Richtungsstatistiken

Richtungsstatistiken, also known as directional statistics or circular statistics, is a subfield of statistics that deals with the analysis of data that are measured on a circle or a sphere. Unlike linear statistics, where data points lie on a line, directional statistics are concerned with angles, directions, and orientations.

Examples of directional data include wind directions, animal migration paths, geological strike and dip measurements, and the orientation of proteins. Analyzing this type of data requires specialized methods because the usual assumptions of linear statistics, such as normality and independence, may not hold. For instance, a simple average of angles can be misleading. If you average 10 degrees and 350 degrees, the arithmetic mean is 180 degrees, which is not representative of either direction.

Key concepts in richtungsstatistiken include circular distributions, such as the von Mises distribution (analogous to the normal distribution on a circle) and the wrapped normal distribution. Measures of central tendency for circular data include the mean direction and the circular median. Measures of dispersion include the circular variance and the circular standard deviation. Statistical tests are also adapted for circular data, allowing for comparisons between groups or hypothesis testing. The field provides tools to understand patterns, variability, and relationships within directional datasets.