BartlettSchätzung

The BartlettSchätzung, often translated as the Bartlett estimator or Bartlett method, is a technique used in statistics for estimating variance. It is particularly useful when dealing with multiple samples or groups. The core idea behind the BartlettSchätzung is to combine information from these different sources to arrive at a more robust estimate of the population variance than would be obtained from any single sample alone.

The method involves calculating the pooled variance, which is a weighted average of the variances from each individual group. The weights are typically related to the degrees of freedom within each group. This pooling of variances assumes that the population variances of all the groups are equal, a condition that can be tested using an F-test (Bartlett's test of homogeneity of variances). If this assumption is violated, the pooled variance estimate may be biased.

Bartlett's test itself is a statistical test designed to assess whether multiple sample variances are equal. It is a more sensitive test for homogeneity of variances compared to Levene's test, especially when the data are normally distributed. However, Bartlett's test is also known to be sensitive to departures from normality. Therefore, when using the BartlettSchätzung, it is important to consider the underlying assumptions and potentially explore alternative methods if those assumptions are not met. The BartlettSchätzung is a foundational concept in statistical analysis, particularly in contexts like analysis of variance (ANOVA) where comparing variances is crucial.