Educational Psychology / Unit 12 EDP 1145 worked example, 60 to 90 seconds
Standard Scores and Percentiles
The idea
Standard scores restate a raw score by its distance from the mean in standard deviations. A z score has a mean of 0 and a standard deviation of 1. A T score has a mean of 50 and a standard deviation of 10, so T equals 50 plus 10 times z. A stanine has a mean of 5 and a standard deviation of 2, running from 1 to 9. On the normal curve, a z of 0 is the 50th percentile, a z of 1 is about the 84th, and a z of 2 is about the 98th.
In practice
Worked example: a student scores 60 on a test with a mean of 50 and a standard deviation of 10. The z score is 60 minus 50, divided by 10, or 1. The T score is 50 plus 10, or 60. The stanine is 5 plus 2, or 7. The percentile is about the 84th. A classmate scoring 40 has a z of minus 1, a T of 40, a stanine of 3 and a percentile of about the 16th.
Where people slip
A z of 2 is about the 98th percentile, not the 84th; the 84th belongs to a z of 1. Every standard score carries the same information on a different scale, so converting through z keeps the conversions straight.
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