Gifted Issues Discussion homepage Forums Identification, Testing & Assessment IQ vs Achievement Tests - Un

My 7 y.o. took both the Wisc V and the Woodcock Johnson Achievement Tests. I'm wondering how it is possible to score at such an outlier on the Applied Problems subtest without what seems to me to be the corresponding WISC scores? Child is not "hot-housed"/accelerated, has never taken any extra math enrichment classes. The achievement scores are due to any natural understanding of math and what he's pick up on own.
I plan to bring this to the school to argue for subject acceleration, but wonder if they'll push back because WISC results are not at the same levels. I imagine his needs are very different depending if we're talking about a child who is in the top 5% vs top 1% versus top .01%-.2%. Could my 7yo have an exceptionally gifted math brain with "only" a 125 IQ? Seems like a disconnect somewhere to me. Anyone have a perspective on this?

Achievement tests:
Applied Problems subtest 154 (99.98%)
Math Overall 143 (99.79%)

WISC
FSIQ 125/GAI 127 (95%/96%)
Highest indices were VSI = 135 (99%) and QRI = 139 (99.5%)
Everything else was ~120s, except working memory/processing speed which were ~100.

The WISC v has brand new norms but i think the woodcock johnson hasn't. But 95th percentile is a pretty good IQ for high achievement - i suspect many of tbe kuds with the top grades are in the 85 - 95 percentile range.

Let's start with the concept of regression to the mean. In simplified terms, very high scores are extremely rare. Two very high scores are much, much rarer. So if one score is extremely high, the likelihood is that the next score will be closer to the mean (in this case, lower). This is why, when looking at achievement scores predicted from cognitive scores, the range of expected scores is fairly large for cognitive scores at the extremities.

Secondly, the cognitive index most relevant to the WJIV Applied Problems subtest is the WISC-V QRI. The difference between the QRI and AP is only 15 SS points--not a huge difference when you consider regression to the mean, and also when you consider that these are comparisons across different (and not co-normed) instruments.

Thirdly, consider the way standard scores and norms are built. The 2,200 children age 6-16 in the WISC-V standardization sample were divided such that each 3-month age bracket had about 67 children. (The WJIV sample was similar, with just under 4,000 school-age children K-12.) Think about how many children a 135 represents. Roughly 2/3s of a child from the standardization sample corresponds to all the scores from 130 up. The distinctions finer than that had to be derived from decisions in statistical analysis of the standardization data. Now, to be clear, I have no problem using these norms, even knowing how little raw data goes into the extremes of the bell curve, mainly because these are the best tools we have at the present time.

Finally, you are talking about a very young student, most likely in the beginning of 1st or 2nd grade. Expectations for age-peers are very low, with a bell curve that is rather tightly packed in the middle, and below the middle, so a child who has mastered a few arithmetic skills (pretty much anything beyond single-digit addition and subtraction), and understands how to apply them, will rapidly climb the bell curve into its upper extremes. Also, based on the Broad Math score you report, I assume that the other math subtest scores were in the 130s, which would be exactly where the QRI is.

From an advocacy standpoint, the simplest approach might be to present the QRI and AP scores, both of which are in the >99 %ile. The presumptive 20 pt gap between AP and math calculations would support the contention that this is native math ability, and not hot-housing, as one would imagine that it is easier to drill procedures into children, than conceptual understanding.

We don't know which WJ the OP's DC took. There is actually a brand-new WJIV out, whose norms are very comparable in newness to the WISC-V.

I'd go by what you know of your child, but it seems to me there are two possibilities, that either the achievement test is an overestimate or the IQ numbers are an underestimate.

FWIW, we have had this situation occur in the case of a late bloomer with processing issues (of a language variety, among other things) that held down the wisc scores even for PR. In later years, another test showed higher IQ scores more in line with achievement, though we have yet to repeat the wisc so it's hard to say for sure what was going on. This kiddo was obviously gifted in math from an early age in spite of his issues and remains advanced.

