What is a z-score in the context of normative data?

What is a z-score in the context of normative data?

• A. Expresses the percentage of scores above the mean.
• B. Expresses how many standard deviations a score is from the reference mean.
• C. Represents the median of the distribution.
• D. Indicates the minimal detectable change.

Answer: (B)

A z-score is a standardized score that shows how many standard deviations a particular score is from the reference mean. It’s calculated by subtracting the mean of the normative sample from the individual’s score and dividing by the standard deviation: z = (X − μ) / σ. This places scores on a common scale, so you can compare results across tests or understand where someone sits relative to the normative group. A z-score of 0 means the score is at the mean; a positive value means above the mean, a negative value means below. For example, a score one standard deviation above the mean has z = +1; one below has z = −1. Under the standard normal assumption, z-scores can be translated into approximate percentile ranks, though exact percentiles depend on the distribution. The other options describe proportion above the mean, the distribution’s median, or a change threshold, none of which are what a z-score represents.

A z-score is a standardized score that shows how many standard deviations a particular score is from the reference mean. It’s calculated by subtracting the mean of the normative sample from the individual’s score and dividing by the standard deviation: z = (X − μ) / σ. This places scores on a common scale, so you can compare results across tests or understand where someone sits relative to the normative group. A z-score of 0 means the score is at the mean; a positive value means above the mean, a negative value means below. For example, a score one standard deviation above the mean has z = +1; one below has z = −1. Under the standard normal assumption, z-scores can be translated into approximate percentile ranks, though exact percentiles depend on the distribution. The other options describe proportion above the mean, the distribution’s median, or a change threshold, none of which are what a z-score represents.