Conferences

In sampling theory from finite population sometimes is necessary to introduce some techniques that are customary use in observational studies of epidemiological type. The reason for introducing these techniques in sampling theory is that instead of estimating the population parameters of reference, we may be interested in measuring the association between a variable object of interest for the study (effect) and other variables which may be causes for it. One of the techniques used in epidemiological studies is the so-called control sample. There are also other variables, named “confounding” in the epidemiological literature, which could be thought as causes but which in fact are kept under control and used to divide “people” into groups of reference. So the aim of this paper is to provide a sampling plan to identify “effect” samples and “control” samples and then identify appropriate measures of association. Given that the effect can be seen dichotomy without loss of generality, indicate with U the population, with E and C the two subsets, the first formed by the units with the variable of attention e and the second where e is absent. In this context the construction of the two types of samples is done by splitting the N units of E and M units of C in H groups using confounding variables independent by e. The Nh units of the E subset are the h-th effect group and the Mh units of the C subset are the corresponding control group. The Nh units are similar to each other compared with confounding variables and also happens to Mh units of the control group which, in turn, are similar to units of the effect group. The confounding variables used to divide people into groups should not be thought as auxiliary variables with which stratify the population or as naturally existing variables with which build clusters designed as at first stage. A first problem, of not trivial solution, is to establish a basis on which set the sample sizes mh in each of the H groups; another, even more difficult, is to identify an appropriate measure of association which takes into account the measures in each of the groups. These are the two objectives addressed in this work.