighting Gamma Estimator for a complementary operation: The one-parameter Prelec model relates objective probability to a decision weight.

References

Thurstone Case V Scale Value Calculator — tool.io

Similar or alternative tools

Prospect Value Function Alpha/Beta Estimator
A power-value model becomes a straight line after logarithmic transformation.
Prelec Probability Weighting Gamma Estimator
The one-parameter Prelec model relates objective probability to a decision weight.