Following a discussion on Gelman’s blog, I was playing around with simulating scientists looking for significant effects. Suppose each of 1000 scientists run 200 experiments in their lifetime, and suppose that 20% of the experiments are such that the null is true. Assume a low power experiment (standard in psycholinguistics; eyetracking studies even in journals like JML can easily have something like 20 subjects). E.g., with a sample size of 1000, delta of 2, and sd of 50, we have power around 15%. We will add the stringent condition that the scientist has to get one replication of a significant effect before they publish it.
What is the proportion of scientists that will publish at least one false positive in their lifetime? That was the question. Here’s my simulation. You can increase the effect_size to 10 from 2 to see what happens in high power situations.
Comments and/or corrections are welcome.