What is the difference between a z-score and a T-score?

A z-score has mean 0 and SD 1 (range typically −3 to +3). A T-score is a linear transformation: T = 50 + 10z, giving mean 50 and SD 10. T-scores are preferred for reporting because they avoid negative numbers and decimals. Most norm-referenced educational assessments use T-scores or scaled scores (mean 100, SD 15).

What is a stanine score?

Stanine (standard nine) divides the normal distribution into 9 bands: 1 (below 4th percentile) to 9 (above 96th percentile). Stanine 5 contains the middle 20% (40–59th percentile). Stanines were developed during WWII for pilot selection tests and are still used in educational measurement for their simplicity.

Test Score Scaling and Standardisation Calculator

How It Works

Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development

Note: Interpret the test score scaling result against the clinical thresholds and context described above.

How to Use

Enter the values for the patient or scenario you are assessing. Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development. Use the test score scaling result to inform your clinical assessment.

Glossary and Definitions

Test score scaling: A key concept in Test Score Scaling: Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development.
Z-score conversion: A key concept in Test Score Scaling: Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development.
T-score: A key concept in Test Score Scaling: Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development.
Stanine: A key concept in Test Score Scaling: Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development.
NCE score: A key concept in Test Score Scaling: Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development.
Standardised score: A key concept in Test Score Scaling: Convert raw test scores to z-scores, T-scores, NCE scores, stanines, and scaled scores. Apply linear equating and area transformation methods. Used in psychometrics, educational assessment, and standardised test development.