From Paul's predictions in the World Cup to the publication bias in genetic studies on complex traits

To the Editors: Recently, the octopus Paul has attracted much attention through the general media by his accurate predictions in the FIFA 2010 World Cup. During the World Cup, Paul predicted the outcomes of eight matches with 100% success. Assuming that Paul has 50% accurate choices as independent coin flips, the probability for a continual eight success prediction is 0.0039. However, we may think that Octopus Paul is more likely to select the box with the German flag, for some reason. For example, when predicting the outcome of the Germany games Paul selected the box with the German flag five times out of seven, giving a percentage rating of 71.4% for selection of the German flag. Assuming Paul is more likely to select the German flag with a probability rate of 0.714, the probability for the correct predictions Paul achieved in FIFA 2010 World Cup is 0.0076 (0.714×0.714×0.714×0.714×0.714×0.286×0.286×0.5). In the academic world, we usually select a probability boundary of 0.05 or 0.01 to reject the null hypothesis 1. Therefore, we may conclude that Paul …