nullhüpotese

The null hypothesis, abbreviated H0, is a default assumption in statistical hypothesis testing that posits no effect, no difference, or no association between variables. It serves as a baseline against which researchers compare observed data. In German-language statistics, the term is commonly given as Nullhypothese or Nullhypothese.

Formulation and testing process: Researchers formulate a null hypothesis (H0) and an alternative hypothesis (Ha) that reflects the research question. A significance level, typically alpha = 0.05, is chosen. Data are collected and a test statistic is computed. The result is expressed as a p-value or compared to a critical value. If the evidence is strong enough (p-value ≤ alpha or the statistic falls into a rejection region), H0 is rejected in favor of Ha; otherwise, researchers fail to reject H0. Note that statistical testing leads to rejection or non-rejection, not proof of truth.

Examples: In a clinical trial, H0 might state that the new treatment has no effect compared with placebo (mean difference = 0). In an A/B test, H0 could assert that the conversion rate of variant A equals that of variant B. Tests can be one-sided or two-sided, depending on whether the research question specifies a direction of effect.

Errors and power: A Type I error occurs when a true H0 is incorrectly rejected (false positive). A Type II error happens when a false H0 is not rejected (false negative). Power, the probability of correctly rejecting a false H0, depends on effect size, sample size, variability, and the chosen alpha.

Limitations: A failure to reject H0 does not prove it true. P-values and confidence intervals depend on sample size and model assumptions, and multiple testing can inflate error rates. Proper interpretation requires considering practical significance, study design, and prior evidence.