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A Full Scale I.Q. (FSIQ) of 158-160 is different than an a General Ability Index (GAI) of 158-160.

According to Pearson's free online pdf document, "The What, When, and How of the Wechsler General Ability Index": emphasis added

A large discrepancy in scores may indicate a learning disability. A gifted child with a learning disability may be called twice exceptional (2e). If this may apply to your child you may benefit by becoming familiar with wrightslaw and the book From Emotions to Advocacy.

sully, was this score on a WISC IV or another test (I believe the WPPSI may have or also has a GAI)? This may be helpful from the Davidson database:

"What does it mean when a child scores within the gifted range on the Verbal Comprehension and Perceptual Reasoning Indices and shows much lower scores on the Working Memory and Processing Speed Indices of the WISC-IV?

It is common for gifted children to show significantly lower scores on the Processing Speed and Working Memory Indices of the WISC-IV, when compared to their performance on the Verbal Comprehension and Perceptual Reasoning Indices. However, very large discrepancies can sometimes be indicative of problems with attention or something else that is getting in the way of a child being able to focus or process and respond to information quickly (i.e., anxiety, depression, visuomotor coordination, perfectionism). When this is the case, a comprehensive neuropsychological evaluation would be required to help tease this apart.

What is the General Ability Index (GAI) of the WISC-IV?

The General Ability Index (GAI; WISC-IV Technical Report No. 4, 2005) provides an estimate of general cognitive ability that is less sensitive to the influence of working memory and processing speed. This may be used as a substitute for Full Scale IQ to determine eligibility for placement classification. The GAI is often used instead of the Full Scale when assessing gifted children. Because the processing speed index (PSI) and working memory index (WMI) of the WISC-IV are not the best indicators of intellectual ability, many clinicians don’t administer them when assessing for giftedness and it is not uncommon to only report the GAI ."

My understanding is that it is NOT uncommon for a HG+ child to have a higher GAI than FSIQ, and that it is not necessarily indicative of a learning disability.

I will defer to someone more knowledgeable about the rarity of the score, but I believe that most charts I have seen suggest that it is well above the 99.9 percentile.

Here's the link I always share:
http://www.iqcomparisonsite.com/iqtable.aspx

From that you can translate the normal score (158-160.) I'd probably round it to 1 in 25,000 if I wanted reference it.

These are standard scores that represent a position on a curve. To translate to a percent, you only need to know the middle point and the size of a standard deviation. These tend to be 100 and 15 respectively.

So, whether it is an achievement test, an IQ, FSIQ, GAI, a military placement score, or whatnot. With the same mean and standard deviation, it translates to the same percentage. It's part of the appeal of standard scores.

Now whether IQ is in truth a Guassian or Ln-Normal or other distribtuion is another topic.

Here is everything you ever wanted to know but were afraid to ask about the GAI and the WISC-IV. All it says is ">99.9" starting at 150. However, it does have a discussion about discrepancies between the GAI and FSIQ.

ETA from that booklet:

Just a small point for OP - are you talking about a GAI calculated from extended norms? It's probably not material to your question since either way it's >99.9. But if you were somehow trying to get more granularity on that (i.e., is it >99.9 or 99.99 or 99.999, etc.), the distinction might be important.

Or not. I'm really ignorant here. But I do see the note re "extended norms" systematically attached to our DS's scores and discussions about them.

Currently, 158-160 is interpreted as meaning 99.99 %ile, or one in 10,000. Above comments on the questionable gaussian distribution of IQ do apply, but we have little hard data on this, due to rather small available population for study.

Another factor is that it's a bit easier to get a high score if you pick your best score out of FSIQ, GAI, VCI, PRI, etc.

Fwiw, I didn't understand how this was a factor either. Could you explain?