Saturday, November 16, 2013

Piling of correlations upon correlations

In a previous blog post, I had linked to R. Plomin et. al.'s results that literacy and numeracy are more heritable than "g" (IQ).    One of the things to understand is that at least one set of "g" measurements they used was a test conducted by telephone.  The paper says, and it is expounded on here, about how much telephone tests correlate with in-person tests.

"Testing cognitive abilities by telephone in a sample of 6- to 8-year-olds" (2002)
Intelligence Volume 30, Issue 4, July–August 2002, Pages 353–360


Telephone-administered measures of cognitive ability have been shown to be efficient and cost-effective alternatives to in-person-based assessments. The current study examined the validity of a telephone-assessed measure of cognitive ability using a sample of fifty-two 6–8-year-old children. The telephone test was composed of verbal- as well as performance-based measures of cognitive ability. The telephone-assessed measure of general cognitive ability correlated r=.65 with in-person-assessed measures. After correction for range restriction, the correlation was r=.72. Thus, measures of cognitive ability administered by telephone appear to be feasible, even in elementary school-age children.

About IQ measurement:

Alan S. Kaufman, clinical professor of psychology at the Yale University School of Medicine:

There's no such thing as "an" IQ. You have an IQ at a given point in time. That IQ has built-in error. It's not like stepping on a scale to determine how much you weigh.

The reasonable error around any reliable IQ is going to be plus or minus 5 or 6 points, to give you a 95 percent confidence interval. So, for example, if a person scores 126, then you can say with 95 percent confidence that the person's true IQ is somewhere between 120 and 132; within our science we don't get any more accurate than that.

But as soon as you go to a different IQ test, then the range is even wider, because different IQ tests measure slightly different things.

But while there is no single IQ – it's a range of IQs – you can still pretty much determine whether a person is going to score roughly at a low level, or an average level, or a high level.

However, IQ is a relative concept. IQ is how well you do on an IQ test compared to other people your age, and that is true whether you are 4 or in your 40s.
Now I'm wondering how much do the errors pile up.  I need to read the papers carefully to see if they indeed say, "what we have measured is "g" +/- 4%.  

PS: another annoying thing about these papers is that they are all about the variance - they do not mention the value of the mean.   I for one, can think of possible anomalies that would be made visible by the mean.