Varianseanalyse

Varianseanalyse, often abbreviated as ANOVA, is a statistical method used to compare the means of two or more groups. Developed by Ronald Fisher, it partitions the total variation in a dataset into different sources of variation. The primary purpose of ANOVA is to determine whether there are statistically significant differences between the group means. It achieves this by comparing the variance between the groups to the variance within each group.

The fundamental principle behind ANOVA is to test a null hypothesis, which states that all group means are equal, against an alternative hypothesis, which suggests that at least one group mean is different. The test statistic used in ANOVA is the F-statistic, which is the ratio of the variance between groups to the variance within groups. A larger F-statistic indicates that the variation between groups is significantly greater than the variation within groups, leading to the rejection of the null hypothesis.

ANOVA can be classified into different types, such as one-way ANOVA, which involves one independent variable with multiple levels, and two-way ANOVA, which involves two or more independent variables. The choice of ANOVA type depends on the research question and the experimental design. Post-hoc tests are often conducted after a significant ANOVA result to identify which specific group means differ from each other. ANOVA is widely applied in various fields, including psychology, biology, economics, and social sciences, to analyze experimental data and draw conclusions about group differences.