alternativhypothese

Alternativhypothese, in statistics, is a statement about a population parameter that contradicts the null hypothesis. The null hypothesis (H0) represents no effect, no difference, or no association, and serves as the baseline for statistical testing. The alternativhypothese (often denoted H1 or Ha) expresses the presence of an effect, difference, or relationship that the researcher aims to detect.

There are different forms of the alternativhypothese. A directional (one-sided) alternative specifies the direction of the effect, such as H1: μ > μ0 or H1: p > p0. A non-directional (two-sided) alternative states that the parameter is different from the null value, such as H1: μ ≠ μ0 or H1: p ≠ p0. An alternativhypothese can be simple (specifying a single value) or composite (covering a range of values), with H1: μ > μ0 being composite and H1: μ = μ1 a simple example.

In hypothesis testing, evidence from data is used to decide whether to reject H0 in favor of the alternativhypothese at a chosen significance level (α). A small p-value indicates that the observed data are unlikely under H0, leading to rejection of H0 in favor of H1. It is important to note that rejection of H0 does not prove H1; it indicates consistency with H1 given the model and data, within the limitations of α and sample size.

Common considerations include choosing between one- and two-sided tests, avoiding post hoc specification of H1, and recognizing the difference between statistical significance and practical significance. In Bayesian approaches, the alternativhypothese may be incorporated through prior odds and Bayes factors.