2x2Tabellen

2x2 tabellen, also called contingency tables, summarize the association between two binary variables. They have two rows and two columns, yielding four cells typically labeled a, b, c, and d. In a common setup, the rows represent exposure (yes/no) and the columns represent outcome (present/absent). The cell counts record how many observations fall into each category.

Measures of association: The odds ratio (OR) is (a*d)/(b*c) and describes how the odds of the outcome differ by exposure. The relative risk (RR) is [a/(a+b)] / [c/(c+d)], comparing probabilities of the outcome between exposure groups. The risk difference (RD) is [a/(a+b)] − [c/(c+d)]. In study designs, OR is common in case-control studies, while RR is preferred for cohort studies.

Statistical testing: The chi-squared test for independence assesses whether there is an association between the two variables in the population; for small samples, Fisher’s exact test is used. Yates’ continuity correction may be applied to 2x2 chi-square tests.

Applications and interpretation: In diagnostic testing, the table is formed from test results versus true condition, with a = true positives, b = false positives, c = false negatives, d = true negatives. From these, sensitivity = a/(a+c) and specificity = d/(b+d) can be computed, along with predictive values. The 2x2 table provides a simple, interpretable summary, but it captures only two variables and does not adjust for confounding factors; more advanced methods, such as logistic regression, are used to control for additional variables. Example values (a=30, b=70, c=10, d=90) yield an OR of about 3.86 and an RR of 3.0.