Summary of z-Score

A z-score indicates how many steps a person is from the mean. A raw score below the mean corresponds to negative z score; a score which is above the mean would have a positive z. The standard deviation indicates how big each step is. Approximately 68% of the scores lie within one standard deviation of the mean. That is, a majority of the distribution is from z = -1 to z = +1.

 There are 5 primary applications of z-scores:

a. locating an individual score 

b. using z as a standard. Individual raw scores are converted to z-scores and compared to a set standard. Two common standards are z = 1.65, which represents a 1-tailed area of 95%, and z = + 1.96 or – 1.96 (between which is a 2-tailed area of 95%).

c. standardizing a distribution and smoothing its data.

d. making a linear transformations of variables; converting the mean and standard deviation to numbers that easier to remember or handle.

e. comparing 2 raw score distributions with different means and standard deviations.