Standardized Test Score Analyzer
Convert raw test scores into standardized metrics including z-scores, T-scores, percentile ranks, and stanines using population mean and standard deviation.
Results will appear here.
Formulas Used
Z-Score: z = (X − μ) / σ
T-Score: T = 50 + 10 × z
Percentile Rank: P = Φ(z) × 100, where Φ is the standard normal CDF
Normal Curve Equivalent (NCE): NCE = 21.06 × z + 50
Stanine: 9-point scale derived from z-score boundaries (−1.75, −1.25, −0.75, −0.25, 0.25, 0.75, 1.25, 1.75)
Percentage Correct: (Raw Score / Max Score) × 100
Assumptions & References
- Scores are assumed to follow a normal (Gaussian) distribution within the population.
- The CDF approximation uses the Horner-form polynomial method (Abramowitz & Stegun, 1964), accurate to ±1.5 × 10⁻⁷.
- T-scores are scaled to a mean of 50 and SD of 10, commonly used in psychological and educational testing (e.g., SAT predecessor scales).
- NCE scores range from 1–99 with a mean of 50 and SD of 21.06, preserving equal-interval properties (RMC Research, 1981).
- Stanine boundaries follow the standard Educational Testing Service (ETS) convention.
- Performance bands are based on percentile thresholds: ≥90th (Exceptional), 75–89th (Above Average), 25–74th (Average), 10–24th (Below Average), <10th (Well Below Average).
- Population mean and standard deviation must be known (e.g., from a norming study or test publisher data).