I asked the school psych how someone could score so much higher by percentile on achievement than IQ testing, by a couple standard deviations, and she didn't seem to have an answer. When I asked the private psych on another occasion, she muttered something about my children being complicated, but mostly referred to the "language processing issue."

It was the WJ IV Test of Achievement (and the Wisc V)

aeh - Thank you for the explanation. My understanding of the achievement test was the he keeps going until a certain number were missed. And the point where he stopped was where the average >30 year old (A.E.) or college aged student (G.E.) would also stop. I fully understand how he can outscore the majority of his age peers, that bar is pretty low, but find it hard to wrap my mind around how the average high school/college/adult would have only gotten as far as he did.

snowgirl - I thought the IQ score was a bit low, but also didn't expect any area, achievement or IQ, to be in the >99.9% range. So I'm having trouble synthesizing the results! Somewhere in the middle is probably right.

And one more way of explaining this kind of difference without seriously questioning either result: all standardized testing is a sampling from a moment in time of an examinee's skills in the area assessed. All instruments have some level of measurement error, and these are no exception. This is why scores should properly be reported as confidence intervals (typically the 95% c.i., for index scores), to capture the sense of an informed estimate of some idealized "true" score. On the WISC-V, the 95% c.i. for the QRI is a range of about 13 to 14 points, centered around the nominal index score. The WJIII or IV subtest in question also has a confidence interval, which is probably about the same magnitude (I don't have the exact figure in front of me). Taken together, one can see that, based purely on standard error of measurement, a difference between the two scores of roughly this size would not be entirely surprising.

The situation reported by snowgirl, of a difference of multiple standard deviations, is a bit more striking. I'd have to have more detail to take a stab at that.

We had similar issues with my 6 year old son. His achievement test numbers on the WIAT III were much higher (140,145,160, etc.) than his IQ scores on the DAS II (129 on verbal the highest). We thought he had ADHD but have since changed schools to a much faster paced curriculum. He is doing incredibly and the best part is that he is completely off medication.
For him, the issue is a connection to meaningful material. He wont play along unless the topic interests him. Perhaps it is the same for your son?
Good luck!

Terrace,

A couple of general thoughts:

AE and GE should not be taken as actual functional or instructional levels. This is not a criterion-referenced test, where, hypothetically, the scores are anchored to mastery of skills demanded or expected at certain age or grade levels. It is a norm-referenced test, based on standing in the population. The AE and GE are derived from the raw score or adjusted raw scores (W score, in this case) obtained by the 50th %ile of the standardization sample at that age or grade. It doesn't even distinguish between getting every item right in sequence, and then suddenly meeting the discontinue criteria with six in a row incorrect, and a very different scenario, where there are incorrect items interspersed with correct items, such that the most difficult item completed correctly is a much higher-level item than in scenario one. These two profiles generally have quite different meanings, but will result in the same AE, GE, and standard score.

If you take a representative sample of 30 year-olds in North America, you will find a highly divergent range of applied mathematics skills among them, even if we restrict our sample to the middle 68 percent (+ or - 1 SD from the mean) of performance levels. Think of the ordinary 30 year-olds you know. Some of them are quite facile with math, as evidenced by their engineering or finance jobs, or their expert bargain shopping. Others can't calculate change at the cash register, and panic at the idea of balancing a checkbook (both skills that require math no higher than third grade level). So there are two issues here: what is the real-life meaning of math applications at the 30 year-old level, and, does the AE score accurately indicate performance or instructional level at this age level?

It's also not clear to me from your account if his ceiling item was at the 30 year-old level, or if his AE score was at that level. Two very different situations, as the ceiling rules for the WJ are a bit different from some other tests, in that the examiner must administer complete pages, and also meet the six-in-a-row wrong discontinue rule. This means a child could, hypothetically, get five items in a row incorrect, then one correct, and then eleven more incorrect, at the ceiling, which would mean, that, for the sake of two raw score points (not that much, IOW), 16 incorrect items were administered, of which the last eleven were wrong. This might result in a highly-inflated estimated age/grade-level of the last item administered.

Which is why I would caution against placing too much weight on the AE and GE scores.