Albert Frank

A frequent confusion is done in many fields, including the estimation of I.Q., for very rare events.

In the following text, we assume that the medium I.Q. is 100, the standard deviation 16, and (VERY sad hypothesis for the extrema of distributions), that we have a Bell (Normal) distribution.

The confusion consists of non differentiate confidence interval and estimation interval.

Here is just an example:

You past a test and a (poor) psychometrician give you the result as the assertion: "In a confidence interval of .95, you I.Q. is 164 plus or minus 8, so is between 156 and 172". (Note: I don’t distinguish between the interval being closed, open, or half closed and half open).

Let’s have a look at the Normal distribution table:

• Probability to have an I.Q > 172 is 0.000003401
• Probability to have an I.Q. > 156 is 0.000232673
• Probability to have an I.Q. between 156 and 172 is 0.000229272

So the difference in probabilities between the two assertions "you I.Q. is > 156" and "you I.Q. is between 156 and 172" is 0.000003401 .

We see immediately that the psychometricians assertion makes no sense.

Any comments are welcome.