What's adequate sample size for single mediator model?

#1
Hi,

I have set up a single mediator model to explain cases of COVID-19/million. I generated four regression equations using online software:

1) Cases COVID-19/million = .44234 x # Christians/10,000 + 2475.65082
2) # international adoptions made by a country between 1999 and 2016 = .46796 x # christians + 161.72965
3) Cases of COVID-19 = .5318 x international adoptions + 3565.13813
4) Cases COVID-19 = 2527.033 + .294 x # christians + .318 x # int. Adoptions.

My model predicts that the number of Christians in a country has a direct effect on # cases of COVID-19 and an indirect effect on # cases of COVID-19/million via the mediator # int. adoptions. That is, Christians create int. adoptions and international adoptions create social interactions leading to the spread of COVID-19.

The calculated indirect effect is .149.

I determined that the indirect effect is statistically significant by the causal steps approach (it proves partial mediation) and also by the Sobel delta method, p= .01 one tailed.

The question is this. My sample size is small (32); however, it uses 32 out of all 214 countries infected with SARS-CoV-2. Is this enough power? Is there a way to calculate how large a sample size I need to acheive a power of .8?
 

spunky

Doesn't actually exist
#2
Power for mediation models can be approximated through simulations as described in:


Schoemann, A. M., Boulton, A. J., & Short, S. D. (2017). Determining power and sample size for simple and complex mediation models. Social Psychological and Personality Science, 8(4), 379-386. https://doi.org/10.1177/1948550617715068

Also, it is well-known that the Sobel test is only accurate at large samples (we're talking in the 100s) so a bootstrapping approach is recommended instead of the Sobel test as described here:

http://quantpsy.org/pubs/preacher_hayes_2008b.pdf