Standard Score

A standard score is an individual score that has been transformed into a number that shows a person's relative status in a distribution of means. To convert an individual score to a standard score, the distance (deviation) of the individual score from its mean (i.e., the average score of the distribution) is computed, and that distance is converted into the number of standard deviations (i.e., the square root of the average squared distance of a set of scores from their mean) that score falls above or below the mean.

Although many different kinds of standard scores have been developed, the ones used most frequently are called Z-scores and T-scores. If the length of an imaginary yardstick is used to define a standard deviation, then that yardstick can be used to measure the distance between the group mean and the individual score being considered. For Z-scores, the mean is fixed at zero and the yardstick's length (i.e., the standard deviation) is set at 1.0. For example, a person whose Z-score is −1.5 would indicate that this individual scored 1.5 standard deviations below the mean. A T-score is a converted Z-score and has a mean of 50 (i.e., the average) and a standard deviation of 10. Suppose a school psychologist has been asked to evaluate the aggressive behavior of a kindergarten student. He or she asks the student's teacher to complete a behavior rating scale, a measure used to assess one or more student behaviors, and finds the student's aggressive behavior score to be a 70, which is two standard deviations above the average score for this instrument. The school psychologist would then know that this child exhibits much higher levels of aggressive behavior than his or her peers.