This is an excerpt from an article about scores on standardized tests.
In determining the screening pool, I learned, Fairfax County Public Schools uses standard age scores. The SAS is based on a normal curve, a curve also known -- because of its shape -- as a bell curve: it is symmetric; high near the middle, where many data points cluster; and tapering off near the ends, where the data thin out. Just how much the data are concentrated in the middle is measured by something called the standard deviation. The bigger the standard deviation, the flatter and thinner the curve and the more spread out the scores. About 68% of data fall within one standard deviation of the midpoint, with half the rest, about 16% of data points, falling more than one standard deviation above the midpoint; about 95% of data fall within two standard deviations, with less than 3% falling more than two standard deviations above the midpoint.
How do these concepts apply to the test data?
The bell curve's high middle and low extremes mean most scores are concentrated near the middle, so that a child who is well above average may still score closer to 100, the midpoint, than to the 150, the high end. According to "Basic Information about the Cognitive Abilities Test" -- which I found on the Web site of Riverside Publishing, (Riverside publishes the CogAT), the CogAT has a standard deviation of 16. That means, for example, that an 84th percentile score translates to 116 on the SAS scale -- in other words, 34 percentile points above the midpoint translates to only 16 SAS points. At the extreme, on the other hand, SAS scores change more quickly relative to percentile scores, so that the 98th percentile comprises SAS scores from 133 through 137. As "Basic Information" puts it, "The SAS scale provides fine discriminations among high-end and low-scoring students."
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