In one-tailed test , we give our decision at $\alpha$ level of significant.
But in two-tailed test , why do we give our decision at $2\alpha$ level of significant? Why do we not give the decision of two-tailed test at $\alpha$ level of significant?
For example , The Durbin-Watson test for autocorrelation
The decision rule for two-tailed test against alternative $\rho\ne0$ is:
If $d<d_L$ or $4-d<d_L$, conclude $d$ is significant, reject $H_0$ at level $2\alpha$ .
Why at level $2\alpha$ ? Why not at level $\alpha$ or $\alpha/2$?
