A Supplement

Here we provide proofs of the statements made in the main text as well as further figures of numerical experiments and a more detailed discussion of heteroskedasticity effects regarding causal discovery. Z. Testing whether the Pearson correlation between X and Y is zero is equivalent to testing whether the slope parameter β is equal to zero. Therefore, this is a homoskedastic problem. A.1.2 Discussion of Effect 2: We start by discussing the homoskedastic case to see where non-constant variance of noise leads to problems within the t-test. For homoskedastic noise the second factor is an estimator of the standard error of ˆβ, which we derive by using the mean of the squared residual as an estimator for the error variance.