Description
rawGain = posttest-pretest; availableGain = ceiling-pretest; normalizedGain = rawGain/availableGain.
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.
rawGain = posttest-pretest; availableGain = ceiling-pretest; normalizedGain = rawGain/availableGain.
When to use this tool
Use Learning Gain Pretest Ceiling Gap when checking a specified retention or ceiling-relative gain convention.
How to use the tool and how it works
- Enter pretest, posttest, ceiling, floor. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read rawGain, availableGain, normalizedGain. Use the output convention below.
Require ceiling > floor, pretest in [floor,ceiling) and posttest in [floor,ceiling]. rawGain = posttest-pretest; availableGain = ceiling-pretest; normalizedGain = rawGain/availableGain.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| pretest | Pretest | Required. Finite number. |
| posttest | Posttest | Required. Finite number. |
| ceiling | Ceiling | Required. Finite number. |
| floor | Floor | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| rawGain | Raw Gain | Required. Finite number. |
| availableGain | Available Gain | Required. Finite number. |
| normalizedGain | Normalized Gain | Required. Finite number. |
{
"input": {
"pretest": 40,
"posttest": 70,
"ceiling": 100,
"floor": 0
},
"output": {
"rawGain": 30,
"availableGain": 60,
"normalizedGain": 0.5
}
}Limitations and assumptions
- Negative normalized gains are allowed. This descriptive ceiling-relative change does not correct measurement error, regression to the mean or establish an instructional effect.
- 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.
- Retention Test Immediate Delayed Gap
loss = immediate-delayed; retainedFraction = delayed/immediate; delayedCeilingGap = maximum-delayed.