With the publication of the new WJ IV, an old score issue has again resurfaced. Examiners have observed that often an individual's overall GIA score is lower than the arithmetic average of the scores for the component tests. This occurs when an individual consistently scores below average on the component tests. For individuals who score significantly above average on most tests, the GIA is higher than the arithmetic average of the components (the opposite effect).
This is not a new phenomenon and is NOT unique to the WJ battery. I've written about this previously with Joel Schneider. A link to a special report can be found here.
Joel Schneider has a great explanation (with videos) of this phenomenon at his awesome blog.
Finally, I first wrote about this in 1994 and have re-posted this material (from my first WJ book) for download (PDF file).
In these explanations one will see that the “total does not equal the sum of the parts” phenomenon also occurs on the Wechslers, but it is HIDDEN from view via the fact that the Wechslers use standard scores (mean=10 plus/minus 3) for subtests. In my 1994 explanation, I present a fictitious case where a child obtains 4's on all WISC-R subtests (-2 SD). Since a standard score on a subtest of 4 is -2 SD, these scores would be equal to a standard score (mean=100; SD=15) of 70. The child would have70's for all subtests. The arithmetic average of all subtests would be 70. So.....is the WISC-R full scale IQ approximately 70? No. It is 59, or 11 points lower!
Bottom line. This phenomenon has been around for years and is present on all IQ tests. It is more obvious on the WJ batteries were all subtests and cluster scores are on a common 100/15 scale. This is nothing new. If you have been using other batteries (e.g.Wechslers) you simply have not had the opportunity to observe it.
I am currently working with a colleague on a special Assessment Service Bulletin to explain this score issue. I will notify readers of its availability as soon as it is completed.