We compare the performance of many effective connectivity measures in detecting statistically significant causal connections between time series drawn from linear and nonlinear coupled systems. Fifteen measures are compared, drawn from two families (information theoretic, and frequency- and time-based multivariate autoregressive models), including common and uncommon measures. Measures were tested on simulated data from three systems: three coupled Hénon maps; a multivariate autoregressive (MVAR) model with and without EEG as an exogenous input; and simulated EEG. Comparisons focus on the effective of parameter choices, e.g. maximum model order or maximum number of lags, for different lengths of data. Performance varies with dataset, and no measure was outstanding for all datasets. Strong performance is obtained where the measure’s model and data source match (eg MVAR model, or frequency domain measures with narrowband data). When there is no match, information theoretic measures and Copula Granger causality generally perform best.