Research on whether perception or other processes depend on the phase of neural oscillations is rapidly gaining popularity. However, it is unknown which methods are optimally suited to evaluate the hypothesized phase effect. Using a simulation approach, we here test the ability of different methods to detect such an effect on dichotomous (e.g., "hit" vs "miss") and continuous (e.g., scalp potentials) response variables. We manipulated parameters that characterise the phase effect or define the experimental approach to test for this effect. For each parameter combination and response variable, we identified an optimal method. We found that methods regressing single-trial responses on circular (sine and cosine) predictors perform best for all of the simulated parameters, regardless of the nature of the response variable (dichotomous or continuous). In sum, our study lays a foundation for optimized experimental designs and analyses in future studies investigating the role of phase for neural and behavioural responses. We provide MATLAB code for the statistical methods tested.