Wikipedia defines
$$\star e_I = (-1)^{\sigma(I)} e_{\overline{I}}$$ where $\overline{I} = [n]\setminus I = \{\overline{i}_1< \cdots < \overline{i}_{n-k}\}$ and $\sigma(I)$ is the permutation $i_1 \dots i_k \overline{i}_1 \dots \overline{i}_{n-k}$. When taking $I = \{1\}$ and $n=2$, we would get $e_I = \text{d}x$, $\sigma(I) = (1\,\,2)$, $e_{\overline{I}} = \text{d}y$. The sign of $\sigma(I)$ is $-1$, so it would seem to me that
$$\star\text{d}x = -\text{d}y.$$ Wikipedia, however, states $\star\text{d}x = \text{d}y$. Where do I go wrong?