From Sample to Population

Summary

Up to now we studied only the sample and the results we obtained are only valid for this sample.

It is time to see now what can be said about the population as a whole, which means for any object of the population. After all, our purpose is to be able to estimate any object of the population ...

The chapter starts by developing the principles on which are based the extrapolations of what was found on the sample to the population. It first reminds the cost analyst that the shape of the relationship between the dependent variable and the parameters or cost drivers is a choice he/she has to make. From the sample we want then to compute estimators of the coefficients which appear in the formula giving the dynamic center of the cost distribution for the whole population. The qualities expected for these estimators are mentioned.

The important question is: how far can be the estimators derived from the sample to the true value of the coefficients? Two solutions are generally proposed, based on hypothesis testing on one hand, confidence interval on the other hand, both being the different faces of the same coin.

Then the way the perceived relationships — in the sample — can be extrapolated to the population is investigated: two solutions are possible:

• 1. The classical solution is illustrated with the correlation coefficient: if a correlation has been found in the sample between two variables, what can be said about these variables for the population?

• 2. The modern approach, based on the Bootstrap, or its “little brother” the Jackknife.

In order to introduce the solutions on a simple case, the principles are first applied to the simple problem of a cost distribution with no cost driver: this is a basic idea, for instance, for the opinion surveys. One shows how, classically, the center of the cost distribution — always for the population — and its spread can be estimated. The important “t” variable is explained. Then the modern approach is illustrated and the results of both approaches compared.

The case of a distribution using one cost driver is then presented, followed by the case involving several quantitative parameters and qualitative parameters.