In phase two, assume you publish a paper if the p-value is less than 0.05, regardless of the effect size. If p >= 0.05, you don't publish anything.

We are now done with the assumptions.

p-values get smaller as the effect size increases, and they get smaller as the sample size increases. There is a concept called statistical power which measures the smallest effect size it is possible for a study to detect at a given p-value, given the (fixed) sample size that that study has to work with. Larger sample sizes mean more statistical power and mean that it's possible to estimate a smaller effect size for the same p-value.

Adding this all up, we can see that:

- if the true effect size is small;

- AND if the sample size is "small", defined relative to the true effect size;

- AND if we filter studies by whether they meet a p-value threshold ("reach statistical significance");

- THEN the only studies that can be published will find effect sizes that are too large. They do not have the power to detect the true effect size; the only possible results are "no effect" and "unrealistically large effect".

The quick summary is that a reduced effect size on replication is a strong indicator that the original finding was spurious. As replications continue they will trend toward the higher of the true effect size or the floor set by the available statistical power.