Adjusting the confidence level after the experiment I am new to statistical significance testing and i am wondering how the confidence level is set.
If for example I am conducting a test to prove that my method is better than an existing one, and i fail to reject the null hypothesis with a confidence interval of 95%, is it allowed to go back and lower the confidence interval to then reject the null hypothesis and verify that my method is better than the existing.
Any help is greatly appreciated 
 A: The short answer is no. A big no-no is going back and re-adjusting your confidence intervals post-hoc (i.e. after you have done the experiment). See for example:http://blog.minitab.com/blog/michelle-paret/alphas-p-values-confidence-intervals-oh-my
This is especially true when you are already using a lax threshold (95%), as in your case. 
In a case like yours, if your method is close to rejecting the null (e.g. .06) and the other method is downright terrible (e.g. .73) and if you know that rejecting the null hypothesis is the correct answer (e.g. from separate expert knowledge), I would look to see if the magnitude of the result in your method is at least pointing in the right direction, and comment on that.You could perhaps suggest that your method is on the right track, while the other method is not at all.
A: I like user3923510's answer, there's just something I wanted to add based off your comments. 
The goal of statistics is not to verify your hypothesis. The goal of statistics is to verify what the data is saying. If we think of simple classical statistics, we might perform an experiment, visualise the data, and then run an analysis to verify whether patterns observed in the visualisation are significantly different or not. 
Positive results are not the only worthwhile results. Negative results are also telling you something about your data. Since you haven't provided details about your data, let me come up with something.
Say there were two rivers. I hypothesise that the average weight of trout is going to be higher in river 1 because I know that river 1 is generally warmer than river 2. So I go and collect fish from each river and weigh them. I then perform a t-test to see whether average weight is significantly different, and I get a p-value of 0.085. Therefore the average weights of fish between the two rivers is the same.
This is my result though!! I do not now try to tweak the data to prove my original hypothesis. The statistics have done their job, and I have learn't something in the process. The weights do not differ! This is an interesting result and I will now design follow up experiments to investigate further. 
Trying to force significant results is dangerous. You have your results. Trust them, use them, figure out what they mean. 
