Velocity distributions in galaxy clusters

We applied five well known normality tests to the velocity distributions of these systems to distinguish Gaussian and non-Gaussian clusters. Using controlled samples, we estimated type I and II errors for each test.

We verified that individual tests minimize the chances of classifying a Gaussian system as non-Gaussian, while the Fisher's meta-analysis method, a procedure to combine p-values from several statistical tests, minimizes the chances of classifying a non-Gaussian system as Gaussian. Taking the positive elements of each method and also including a modality analysis of the velocity distribution, we defined objective criteria to split up the sample into Gaussian and non-Gaussian clusters.