Stupid mathematical nitpick:

The chances of this happening are only .95 ^ 39 = 0.13, even before taking into account publication and error bias.

Actually, it is more correct to say that .95 ^ 39 = 0.14.

If we calculate it out to a few more decimal places, we see that .95 ^ 39 is ~0.135275954. This is closer to 0.14 than to 0.13, and the mathematical convention is to round accordingly.

*3 points [-]