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Statistical background

In statistical test theory, the notion of a statistical error is an integral part of hypothesis testing. The test goes about choosing about two competing propositions called null hypothesis, denoted by H 0 {\textstyle H_{0}} and alternative hypothesis, denoted by H 1 {\textstyle H_{1}}. This is conceptually similar to the judgement in a court trial. The null hypothesis corresponds to the position of the defendant: just as he is presumed to be innocent until proven guilty, so is the null hypothesis presumed to be true until the data provide convincing evidence against it. The alternative hypothesis corresponds to the position against the defendant. Specifically, the null hypothesis also involves the absence of a difference or the absence of an association. Thus, the null hypothesis can never be that there is a difference or an association.

If the result of the test corresponds with reality, then a correct decision has been made. However, if the result of the test does not correspond with reality, then an error has occurred. There are two situations in which the decision is wrong. The null hypothesis may be true, whereas we reject H 0 {\textstyle H_{0}}. On the other hand, the alternative hypothesis H 1 {\textstyle H_{1}} may be true, whereas H 0 {\textstyle H_{0}} is rejected. Two types of error are distinguished: type I error and type II error.