Many of the test statistics which used to test $H:\theta=\theta_0$ are constructed under a postulated model. However, when the postulated model is not correct, the true significance level $\alpha^{'}$ will be different than the significance level of the postulated model $\alpha$. The significance level $\alpha$ is used in the test statistic whether or not the hypothesis is rejected or not rejected, so determining the true significance level is important in the hypothesis tests. In this paper, when the normality assumption in hypothesis tests is violated, the true significance level for testing hypothesis about the location $\mu$ and scale $\sigma$ parameters under different contaminated distributions is obtained. As a result, the robustness of significance levels  is investigated.