Die Chi-Quadrat-Verteilung ist eine probability distribution that arises in statistics when analyzing the variability of categorical data. It is particularly useful in Hypothesentests, especially for tests of independence and Güte der Anpassung.
A Chi-Square test evaluates how well the observed data fits a specific distribution model, comparing the observed frequencies to the expected frequencies under the Nullhypothese. The distribution is characterized by a single parameter, the degrees of freedom (df), which is determined by the number of categories or groups in the data.
The Chi-Square Distribution is defined only for non-negative values, and its shape changes based on the degrees of freedom. With lower degrees of freedom, the distribution is skewed to the right, while as the degrees of freedom increase, it approaches a Normalverteilung. This makes it a versatile tool for various statistical analyses, including assessing relationships in contingency tables and testing variance in populations.
In praktischen Anwendungen analysieren Forscher oft use the Chi-Square test to determine if there is a significant association between two categorical variables or to test the fit of observed data to a theoretical model. The resulting Chi-Square statistic is then compared to a critical value from the Chi-Square distribution to determine the statistical significance of the results.