On the FSIQ, the apparent difference between index scores and the IQ is most likely because of the infrequency of earning high index scores in all of the index areas at the same time. It is more likely that someone in the standardization sample received only one of those high index scores than that they received multiple high scores, and this is reflected in the IQ. However, it looks like you received the WPPSI-III, which is not the latest version. (The WPPSI-IV came out in North America in 2012, and in AU/NZ in 2014. If you are in AU/NZ, it is still okay to have used the III, as that was just this year.)
(I'm assuming, by the way, that you are talking about the North American edition of the WIAT-III. If this is an international version of the WIAT-II, there will be some slight differences.)
apm221, you are correct about the WIAT. One of the disadvantages for young high-performers is that the test is not welcoming to out-of-level testing. At age 5, there are age norms only for preK and K skills, which are largely pre-academic. The first grade subtests were probably more skill-appropriate. However, in this situation, I would have given all of the age-appropriate subtests, in order to be able to generate some age-normative achievement data, and then added what was necessary to obtain a complete set at the estimated grade-appropriate level, so that I would be able to compute composite scores.
These are the composites that should have been available for kindergarten:
Oral Language (probably not that important in this case): 2 subtests (listening comprehension, oral expression)
Written Expression: 2 subtests (alphabet writing fluency, spelling) (not available for AU/NZ)
Mathematics: 2 subtests (math problem solving, numerical operations)
If awf and mps had been administered, you should have been able to get age-normed composite scores in writing and mathematics. The same subtests (plus sentence composition) would get you the writing composite on the first-grade norms, and the same subtests unchanged would get you math on the first-grade norms. In order to get composite scores in reading, you would have had to go up to first grade norms and have reading comprehension, word reading, pseudoword decoding, and oral reading fluency.
Early Reading Skills does not go into any composite, except the Total Achievement Composite, which samples all academics. I suppose if you wanted to, you could make a case for using it as a reading composite, since it is the only age-normed measure of reading for 5-year-olds on the WIAT-III.
So, in summary:
1) Yes, the psych skipped some necessary subtests for age-normed composite scores in writing and math.
2) Puzzling: the psych should not need additional tables to calculate age norms, as the age and grade norms are all in the same document (paper or pdf).
3) Partially: it is possible to calculate some of the composites at age 5 (writing, math), but not others (reading). Unless this is the WIAT-II, in which case math is an option, but not the others.
With regard to reading comprehension and oral reading fluency, there are particular limits on those subtests, because there are grade-restricted item sets, with provision for dropping levels for low-performers, but not for upping levels for high-performers. Early reading skills is indeed not administered after third grade.
I think what the psych did was to give three out of the seven possible kindergarten subtests, and then to score them using first grade norms. Or, the WIAT-II abbreviated (international edition), which only has those three subtests. Or the Wechsler Fundamentals, which is the NA abbreviated form (except that it has reading comprehension, which could have been administered to generate a reading composite).
Bottom line, you did not receive a comprehensive assessment of achievement. Effectively, this was only a screening of achievement. Perfectly reasonable for an NT or low-performing K student, but not for a high-performing student.
