Kontinuitätskorrektur

Kontinuitätskorrektur refers to a statistical technique used in the analysis of categorical data. It is applied when approximating a discrete distribution with a continuous distribution. The most common application is in the context of the chi-squared test for independence or goodness-of-fit.

Specifically, when performing a chi-squared test with a small sample size, the distribution of the test statistic under the null hypothesis is discrete. However, the chi-squared distribution is continuous. To improve the accuracy of the approximation, the continuity correction is applied. This involves adjusting the observed frequencies by adding or subtracting 0.5 before calculating the chi-squared statistic. For example, in a 2x2 contingency table, the expected frequencies are adjusted by 0.5.

The purpose of the continuity correction is to reduce the error introduced by approximating a discrete distribution with a continuous one. By slightly shifting the boundaries of the observed categories, the correction helps to better match the shape of the continuous chi-squared distribution. This can lead to more accurate p-values, especially when sample sizes are small.

While widely used, the necessity and optimal application of the continuity correction are still debated among statisticians. Some argue that for larger sample sizes, the correction has little effect and may even be overly conservative, leading to a loss of power. Others maintain its value for smaller datasets where the approximation is more critical. The decision to apply it often depends on the specific research context and statistical guidelines.