Kongruenztests

Kongruenztests, also known as congruence tests, are statistical methods used to determine whether two or more categorical variables are independent of each other. These tests are commonly applied in fields such as epidemiology, social sciences, and biology to assess associations between variables that are measured categorically.

The most widely used Kongruenztest is the Chi-Square Test of Independence, which compares observed frequencies in a contingency table with the expected frequencies under the assumption of independence. The test statistic is calculated by summing the squared differences between observed and expected values, adjusted by the expected values. If the resulting test statistic exceeds a critical value from the Chi-Square distribution, the null hypothesis of independence is rejected, suggesting a statistically significant association between the variables.

Another variant is Fisher’s Exact Test, which is used when sample sizes are small, making the Chi-Square approximation unreliable. This test calculates the exact probability of obtaining the observed distribution—or one more extreme—under the null hypothesis of independence.

Kongruenztests rely on the assumption that the sample is randomly selected and that expected frequencies in each cell of the contingency table are sufficiently large (typically at least five) for the Chi-Square test to be valid. Violations of these assumptions may lead to incorrect conclusions.

These tests are not limited to binary variables but can be applied to any categorical data structured in a contingency table format. While they provide insight into associations, they do not imply causation. Additionally, they are sensitive to sample size, as larger samples may detect even trivial associations as statistically significant.