TestsRestfunktion

TestsRestfunktion is a term sometimes used in German-language statistics and software testing to denote a residual or remainder function associated with hypothesis testing. It refers to the part of a test result that remains after subtracting the expected contribution given a reference model or null hypothesis. The concept helps to separate signal from noise or nuisance effects in the analysis of test outcomes.

In a formal setting, the TestsRestfunktion can be defined for a data set D and a null model M0. If T(D) is a test statistic, the rest function may be written as R(D) = T(D) − E0[T(D)], where E0 denotes the expectation under the null model M0. The rest function is useful for diagnostic checks, such as assessing the adequacy of the null model, investigating deviations from assumptions (for example normality or independence), and guiding the construction of robust or adaptive tests.

In practice, the term is not universally standardized and may appear under related names in different texts, such as residual function or remainder term. In regression contexts, the concept aligns with residuals e_i = y_i − ŷ_i, which serve a similar purpose: decomposing observed variation into modeled and unexplained parts and feeding into test procedures like F-tests or bootstrap-based analyses.

Construction and properties: The rest function depends on the chosen statistic T and the null model M0. Under the null, its expectation is typically zero, and its distribution can be studied analytically or via resampling. It enables sensitivity analysis by examining patterns in R(D) to detect model misspecifications, heteroskedasticity, or omitted variables.

See also: Test statistics, residuals, hypothesis testing, model diagnostics, bootstrap.