Crawford-Howell t
Compare one case with a small normative control sample using Crawford–Howell t and n−1 degrees of freedom; no p-value, tail choice or clinical interpretation is invented.
Description
A single-case comparison must account for uncertainty in a small control sample.
A single-case comparison must account for uncertainty in a small control sample. The Crawford–Howell statistic uses control sample SD and N−1 degrees of freedom.
The tool returns controlMean (control mean); controlSampleSd (control sample sd); tValue (t value); degreesOfFreedom (degrees of freedom). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Crawford-Howell t
Use Crawford-Howell t when you already have caseScore, controlScores and want controlMean, controlSampleSd, tValue, degreesOfFreedom. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Crawford-Howell t and understand its results
- Enter caseScore, controlScores using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read controlMean, controlSampleSd, tValue, degreesOfFreedom. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| caseScore | Case score | number | Required |
| controlScores | Control scores | list of number | Required |
Require at least two control scores with positive sample variance, then return the mean, SD, t value and degrees of freedom.
t = (case−controlMean)/(sampleSD×sqrt((N+1)/N)); df = N−1 The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"caseScore": 20,
"controlScores": [
8,
10,
12
]
},
"output": {
"controlMean": 10,
"controlSampleSd": 2,
"tValue": 4.330127018922194,
"degreesOfFreedom": 2
}
}Limitations and assumptions
No p value or abnormality percentage is calculated. Control comparability and distributional assumptions require separate review.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Reliable Change Index: Compute a practice-adjusted Jacobson–Truax reliable-change index from caller norms and criterion; not a diagnosis or a universal improvement cutoff. GLM t-Statistic: Evaluate a GLM contrast using the full already-scaled coefficient covariance; no additional residual variance multiplier is applied.
Methodological background: Comparing an individual's test score against norms derived from small samples.1
References
-
Comparing an individual's test score against norms derived from small samples — Crawford and Howell; The Clinical Neuropsychologist
Similar or alternative tools
- Reliable Change Index
Compute a practice-adjusted Jacobson–Truax reliable-change index from caller norms and criterion; not a diagnosis or a universal improvement cutoff.
- GLM t-Statistic
Evaluate a GLM contrast using the full already-scaled coefficient covariance; no additional residual variance multiplier is applied.