This bachelor’s thesis focuses on the effect of outliers on the one-way analysis of variance and examines whether the estimate in ANOVA is robust and whether the actual test itself is robust from influence of extreme outliers. The robustness of the estimates is examined using the breakdown point while the robustness of the test is examined by simulating the hypothesis test under some extreme situations. This study finds evidence that the estimates in ANOVA are sensitive to outliers, i.e. that the procedure is not robust. Samples with a larger portion of extreme outliers have a higher type-I error probability than the expected level.