Hypotheses, Tests, Decisions, and their Risks

People formulate more or less explicit hypotheses in order to derive information from measurements performed on objects, or simply from observation of reality. 

In science one may distinguish between working hypotheses, scientific hypotheses, research hypotheses, and statistical hypotheses. In this ranking the degree of generality of a hypothesis decreases whereas its precision increases. 

In the following we will therefore focus on statistical hypotheses. Every time one formulates a hypothesis an alternative hypothesis is possible. How can it be determined which 

Because possible wrong decisions usually have different consequences (weights) one hypothesis is called the null hypothesis, H0, and the alternative hypothesis is designated //, or II,. 

What about the risks of decisions As we already know from the construction of confidence intervals, the probability, P, is connected with the complementary error probability, a. In a similar manner here the probability, a, characterizes the risk (of the first kind) of making a wrong decision as a result of using a statistical test. But the notion wrong may be seen from two different sides. 

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