An important goal in systems neuroscience is to understand the structure of neuronal interactions, frequently approached by studying functional relations between recorded neuronal signals. Commonly used pairwise measures (e.g., correlation coefficient) offer limited insight, neither addressing the specificity of estimated neuronal interactions nor potential synergistic coupling between neuronal signals. Tripartite measures, such as partial correlation, variance partitioning, and partial information decomposition, address these questions by disentangling functional relations into interpretable information atoms (unique, redundant, and synergistic). Here, we apply these tripartite measures to simulated neuronal recordings to investigate their sensitivity to noise. We find that the considered measures are mostly accurate and specific for signals with noiseless sources but experience significant bias for noisy sources.We show that permutation testing of such measures results in high false positive rates even for small noise fractions and large data sizes. We present a conservative null hypothesis for significance testing of tripartite measures, which significantly decreases false positive rate at a tolerable expense of increasing false negative rate. We hope our study raises awareness about the potential pitfalls of significance testing and of interpretation of functional relations, offering both conceptual and practical advice. Author Summary Tripartite functional relation measures enable the study of interesting effects in neural recordings, such as redundancy, functional connection specificity, and synergistic coupling. However, estimators of such relations are commonly validated using noiseless signals, whereas neural recordings typically contain noise. Here we systematically study the performance of tripartite estimators using simulated noisy neural signals. We demonstrate that permutation testing is not a robust procedure for inferring ground truth statistical relations from commonly used tripartite relation estimators. We develop an adjusted conservative testing procedure, reducing false positive rates of the studied estimators when applied to noisy data. Besides addressing significance testing, our results should aid in accurate interpretation of tripartite functional relations and functional connectivity.