General points about IQ measurement
IQ scores are standardised scores typically with a mean of 100 and a standard deviation of 15. As Ben Cole notes, IQ scores are typically normed relative to age groups in children, and then normed relative to the adult population for adults.
Can the IQ scores of exceptionally and profoundly gifted children be extrapolated into adulthood?
IQ scores correlate very highly over time. That said, correlations decrease as (a) the period of time between testing sessions increases, and (b) the earlier the age of initial testing (e.g., testing at 2,3, 4, 5 years of age, etc.). Presumably greater periods of cognitive change have the potential for greater individual differences in that change, and such greater potential for reductions in the correlation over time.
Here's an extract from a major review of IQ testing and intelligence relevant to stability that reiterates these points with sources (Neisser et al, 1996):
Stability. Intelligence test scores are fairly stable during
development. When Jones and Bayley (1941) tested a sample of children
annually throughout childhood and adolescence, for example, scores
obtained at age 18 were correlated Y = .77 with scores that had been
obtained at age 6 and r = .89 with scores from age 12. When scores
were averaged across several successive tests to remove short-term
fluctuations, the correlations were even higher. The mean for ages 17
and 18 was correlated r = .86 with the mean for ages 5, 6, and 7, and
r = .96 with the mean for ages 11, 12, and 13. (For comparable
findings in a more recent study, see Moffitt, Caspi, Harkness, &
Silva, 1993.) Nevertheless, IQ scores do change over time. In the same
study (Jones & Bayley, 1941), the average change between age 12 and
age 17 was 7.1 IQ points; some individuals changed as much as 18
So, in summary exceptionally gifted children will tend generally to be highly intelligent adults. However, there are a few notes of caution:
- Any IQ measurement has error. Thus, the IQ measurement is only an estimate of the individual's true IQ. For standard IQ tests, the size of this measurement error is greater as you move towards the tails of the distribution of IQ scores, such as is the case with the very gifted.
- There is an effect known as regression toward the mean. This says, among other things, that when two measures are imperfectly correlated, extreme scores on one variable will tend to be relatively less extreme on the other. This can be explained both in terms of measurement error (i.e., those identified as having a 160 IQ might just have got luck on the test) and in imperfect correlation of latent IQ over time. Thus, in general if you identify a sample of very high IQ children and select them, you may find that there average IQ drops at a second time point. They'll still of course be measured as very intelligent on average.
Is it true that that a profoundly gifted child with an IQ of 170 would score better than 99.9998% of the general population?
A child's IQ is defined relative to a population of children of the same age as that child, and not the general population.
Based on a definition of IQ as a normative score, you get the following percentiles using R:
> iq <- c(100, 115, 130, 145, 160, 170)
> percentile <- 100 * pnorm(iq, 100, 15)
> cbind(iq, percentile=round(percentile, 6))
[1,] 100 50.00000
[2,] 115 84.13447
[3,] 130 97.72499
[4,] 145 99.86501
[5,] 160 99.99683
[6,] 170 99.99985
Thus, yes, you are correct in a theoretical sense that a true IQ of 170 by definition implies that that individual has an IQ greater than 99.99985% of the relevant normative population.
However, the reality is that you never measure true IQ. You only get responses to an individual on a test. And this measurement is made with error, and this error in measurement is typically greater at the high end. Thus, you get a measure with confidence intervals or some form of bayesian estimate of IQ. Furthermore, there is also error in measuring population norms as well. Thus, if you want to be more precise in your description of what a test says about an individual's IQ, then you need to specify a range on that individual's IQ, and this range would be larger at the high end, because intelligence tests are not typically optimised to the high end and normative estimates of IQ at the high end would be less precise.
- Neisser, U., Boodoo, G., Bouchard Jr, T. J., Boykin, A. W., Brody, N., Ceci, S. J., ... & Urbina, S. (1996). Intelligence: Knowns and unknowns. American psychologist, 51(2), 77. PDF