Zähltradatenanalyse

Zähltradatenanalyse, often translated as count data analysis, is a statistical field focused on modeling and understanding data that represents the number of occurrences of an event within a specified interval or unit. This type of data is inherently non-negative and discrete, meaning it can only take on integer values starting from zero. Examples of count data include the number of customers visiting a store per hour, the number of defects on a manufactured item, or the number of calls received by a call center in a day.

Traditional statistical methods like linear regression are often inappropriate for count data because they assume normally distributed errors and can produce predicted values that are negative, which is nonsensical for counts. Therefore, specialized statistical models have been developed. The most common is the Poisson regression model, which assumes that the count data follows a Poisson distribution. The mean and variance of a Poisson distribution are equal.

However, count data frequently exhibits overdispersion, meaning the variance is greater than the mean. This violates the assumptions of the standard Poisson model and can lead to inaccurate standard errors and inferences. To address overdispersion, alternative models such as the negative binomial regression model are employed. This model allows the variance to be a function of the mean, accommodating a wider range of dispersion patterns. Other advanced techniques may involve zero-inflated models, which are used when there are more zeros in the data than expected by standard count distributions, suggesting a two-part process: one that generates zeros and another that generates positive counts. Zähltradatenanalyse is crucial in fields like ecology, public health, economics, and manufacturing for making predictions, identifying risk factors, and understanding underlying processes.