So a 10 point deviation between groups is 5 sd's, p <.001 ?
So a 10 point deviation between groups is 5 sd's, p <.001 ?
def test():
... n1 = numpy.average(numpy.random.normal(100,15,52))
... n2 = numpy.average(numpy.random.normal(100,15,40))
... return abs(n1-n2) / ((n1+n2)/2.0)
...
>>> vals = [test() for i in xrange(0,1000)]
>>> numOver10 = len([v for v in vals if v > .1])
>>> numOver10
2
Ah, I see. Standard IQ normalizations.
P.S. I would take four standard deviations up or down (the IQ range of 40 to 160) as the outer limit of validated IQ scores, and indeed few modern IQ test batteries purport to report scores outside this range. See
https://en.wikipedia.org/wiki/IQ_classification
and the published reference books cited there for more background.
P.P.S. I should have mentioned when I first posted this comment that any IQ test has a standard error of measurement even if it is faultlessly administered and scored. Sometimes small-n studies like the study reported here have IQ score differences between two groups that are simply the result of the test errors showing a difference where no actual difference exists. IQ tests are often also very frequently administered incorrectly or scored incorrectly even if correctly administered, magnifying the size of the error band around the obtained score. For this study, I'm not sure if the human subjects tested were tested by test-givers who were "blind" to what group the test-takers were in, which could also be an issue.
Correct me if I'm wrong but I thought the Cattell tests were obviously scored in the Cattell scale (24 s.d.) and the Stanford-Binet tests in the Binet scale (16 s.d.).
When I was into reading about psychometrics it seemed to me that the cut off percentile was a more straightforward way to talk about IQ than using either of those three scales (Wechsler, Binet, Cattell).
doi:10.1016/j.bbi.2008.04.156