No abstract

No abstract

The design of complex samples induces correlations between element values. In stratification negative correlation reduces the variance; but that gain is less for subclass means, and even less for their differences and for complex statistics. Clustering induces larger and positive correlations between element values. The resulting increase in variance is measured by the ratio deff, and is often severe. This is reduced but persists for subclass means, their differences, and for analytical statistics. Three methods for computing variances are compared in a large empirical study. The results are encouraging and useful.