In choosing the intended confidence level for rejecting a hypothesis, the researcher may make type I and type II errors. Seemingly the two act against each other. How can we best resolve the problem and find a logical way out.
Best regards ,
R. Biria
The only logical way out is to assess the expected win of a correct decision and the expected losses for wrong decision. Based on this information and the required investment for the experiment one can select the power and the level of significance that maximize the expexted net win.
This method is not sensibly applicable in (basic) research because it is usually absolutely unclear how wins and losses associated with correct and wrong decisions could be quantified.The application of hypothesis tests in research is based on subjective beliefs that the chosen errror-rates are "somehow resonable". Practically, it is not the matter what the test tells you about your research (they do not tell you much about that anyway) but to convince reviewers.
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If all of your study parameters are already fixed then the trade-off between Type I and Type II errors should be based on a loss function--that is, if you are dealing with an applied problem that requires a decision. It is unclear if this is the case given your question about rejecting a "research hypothesis." If the problem is regarding a scientific question, then optimization is out the window. Your only concern is convincing the community of researchers that your error probabilities are within the prudent range. Here, the literature on the topic will be your best guide. Alpha = 0.05 and 1-beta = 0.80 WILL NOT be optimal from a loss function perspective, but if this is what your colleagues expect that will not matter.
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