A standard score measures how far a particular value, or score, is from the mean, or average value of a set of scores. This distance from the mean value is the standard deviation (SD). There are many different types of standard score scales, each with specific known mean value and SD. T scores are one type of standard score, with a mean value of 50 and a SD of 10. Standard scores are equivalent scores, so that a standard score of one scale, such as a T score, can be converted to the standard score of another scale, using the mean value and SD for each scale.
Things You'll Need
Original T score value
Mean value and SD value of T score
Mean value and standard deviation (SD) value of standard score
Calculator
Show More
Instructions
1
Record the mean value and the SD for both the T score and the standard score to be calculated. Remember that the T score has a mean value of 50 and a SD of 10.
2
This is just a simple linear transformation.
Subtract the T score's mean value of 50 from the T score value you wish to convert. Divide this number by the T score's SD of 10. This formula gives the "standardized" value for the T score: (score - mean) / standard deviation.
3
Multiply this standardized value by the SD of the standard score to which you are converting.
4
Add this value to the mean value of the standard score. This value is the standard score that is equivalent to the original T score.