I see your point about an extra percent or two�it is theoretically possible, given a standard rounding assumption, that 15/1000 outscored (versus just tied) my son on math, and 25/1000 outscored (versus just tied) my son on reading...and it is possible that all of the 25 who possibly outscored by son on reading were one lower on the math section (thus met or exceeded my son's total score); and all of the 15 that possibly outscored my son on math were one lower on the reading section (thus met or exceeded my son's total score); no overlap between the perfect or one point from perfect scores in the two sections; thus yielding 40 total students (4%) at or above my son's score. Everyone else who was one point lower than my son in either the math or reading section could not catch up to meet his total score, as the 25/1000 and 15/1000 who met or exceeded (in this extreme example exceeded) my son�s scores in the other sections are already accounted for in the 4% figure�.so absolute worst case you could come up with 96.0% total percentile, I think��
However...it is also theoretically possible that only 5 (or 0)/1000 were at or ahead of him in math, and 15 at or ahead of him in reading, with zero overlap/zero ties/zero one point lower in the other section, yielding 0% at or above his overall score (100.0 percentile). The median between these two extreme endpoints would be 98.0%.
93% is just too low, if the samples taking each piece of the battery are reasonably similar in quality (quantity could float and there should be no impact), or there is something off about the 99% math and 98% reading percentiles.
I read elsewhere that the 100 percentile is not given by Stanford Achievement. If this is true, 99% could be 98.5% � 100% (let�s say 99.0% to be conservative), and 98% could be 97.5% - 98.5% (let�s say 97.75% to be conservative). A reasonable person would estimate 1.0% math + 2.25% reading = 3.25% worst case, with some shrinkage due to overlap, and you are in the 97.5 to 98.5 range again (98%).
Of course all of this is academic as the �headroom� on this exam is clearly lacking in the high 90 percentiles (as a previous poster pointed out)�especially given that this test was being taken by 7 year olds who could easily get distracted/bored.
I will look into other IQ/achievement tests he could possibly take. Suggestions are welcome.
