Description
loss = immediate-delayed; retainedFraction = delayed/immediate; delayedCeilingGap = maximum-delayed.
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.
loss = immediate-delayed; retainedFraction = delayed/immediate; delayedCeilingGap = maximum-delayed.
When to use this tool
Use Retention Test Immediate Delayed Gap when checking a specified retention or ceiling-relative gain convention.
How to use the tool and how it works
- Enter immediate, delayed, maximum. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read loss, retainedFraction, delayedCeilingGap. Use the output convention below.
Require positive immediate, maximum >= immediate and delayed in [0,maximum]. loss = immediate-delayed; retainedFraction = delayed/immediate; delayedCeilingGap = maximum-delayed.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| immediate | Immediate | Required. Finite number; strictly above 0. |
| delayed | Delayed | Required. Finite number; minimum 0. |
| maximum | Maximum | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| loss | Loss | Required. Finite number. |
| retainedFraction | Retained Fraction | Required. Finite number. |
| delayedCeilingGap | Delayed Ceiling Gap | Required. Finite number. |
{
"input": {
"immediate": 80,
"delayed": 60,
"maximum": 100
},
"output": {
"loss": 20,
"retainedFraction": 0.75,
"delayedCeilingGap": 40
}
}Limitations and assumptions
- Delayed performance can exceed immediate performance, producing negative loss and a retained fraction above one. No causal learning effect or retention model is inferred.
- 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 Ceiling Normalizer
remainingHeadroom = ceiling-before; normalizedChange = (after-before)/remainingHeadroom.
- Learning Gain Pretest Ceiling Gap
rawGain = posttest-pretest; availableGain = ceiling-pretest; normalizedGain = rawGain/availableGain.