Understanding Standard Scores

The major purpose of standard scores is to place scores for any individual on any variable having any mean and standard deviation on the same standard scale so that comparisons can be made. Without some standard scale, comparisons across individuals and/or across variables would be difficult to make (Lomax,2001, p. 68). In other words, a standard score is another way to comapre a student's performance to that of the standardization sample. A standard score (or scaled score) is calculated by taking the raw score and transforming it to a common scale. A standard score is based on a normal distrbution with a mean and a standard deviation (see Figure 1). The black line at the center of the distribution represents the mean. The turquoise lines represent standard deviations.


Figure 1.

standard normal distribution.jpg


On many standardized assessments the publishers base the standard score on a distribution with a mean of 100 and a standard deviation of 15. A score of 100 on such a test (e.g., WJIIIDRB) means that if the student scored in the middle of the distribution (Mercer & Pullen, 2009). A Standard Score of 85 indicates that the student scored one standard deviation below the mean of the normative sample. Figure 2 illustrates a normal distribution of test scores with a mean of 100 and a standard deviation of 15. The standard deviation is an indication of the variability of scores in a population (Mather & Jaffe, 2002).


Figure 2.