When the experimental and control groups can communicate with each other, the control group may learn from the experimental group information about the treatment and create a threat to internal validity....so how we can control statically if possible?
The experimental and control groups are never permitted to communicate with each other of course. There is no preferred test in psychology- if you ask for one I would say t-test. You have a lot of tests in psychological research to choose from and you decide what to do by which means at which level before the experiment is done.
I think, you could measure mmm... let's call it "the degree of information" witch control's get from treatment group and use this metric as a regressor in a regression analysis (it possible to apply a regressor and then to use residuals for future analysis) or you could use a partial correlation analysis (similar way to solve the problems of confound variables).
How to measure the "degree of information" I really don't know. Your should create some kind of questionnaire and give it for your experimental and control groups to measure how much each subject knows about the treatment.
The main statistical procedures in data analysis are descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics which deals with more complicated operations.
Read a textbook called Fundations of behavioral research (Kerlinger) and another one called nonparametric statistics (S. Siegel) and you will see that this kind of question does not have one simple answer.