Analysis of mutual information measures in cluster sampling
In many studies in which we need to estimate the diversity of categories (or entropy) in a finite population with respect to a classification process, it is usually easier to take cluster units than individual ones. On the other hand, to obtain a gain in the estimate precision, it is interesting to stratify the population by means of a factor that exerts a strong influence on the distribution of categories (more precisely, a factor supplying a high ''mutual information'' value between the classification process and itself). For these reasons, we are now going to examine the problem of drawing statistical conclusions concerning several indices of mutual information in a simple-stage cluster sampling. A procedure to test the suitability of a factor for stratification in estimating diversity or entropy will be also discussed.