Whenever the signal to noise ratio is smaller than one, identification is likely to be unclear, unconvincing and open to discussion. For instance, it is because the signal in the Werther effect is of the same magnitude as the noise that the very existence of this effect is still a matter of debate thirty years after Phillips's pioneering paper. Similarly, many variables which are of central importance in economics, e.g. the elasticities of commodity prices with respect to supply or demand, are not known with a precision better than 30% or 50%. Other figures regarding the accuracy of economic data can be found in Morgenstern (1950). Raising the signal to noise ratio is a crucial challenge for the social sciences. In this chapter we describe three methods for improving signal identification and we illustrate them through specific social phenomena.

Before we begin, an additional remark is in order. Signal detection is an important topic in mathematical statistics. Here however, we propose upstream solutions to be used in the design phase of an experiment. Once the data have been recorded the fate of the battle against noise is largely settled. Using one statistical technique rather than another will improve matters only marginally.

The extreme value technique

Suppose we wish to study how the period of a pendulum depends upon the initial angular deviation θ0. If we try initial amplitudes of 5, 10, 15, 20, 25 and 30 degrees the corresponding periods will differ by less than 5%.