Kritikalbereich

Kritikalbereich is a term used in statistics and hypothesis testing. It represents the set of outcomes or values of a test statistic that would lead to the rejection of the null hypothesis. In simpler terms, if the result of a statistical test falls within the kritikalbereich, it is considered unlikely to have occurred by random chance alone, and therefore, the null hypothesis is deemed false. The selection of the kritikalbereich is determined by the chosen significance level (alpha) and the distribution of the test statistic under the null hypothesis.

The significance level, commonly denoted as alpha ($\alpha$), is the probability of rejecting the null hypothesis when it is actually true (a Type I error). A typical significance level is 0.05, meaning there is a 5% chance of incorrectly rejecting a true null hypothesis. The kritikalbereich is defined such that the probability of the test statistic falling within it, assuming the null hypothesis is true, is equal to alpha.

Identifying the kritikalbereich involves understanding the alternative hypothesis. If the alternative hypothesis suggests a difference in a specific direction (e.g., greater than), it is a one-tailed test, and the kritikalbereich will be in one tail of the distribution. If the alternative hypothesis suggests a difference in either direction, it is a two-tailed test, and the kritikalbereich will be split between both tails of the distribution. The critical values, which mark the boundaries of the kritikalbereich, are obtained from statistical tables or software based on the chosen alpha and the degrees of freedom if applicable.