Definition
A z score is a standard score. Standard scores (e.g., z scores, T scores, and IQ scores) result from a transformation of raw scores to facilitate interpretation. A z score has a mean of zero and a standard deviation of 1. The formula for a z score, commonly used in neuropsychology, is provided below:
where
x is a raw score to be standardized.
M is the mean of the control or normative sample.
SD is the standard deviation of the control or normative sample.
Current Knowledge
For ease of communication in clinical reports, z scores can be converted to percentile ranks. The percentile rank represents the percentage of scores in a frequency distribution that are lower than the obtained score (e.g., the 25th percentile means that 25% of scores are lower). This conversion is illustrated in Table 1.
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References and Readings
Brooks, B. L., Strauss, E., Sherman, E. M. S., Iverson, G. L., & Slick, D. J. (2009). Developments in neuropsychological assessment: Refining psychometric and clinical interpretive methods. Canadian Psychology, 50, 196–209.
Strauss, E., Sherman, E. M. S., & Spreen, O. (2006). A compendium of neuropsychological tests: Administration, norms, and commentary (3rd ed.). New York: Oxford University Press.
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Iverson, G.L. (2011). Z Scores. In: Kreutzer, J.S., DeLuca, J., Caplan, B. (eds) Encyclopedia of Clinical Neuropsychology. Springer, New York, NY. https://doi.org/10.1007/978-0-387-79948-3_1263
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