Z-Score (Standard Score)
The Universal Translator of Statistics
In the world of psychometrics, raw scores are meaningless. Getting a “35/40” on a test tells you nothing unless you know how hard the test was and how everyone else did.
A Z-Score (or Standard Score) solves this by converting any raw score into a universal language based on the Normal Distribution. It tells you exactly how far a score deviates from the average.
How to Read a Z-Score
The formula is: Z = (Score - Mean) / Standard Deviation.
On most modern IQ tests (like the WAIS or Stanford-Binet), the Mean is 100 and the Standard Deviation (SD) is 15.
- Z = 0: The score is exactly average (IQ 100).
- Z = +1.0: The score is 1 SD above average (IQ 115). This is the top 16% of the population.
- Z = +2.0: The score is 2 SD above average (IQ 130). This is the threshold for Giftedness and the top 2%.
- Z = +3.0: The score is 3 SD above average (IQ 145). This is the level of “Genius” or high achievement, occurring in only 1 in 740 people.
- Z = -1.0: The score is 1 SD below average (IQ 85).
Why It Matters
Z-Scores allow psychologists to compare results across different tests. If you score an IQ of 130 on the WAIS (SD 15) and an IQ of 132 on the Stanford-Binet (SD 16), which is better?
- WAIS Z-Score: (130-100)/15 = +2.0
- Stanford-Binet Z-Score: (132-100)/16 = +2.0
They are identical. Z-Scores reveal the truth behind the numbers, making them essential for diagnosing intellectual disabilities or identifying high potential.