Why Might the Full-Scale IQ Be Lower Than the Index or Ability Scores?
Why is the Full-Scale IQ sometimes lower than each of the index scores that compose it? This phenomenon is called the Composite Score Extremity Effect and it occurs when several of the index scores, though not necessarily all of them, are low. This is not a flaw in the test. This occurs in every test that includes composite or index scores—that is, scores calculated from several other scores. For example, when a child has a scaled score of 85 (when the mean is 100 and the standard deviation is 15) on every test in a battery, the child’s Full-Scale IQ may be 80, not 85. Why does this happen?
When one broad ability is low while the child’s other abilities or index
scores are within the average range, the low broad-ability score may indicate a
specific area of weakness within otherwise average overall functioning. However,
when several cognitive abilities or index scores are low, a cumulative effect
occurs. The low abilities
interact with one another and “pull” one another down. The resulting
level of overall functioning may therefore be lower than any one of the
individual ability scores. A person with a sprained ankle limps; a person with
two sprained ankles may be unable to walk at all.
For example, suppose a child has low crystallized knowledge, low fluid
ability, and poor short-term memory. None of these difficulties affects only
its own domain. They also affect one another. Difficulty with abstraction,
which is related to fluid ability, interferes with the accumulation of
crystallized knowledge. Poor short-term memory interferes with fluid reasoning,
because one cannot think about pieces of information and integrate them when one
is not able to hold them in short term memory
The Composite Score Extremity Effect becomes stronger when an ability,
index, or Full-Scale IQ score is based on a larger number of tests; when the
correlations among those tests are lower; and when the child’s test scores are
more extreme, whether very low or very high.
The effect applies equally to high scores. When a child’s cognitive
abilities or index scores are above average, the child’s Full-Scale IQ will
tend to be even higher than each of the individual ability or index scores. A
person who sings extremely well may have a successful career as a soloist or as
a member of a musical ensemble. A person who can sing, dance, and act extremely
well has many more possible career paths.
The Composite Score Extremity Effect also has a statistical explanation.
When scores with the same standard deviation are averaged, the standard
deviation of the average is smaller than the standard deviation of the original
scores. To give the resulting index or ability score the same mean and standard
deviation as the scores from which it was calculated, the average score must be
converted to the standard reporting scale. This conversion from a distribution
with a smaller standard deviation to one with a larger standard deviation
causes the index or ability scores to become more dispersed. They move farther
away from the mean and therefore become more extreme. Had the test developers
not performed this conversion, each index or ability score would have had its
own standard deviation, making the scores much less convenient to interpret.
The potential confusion caused by the Composite Score Extremity Effect is therefore
the price we pay for the convenience of reporting all scores on the same scale,
with a mean of 100 and a standard deviation of 15.
Schneider, W. J. (2016). Why are WJ IV cluster scores more extreme
than the average of their parts? A gentle explanation of the composite score
extremity effect. Itasca, IL.
http://www.nelson.com/assessment/pdf/wjiv_asb_7.pdf
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