A standard deviation (SD) is a quantity derived from the distribution of scores from a normative sample. The standard deviation is the average distance (or deviation) from the mean.
If the mean score is 50 and the average distance of the scores from the mean is 15, then one standard deviation is equal to 15 in this sample. Standard deviation is also a measure of how closely centered scores are around the mean. If scores are widely distributed, the average distance will be further than if they are closely centered around the mean.
Standard deviations are often used in norm-referenced tests to diagnose language impairment. Those scores that fall within one SD of the mean are considered to be typically developing. Disability is often diagnosed at 1.5 to 2.0 SD below the mean. However, research has demonstrated that using standard deviations to diagnose language impairment does not accurately identify language impairment with acceptable specificity and sensitivity (Spaulding, Plante & Farinella, 2006).
Issues in norm-referenced testing with culturally and linguistically diverse children
As with any statistical measure used in norm-referenced testing, it is important to remember that it is comparing (i.e., deriving how many standard deviations away from the mean it is) the child’s performance to the test’s normative sample. If this sample is not representative of the child’s speech community, it is not a valid measurement of the child’s speech and language development.
Spaulding, T.J., Plante, E. & Farinella, K.A. (2006). Eligibility criteria for language impairment: Is the low end of normal always appropriate? Language, Speech, and Hearing Services in Schools, 37, 61-72.