T Scores

A T score is a type of standard (not standardized) score that has a mean of 50 and a standard deviation of 10. It is very similar in concept to a z score, which has a mean of 0 and a standard deviation of 1.

T scores are used when the researcher wants to convert raw scores to a metric that is comparable across distributions (different sets of scores) and where there is a desire to have all scores as positive values (which is the case unless a raw score is more than 3 standard deviations below the mean).

The formula for T score is

where

T is the T scores,

50 is the mean of the set of T scores,

10 is the amount that one T score deviates from the mean, and

z is the corresponding z score for a particular raw score.

For example, here is a set of raw scores and their corresponding z scores and T scores:

Raw Score	z Score	T Score
6	1.17	61.65
4	−0.78	42.23
5	0.19	51.94
4	−0.78	42.23
3	−1.75	32.52
6	1.17	61.65
5	0.19	51.94
4	−0.78	42.23
5	0.19	51.94
6	1.17	61.65

You can see that a raw score with a z score close to the mean of the distribution (which is 4.8) is the closest to 50 and that all the T scores are well within the positive range.