Brian Josephson's arguments are scientifically and statistically correct.
In contrast, the statement of Richard Wiseman - "I don't see how you could argue there's anything wrong with having to get five out of seven when (Natasha) agrees with the target in advance" - demonstrates a lack of understanding of how experimental data should be interpreted statistically.
The experiment is woefully inadequate. The chance of the observed four successes in seven subjects by pure guessing is 1 in 78. But suppose Natasha had a diagnosis rate of 1 in 2, compared with the chance rate of 1 in 7: then there is equal chance of getting 4 or more from 7, or 3 or less from 7. That is, the probability of detecting a true 50 per cent diagnosis rate on 7 subjects using a 0.01 significance level is only 50 per cent. There should have been at least 21 subjects to ensure a 90 per cent probability of detecting a true diagnosis rate of 50 per cent (using a 0.01 significance level test). Only if Natasha had a true diagnosis rate as high as 72 per cent would there have been a 90 per cent chance of detecting the effect using a 0.01 test on 7 subjects.
The experiment had high chances of failing to detect important effects, but this may have been due merely to no statistician being involved.
Professor of applied statistics
University of Greenwich