Reasonable sample sizes for convergence to normality - Carsten Schröder; Shlomo Yitzhaki (Deutsches Institut für Wirtschaftsforschung (DIW), 2014)
The central limit theorem says that, provided an estimator fulfills certain weak conditions, then, for reasonable sample sizes, the sampling distribution of the estimator converges to normality. We propose a procedure to find out what a "reasonably large sample size" is. The procedure is based on the properties of Gini's mean difference decomposition. We show the results of implementations of the procedure from simulated datasets and data from the German Socio-economic Panel.
Keywords: C1; C4; 330; central limit theorem; Gini's mean difference composition