No need for mathematical proofs, the test provider calculates this information for you, and it's typically presented along with the results. While intelligence tests are quite good in terms of reliability - what you're talking about would require a near perfect test. At best (middle of the distribution), the Wechsler FSIQ composite has a standard error of measurement of around 2.5 or so. That means if you score an average 100...i look forward to seeing your mathematical proof which will show us why the measured IQ differential was unreliable and unmeaningful.
The 68% confidence interval is 97.5-102.5
The 95% confidence interval is 95-105
The 99% confidence interval is 92.5-107.5
Last edited by Taylor; 02-09-11 at 03:15 AM.