Standard Scores
A standard score indicates how far a given raw score is from the mean, in terms of standard deviation units. A standard score is the appropriate measure of relative position when the data represent an interval or ratio scale. The most commonly used standard scores are z scores and stanines.
z Scores. The z score is the most basic standard score, with a mean of 0 and a standard deviation of 1. Thus, a z score of +1 is at the 84th percentile for a normal distribution, –1 is at the 16th percentile, and –2 is at the 2nd percentile. Other standard scores are linear transformations from the z score, with arbitrarily selected means and standard deviations. That is, it is possible to choose any mean and any standard deviation. Most IQ tests, for example, use 100 as the mean and 15 or 16 as the standard deviation. The resultant IQ score is a standard score (the ratio IQ, mental age divided by chronological age times 100, is rarely used today).
