Standard score

by Yuvi - March 12, 2022

Standard scores: Z AND T

Z-Scores

Definition of Z-scores:

Z-Scores are a transformation of raw scores into a standard form, where the transformation is based on knowledge about the population’s mean and standard deviation.

Z-Scores are a transformation of individual raw scores into a standard form, where the transformation is based on knowledge about the standardization sample’s mean and standard deviation. The formula for computing Z-scores is the individual raw score (X) minus the mean of the scores obtained by the standardization sample (M), divided by the standard deviation of scores obtained by the standardization sample.

Z-scores have a mean of 0 and a standard deviation of 1. A score that is one standard deviation below the mean has a Z-score of -1. A score that is at the mean would have a Z-score of 0.

What is T-Scores

T-scores are standard scores with a mean of 50 and a standard deviation of 10. Z-scores can be transformed into T-scores scores by multiplying the given Z-score by 10 (the standard deviation of the distribution of T-scores), and adding 50 (the mean of the distribution of T-scores) to this product. For example, a Z-score of –1 equals a Deviation IQ of 40 [50 + 10(-1) = 40].

Definition of  T-scores

T-Scores are a transformation of raw scores into a standard form, where the transformation is made when there is no knowledge of the population’s mean and standard deviation.

The scores are computed by using the sample’s mean and standard deviation, which is our best estimate of the population’s mean and standard deviation.

Output:-