Identify a critical value. Something like a p-value of 0.05. Determine the accuracy with which you need to estimate this value. Say I am happy if my calculated value is within 0.01 of this cutoff. Take the inverse and multiply by 100. that will be the number of iterations that you need.

Note that you will need enough data to make this estimate meaningful. It does no good to have 10,000 iterations if there are only 10 data values. The number of permutations of your data need to be much larger than the number of iterations. Sure you can do 10,000 iterations on a data set with 20 permutations because you replace values after selecting them. However, this overfits your data. The results are only as good as the original data no matter how many iterations.

Hi,

Hayes recommended 5,000 draws.

Hayes, A. F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76(4), 408-420.

Best,

Holger

Dear Holger Steinmetz

Thank you so much for your answer! May I ask a specific a question on 5,000 draws?

Is this use of number of draws also applicable to testing mediation using bias-corrected (bc) bootstrap approach?

Hi Andrew,

I don't know but would guess yes. I actually don't understand the 5,000 btw. At a certain number of draws, the distribution should have stabilized. Perhaps, try it out and see whether the distributions (mean, variance) changes beyond a reasonable number (say 2,000).

Best,

Holger