Tiivisyystestit

Tiivisyystestit, often translated as "compactness tests" or "tightness tests," are a category of statistical procedures used in hypothesis testing. These tests are designed to evaluate whether a given statistical model or hypothesis is sufficiently "simple" or "compact" to be accepted. The core idea behind Tiivisyystestit is to assess if the observed data is consistent with a restricted or simplified version of a more general model.

A common application of Tiivisyystestit is in the context of model selection. For example, when comparing nested models, where one model is a special case of another, a Tiivisyystesti can be used to determine if the additional complexity of the more general model is statistically justified by the data. If the test indicates that the data is consistent with the simpler, restricted model, then the more complex model may be rejected in favor of the simpler one, adhering to principles like parsimony.

The theoretical underpinnings of Tiivisyystestit often involve comparing likelihoods or other measures of fit between the restricted and general hypotheses. The test statistic is typically constructed to be large when the data strongly favors the more general model, and small when the data is more consistent with the restricted model. Significance is then assessed by comparing the observed test statistic to its distribution under the null hypothesis (which usually corresponds to the restricted model being true). Examples of tests that can be framed as Tiivisyystestit include likelihood ratio tests, score tests, and Wald tests in certain contexts.