Significance level in sample size calculation and in final analysis Imagine that for the purpose of a study a sample size is computed with the following formula for a given power $1-\beta$, difference in means $\epsilon$, standard deviation $\sigma$ and significance level $\alpha$
\begin{equation}
n = \frac{2(z_{\alpha/2} + z _{\beta})\sigma^2}{\epsilon^2}
\end{equation}
When all $n$ subjects completed the study, we have the data required to perform the analysis, e.g. t-test. When I apply this t-test, does the significance level $\alpha$ has to be the same as the one used in the sample size calculation?
Are the choices of $\alpha$ "before" and "after" the conduct of the study, if may say so, have to be identical?
 A: No they don't "have" to be the same. The $\alpha$ you used in your power analysis before conducting the study, and the $\alpha$ you used in your test don't technically have to be the same. But, if you're only "relaxing" $\alpha$ in your test because you didn't get the result you wanted/expected -- and you're only changing this between your design and your analysis because you want to report a "statistically significant" result -- I would discourage this. That's not how hypothesis testing works. Instead, report your design; report your results (even if $p \ge 0.05$); and discuss the implications. Don't let your p-value be your only metric of success or failure in your research. Null findings can also have a great deal of scientific merit.  
A: The $\alpha$ is usually 0.05 unless multiple tests correction is applied.
(The problem is usually in the effect size (in other words, in $\epsilon$). If the effect size is not exactly known, the sample size calculations are only approximate. Even after the experiment is done you can't know the power.)
