Description
Normalize the same response against each range; normalizedGap = secondFraction-firstFraction.
Numeric score transformations can reverse a scale, map anchors or change its mean and standard deviation. Such arithmetic does not establish equal category spacing, comparable constructs or statistical equating between assessments.
Normalize the same response against each range; normalizedGap = secondFraction-firstFraction.
When to use this tool
Use Research Response Scale Gap when checking an explicit scale or anchor transformation.
How to use the tool and how it works
- Enter firstMinimum, firstMaximum, secondMinimum, secondMaximum, response. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read firstFraction, secondFraction, normalizedGap. Use the output convention below.
Require each maximum > its corresponding minimum. Normalize the same response against each range; normalizedGap = secondFraction-firstFraction.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstMinimum | First Minimum | Required. Finite number. |
| firstMaximum | First Maximum | Required. Finite number. |
| secondMinimum | Second Minimum | Required. Finite number. |
| secondMaximum | Second Maximum | Required. Finite number. |
| response | Response | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| firstFraction | First Fraction | Required. Finite number. |
| secondFraction | Second Fraction | Required. Finite number. |
| normalizedGap | Normalized Gap | Required. Finite number. |
{
"input": {
"firstMinimum": 0,
"firstMaximum": 10,
"secondMinimum": 0,
"secondMaximum": 20,
"response": 5
},
"output": {
"firstFraction": 0.5,
"secondFraction": 0.25,
"normalizedGap": -0.25
}
}Limitations and assumptions
- The response is not required to lie within either range, so fractions can be outside [0,1]. This is endpoint rescaling, not statistical score equating or construct comparability.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use appropriate measurement validation or equating methods before treating transformed scales as interchangeable.
References
Similar or alternative tools
- Scale Direction Reversal Flag
When reverse is true return lower+upper-value, otherwise preserve value; reversed echoes the flag.
- Scale Reverse Item Midpoint
midpoint = lower/2+upper/2; reversed = lower+(upper-score).