In recent years, a lot of research has been conducted within the area of\ncausal inference and causal learning. Many methods have been developed to\nidentify the cause-effect pairs in models and have been successfully applied to\nobservational real-world data to determine the direction of causal\nrelationships. Yet in bivariate situations, causal discovery problems remain\nchallenging. One class of such methods, that also allows tackling the bivariate\ncase, is based on Additive Noise Models (ANMs). Unfortunately, one aspect of\nthese methods has not received much attention until now: what is the impact of\ndifferent noise levels on the ability of these methods to identify the\ndirection of the causal relationship. This work aims to bridge this gap with\nthe help of an empirical study. We test Regression with Subsequent Independence\nTest (RESIT) using an exhaustive range of models where the level of additive\nnoise gradually changes from 1\\% to 10000\\% of the causes' noise level (the\nlatter remains fixed). Additionally, the experiments in this work consider\nseveral different types of distributions as well as linear and non-linear\nmodels. The results of the experiments show that ANMs methods can fail to\ncapture the true causal direction for some levels of noise.\n