Randomness appears in the evolution of many natural phenomena which are developed under uncertainty (weather, size of populations, epidemics, etc.) and systems created by the human beings (signal transmisions, useful life of electrical appliances, etc.). To study any of them stochastic processes are the appropriate mathematical tool.
The main target of statistical experiments is to obtain a set of data with which a statistical model is fitted to explain, predict or compare. The applicability spreads over many scientific fields. and the techniques are easy to translate among them. In a random experiment there are two main facts: the random selection of subjects to be observed and the random allocation of the individuals among treatments. The former is known as sampling and is assumed to be controlled out of the experiment; the latter allows the statistical analysis and is internally controlled.
We have focused our research on clinical trials. In this field the experiment consists in comparing two treatments in order to establish the superiority of one of them. Several techniques have been developed for the inference when a random sample is not acceptable (permutation tests) due to the deterministic selection of patients and, also, several randomization techniques to allocate patients among treatments have been proposed in the specialized literature.
We also study optimal techniques to collect data and design an experiment by optimizing, simultaneously, ethical, inferential and random issues.