Gesamtstreuung

Gesamtstreuung, often abbreviated as SST, is a term used in statistical analysis, particularly in the context of analysis of variance (ANOVA). It represents the total variability present in a dataset. This total variability is broken down into different components to understand the sources of variation. In ANOVA, Gesamtstreuung is the sum of the squared deviations of each individual data point from the overall mean of all data points. It encompasses all sources of variation, including systematic effects (differences between groups) and random error (variability within groups).

Mathematically, Gesamtstreuung is calculated as the sum of (xi - x_grand_mean)^2 for all observations xi, where x_grand_mean is the mean of all data points across all groups. This value serves as the numerator in calculating the F-statistic in ANOVA, which compares the variance explained by the group means to the unexplained variance within the groups. A higher Gesamtstreuung indicates greater overall dispersion in the data. Understanding Gesamtstreuung is fundamental to determining whether observed differences between groups are statistically significant or merely due to random chance. It provides the baseline for assessing the impact of different factors on the outcome variable.