We address the problem of reliability of independence-based causal discovery algorithms that results from unreliable statistical independence tests. We model the problem as a knowledge base containing a set of independences that are related through the well-known Pearl's axioms. Statistical tests on finite data sets may result in errors in these tests and inconsistencies in the knowledge base. Our approach uses an instance of the class of defeasible logics called argumentation, augmented with a preference function that is used to reason and possibly correct errors in these tests, thereby resolving the corresponding inconsistencies. This results in a more robust conditional independence test, called argumentative independence test. We evaluated our approach on data sets sampled from randomly generated causal models as well as real-world data sets. Our experiments show a clear advantage of argumentative over purely statistical tests, with improvements in accuracy of up to 17%, measured as the ratio of independence tests correct as evaluated on data. We also conducted experiments to measure the impact of these improvements on the problem of causal structure discovery. Comparisons of the networks output by the PC algorithm using argumentative tests versus using purely statistical ones show significant improvements of up to 15%.