Standard scores are based on which concept?

Standard scores are based on which concept?

• A. T-scores
• B. Z-scores
• C. Percentile ranks
• D. Raw scores

Answer: (B)

Standard scores come from expressing a raw score in terms of how far it lies from the mean, using the spread of the distribution. This is the z-score idea: Z = (X − μ) / σ, where μ is the mean and σ is the standard deviation. By converting scores this way, you get a distribution with a mean of 0 and a standard deviation of 1, which lets you compare performance across different tests or groups. That foundational concept is what standard scores hinge on. T-scores and other scaled scores are just convenient linear transforms of those z-scores (for example, T equals 50 plus 10 times Z), but they still rest on the same idea of standardizing via the mean and standard deviation. Percentile ranks, on the other hand, reflect relative position in the distribution rather than distance from the mean in standard deviation units. Raw scores are the original values, not standardized at all.

Standard scores come from expressing a raw score in terms of how far it lies from the mean, using the spread of the distribution. This is the z-score idea: Z = (X − μ) / σ, where μ is the mean and σ is the standard deviation. By converting scores this way, you get a distribution with a mean of 0 and a standard deviation of 1, which lets you compare performance across different tests or groups. That foundational concept is what standard scores hinge on.

T-scores and other scaled scores are just convenient linear transforms of those z-scores (for example, T equals 50 plus 10 times Z), but they still rest on the same idea of standardizing via the mean and standard deviation. Percentile ranks, on the other hand, reflect relative position in the distribution rather than distance from the mean in standard deviation units. Raw scores are the original values, not standardized at all.