Comment by tripletao

They show a 95% CI excluding zero in Figure 1. By the usual standards of social science, that's not a null finding. They give their methodology in Appendix D.

For intuition on why it's insufficient to consider N alone, I assume e.g. that you'd greatly increase your belief that a coin was unfair long before 16 consecutive heads--as already noted, the size of the effect also matters. That relationship isn't intuitive in general, and attempts to replace the math with feelings tend to fail.