The Bell Curve
(Also called the Normal Curve, or the Gaussian Curve)
Below average Above average
About 2/3 (i.e., 68%) of those tested obtain Standard Scores between 85 – 115.
50% (i.e., half) score below the mean | 50% or half score above the mean.
Colored bell curve courtesy of David W. Stockburger, Introductory Statistics: Concepts, Models, and Applications, http://www.psychstat.smsu.edu/introbook/sbk11m.htm; scales and text added.
Standard Score (SS)
Educational and psychological total test results are re-expressed in Standard Scores, where the mean (i.e., average) is set to be 100. In general, the examiner determines the total correct responses (with or without a correction for guessing) to obtain a “raw score.” The raw score is then converted to the Standard Score using charts and tables that are provided with each test.
Scaled Scores have a mean (or average) score of 10 with a Standard Deviation of 3. Thus, a Scaled Score of 13 is ABOVE the AVERAGE. On the WISC-III, Scaled Scores on the sub-tests are used to make up the total or Composite Score – on the WISC-III, this is called the Full Scale IQ Score.
Percentile Score* or Rank shows in a more familiar format how the child scored when compared to other children who are the same age or grade. If a child has an IQ of 85, he or she scored at the 16thpercentile, which means that 84% of the children tested scored higher than that child. Like Standard Scores, Percentile Scores can be compared from one test to other tests, if each of the tests are Norm-Referenced.
*NPR scores are not the same statistically as “percentile.” See page 257 of the Home Educators of Virginia Manual for detail.
Stanine Scores essentially represent Standard Scores, with a range from 1-9. The average (or mean) score is 5. It is a relatively “coarse” measurement that allows comparison of scores from one test standardized test to another.
1 2 3 4 5 6 7 8 9
low | AVERAGE | high
WHAT DOES “AVERAGE” MEAN?
One half of all children tested on a given test will obtain a total test score between the 25th percentile and the 75th percentile. This is considered the “AVERAGE” percentile range.
- On Scaled Scores, the “AVERAGE” score falls between 8 – 12.
- On IQ tests, the “AVERAGE ” is a full scale Standard Score between 90 – 110 (or sometimes 85 – 115.)
Two thirds or 68% of all children tested obtain Standard Scores between 85-115 on an IQ test. On the Bell Curve, these scores fall between: One standard deviation above the mean of 100 (i.e., 115) and one standard deviation below the mean of 100 (i.e., 85).
When your child is tested with standardized tests, it is very helpful to hand draw a “bell curve” and arrange your child’s scores along the Standard Score axis (SS number line) to see how scores have changed from previous test data. Declining scores are a warning that some adjustments are needed.
Grade Equivalent Score
A child’s actual performance on a test — the number answered correctly and termed a “raw score” — may be converted to a Grade Equivalent score. The Grade Equivalent score expresses the grade level of students who on average get that raw score. So, for example, if a 3rd grade child who is tested achieves a raw score of 10 points, and children near the end of 1st grade (at the 9th month) on average earn a raw score of 10 points, the 3rd grade child will be assigned a GE score of 1-9 (sometimes written 1.9). “Grade Equivalent scores are based on the assumption that it is helpful to define progress in terms of the grade-level at which an average student attains a given level of knowledge or skill.” (www.ets.org/letstalk, p. 3)
This information can be very interesting, but the parent should not conclude that the 3rd grade child has math skills that are identical to those of a student at the 1-9 level. Let’s say the child gets a few addition problems correct, a couple of subtraction problems correct, but not subtraction with regrouping, and several single digit multiplication problems correct. The testing shows some skills are lacking, but shows some good 2nd and 3rd grade math skills as well, beyond those expected for a 1st grade child.
Parents need to use caution with Grade Equivalent scores. They present an overall approximation of grade level achievement, but it is important to analyze the error pattern to fully understand strengths and weaknesses.
GE score differences from one school year to the next are less meaningful at upper grade levels, since students do not make as much steady progress in skill mastery as they do in lower grade levels.
Standard Scores are converted to GE scores with tables provided by the test manufacturer. The GE score permits the examiner to state the approximate grade level at which the child is performing in a specific skill or on a certain test. Recently fallen out of favor with educational testing researchers, GE scores can still provide some useful information if it is understood that a single GE score does not mean the child is working at that grade level in all areas. It most certainly does not mean that the child should be placed at the corresponding grade level, unless there is solid supporting documentation.
Age Equivalent Score
The Standard Scores can also be statistically converted to show the typical age of the norm group that obtained a similar score. Like the Grade Equivalent Scores, Age Equivalent Scores permit comparison of the child’s scores with those of others who were tested on the same test. Age Equivalent Scores have the same limitations as Grade Equivalent Scores.
Additional Information on Test Terms and Skill Remediation
http://www.bjup.com/services/testing — A link for Bob Jones University testing services. A very helpful page with information that will help parents understand the terms used in test reports on their children. The site also provides useful suggestions for addressing skills found to be below average, with specific ideas for remedial actions.