Description
remainingHeadroom = ceiling-before; normalizedChange = (after-before)/remainingHeadroom.
A change score can be expressed as raw difference, retention ratio or fraction of remaining headroom. These denominators answer different questions, and descriptive change does not by itself establish a causal learning effect.
remainingHeadroom = ceiling-before; normalizedChange = (after-before)/remainingHeadroom.
When to use this tool
Use Retention Ceiling Normalizer when checking a specified retention or ceiling-relative gain convention.
How to use the tool and how it works
- Enter before, after, suppliedCeiling. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remainingHeadroom, normalizedChange. Use the output convention below.
Require suppliedCeiling > before and after <= suppliedCeiling. remainingHeadroom = ceiling-before; normalizedChange = (after-before)/remainingHeadroom.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| before | Before | Required. Finite number. |
| after | After | Required. Finite number. |
| suppliedCeiling | Supplied Ceiling | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remainingHeadroom | Remaining Headroom | Required. Finite number. |
| normalizedChange | Change divided by initial ceiling headroom, potentially negative below -1. | Required. Finite number. |
{
"input": {
"before": 40,
"after": 70,
"suppliedCeiling": 100
},
"output": {
"remainingHeadroom": 60,
"normalizedChange": 0.5
}
}Limitations and assumptions
- No lower bound is imposed on scores here. Negative change can be below -1; this one-sided ceiling normalization does not validate a scale or estimate causal improvement.
- 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 an appropriate study design and measurement-error analysis when assessing instructional effectiveness or individual change.
References
Similar or alternative tools
- Retention Test Immediate Delayed Gap
loss = immediate-delayed; retainedFraction = delayed/immediate; delayedCeilingGap = maximum-delayed.
- Learning Gain Pretest Ceiling Gap
rawGain = posttest-pretest; availableGain = ceiling-pretest; normalizedGain = rawGain/availableGain.