Calculating effect sizes in animal social network analysis

1. Because of the nature of social interaction or association data, when testing hypotheses using social network data it is common for network studies to rely on permutations to control for confounding variables, and to not also control for them in the fitted statistical model. This can be a problem because it does not adjust for any bias in effect sizes generated by these confounding effects, and thus the effect sizes are not informative in the presence of confounding variables. 

2. We implemented two network simulation examples and analysed an empirical dataset to demonstrate how relying solely on permutations to control for confounding variables can result in highly biased effect size estimates of animal social preferences that are uninformative when quantifying differences in behaviour. 

3. Using these simulations, we show that this can sometimes even lead to effect sizes that have the wrong sign and are thus the effect size is not biologically interpretable. We demonstrate how this problem can be addressed by controlling for confounding variables in the statistical dyadic or nodal model. 

4. We recommend this approach should be adopted as standard practice in the statistical analysis of animal social network data.