Powering versus statistical significance in clinical trial design I think I have a simple question that I have not seen directly answered elsewhere, and as a stats beginner, I'm wary to translate answers that are not directly answering this question - apologies if it is viewed as duplicate. 
My question is this - clinical trials are generally powered at 80% to show some level of treatment effect, but how can you calculate the minimum detectable treatment effect that would yield statistical significance?
For example let's say that a trial is 80% powered to show a treatment effect delta of 2.2 (e.g., the difference between treatment and control on a specific metric is 2.2)
Furthermore, we initially target an N of 210 for the entire trial and each arm is 1:1 randomized (105 per arm). 
The standard deviation is assumed to be 8.05, statistical significance is defined as having a p-value < 0.05. 
Applying the often used: 
We can solve for the treatment effect (the difference of the means) based on changing the other variables - specifically: 
Since we cannot change n, or Z(1-a) we can only reduce Z(1-b) and presumably assume a lower standard deviation. 
Does this mean then that the true minimal difference that would be considered statistically significant, and thus a trial success, would be:
In other words, simply letting Z(1-b) equal 0 for a powering of 50%?
Thus, on one hand, based on the example a minimum treatment effect could be 2.2 or 1.54 which could be a major difference in the likelihood of the trial being viewed as "successful" (showing stat sig) or not. 
Many thanks!
 A: The false positive error rate, power, sample size, and minimally detectable effect are all 4 tractably related in the first equation you specify above.
Your later derivation is correct. And you are correct that for a prespecified alpha level, desired power, fixed sample size, and known standard deviation, you can report the minimally detectable effect.
Mathematically, all these approaches should lead to equivalent findings. The goal is a judgement of whether or not the study is viable. It is efficient to focus on the "unknowns". It just so happens that it's rarely unknown what the effect should be. However, you should take care with prior knowledge about effect size. Preliminary studies are often hypothesis generating rather than hypothesis confirming, and tend to be selected on the basis of showing significant results. There will be regression to the mean.
The convention of 80% power is rarely appropriate for clinical studies. Considering the cost and time of running a trial, a 4/5 chance of correctly saying there's an effect if there is one is far too risky.
