We tested younger DD at 3 yr 9 months. Her results came back at substantially lower than older DD (who was tested at 3 yr 11 months). The difference is an astounding 18 points lower (high average) and 22 percentile points lower. Needless to say I am a bit shocked. We expected younger DD to test lower, but not that much lower.
The standard deviation of the difference of IQs of two children of the same biological parents is about 15, so a difference of 18 points is not too unusual.
Here is the math. If x1 and x2 are drawn from a distribution with standard deviation s, and common mean, and have correlation p, the standard deviation of (x1-x2) is s*sqrt(2*(1-p)), where p is the correlation of x1 and x2. This is because
variance(x1-x2) = <(x1-x2)^2> -
^2 = + - 2* = 2*(1-p)*s^2
The Heritability of IQ article of Wikipedia says p is about 0.5 for siblings, and plugging p=0.5 into s*sqrt(2*(1-p)) gives s, which is about 15 for IQ tests.
