Note that the SB-4 has been obsolete for a long time now... not sure why anyone is still using it. Also, note that whoever did the testing is responsible ethically for answering at least this kind of basic question in a written report.
Scores are calculated by comparing the raw score of the individual to the raw scores of the norming sample at the same age. The scaled score is based upon the number of standard deviations off the population mean that this individual's raw score was. Subtest scaled scores on most measures are set to mean=10, standard deviation=3, composite standard scores on most measures (and subtest scaled scores for many measures) are set to mean=100, standard deviation=15. So if you were two standard deviations above the mean, you get a scaled score of 16 or a standard score of 130.
To make the composite scores, the scaled scores are added together and this number becomes the new "raw score." It gets compared to the sums-of-scaled-scores for the rest of the norming sample, same as before.
No, the "Q" no longer stands for "quotient." It doesn't stand for anything. IQ just means IQ.
Yes, if all of the scores that go into a composite are different from the mean in the same direction, then the resulting composite is going to generally be further from the mean in that same direction than the average of those scores might suggest. That is, if you get subscores of 125, 130, and 135, the composite might be 135 or even 140. It's more unusual to be unusual at lots of things simultaneously than it is to be unusual at only one.
Does that help?
Thanks! Yes, it is obsolete. I decided to check out the only piece of paper I have... these were my scores when I was 6 or something. The school counselor had sas standard sub scores and added them up incorrectly for the sum of sas, leaving off 10 points. But by using the stuff you just told me, if my shaky memory of stats is right, it would seem it only cost me 3 composite IQ points, which still would have left me a few points short of the gifted program. (Though, I wonder at the fact that he could make an error like that on a test that is so important to a child's academic future...)
But, anyway, I just had a whole lot of fun trying to remember statistics to see if I could get the right numbers to come out, though. My lowest score was a modest .7+ sd from the norm in abstract reasoning and it still shows. I muddle through math problems and come up with half forgotten things and somehow / sometimes / maybe solve them... as long as I know what the answer should look like. lol
