How to Calculate a Japanese Deviation Value (T-score)

Calculates the Japanese deviation value (T-score) as 50 + 10 × (score − mean) ÷ standard deviation. A score at the mean gives 50, and one standard deviation above gives 60.

Explanation

The deviation value, or T-score, is the standard way of expressing a position within a group in Japan. It rescales scores so that the mean becomes exactly 50 and one standard deviation becomes 10.

T = 50 + 10 \times \dfrac{x - \bar{x}}{\sigma}

Here $x$ is the score, $\bar{x}$ the mean and $\sigma$ the standard deviation.

Example

With a score of 80, a mean of 60 and a standard deviation of 10:

T = 50 + 10 \times \dfrac{80 - 60}{10} = 50 + 10 \times 2 = 70

The score sits two standard deviations above the mean, giving a T-score of 70.

Rough guide

If the scores are close to a normal distribution, the T-score maps onto a percentile roughly like this:

60 — top 16% or so
70 — top 2.3% or so
80 — top 0.13% or so

Watch out

The same raw score gives different T-scores in different groups. Scoring 60 on a hard exam is worth far more than 60 on an easy one
T-scores are not confined to the 0–100 range; an extreme result can exceed 100 or fall below 0
If the score distribution is far from normal, the percentile guide above does not hold
A standard deviation of zero, where everyone scores the same, makes the calculation impossible