A - Basic Analysis of Numerical Data

Summary

Often, the goal of an experiment is the taking of some measurement or a series of measurements. Although it may seem that, with such data in hand, the important work has been done, and all that remains is the mopping up of data analysis, the interpretation of the raw numbers may be as involved and difficult as any experimental setup. Numbers by themselves tell you nothing and extracting meaning from them is an art.

In this appendix, we look at some of the basic ideas involved in interpreting numerical data. We will not focus on any particular type of experiment, but rather imagine the likely outcomes of many measurements and learn the simplest ways of extracting information from large batches of numbers. Although not all data are numerical in nature (you might record qualitative information such as color, for example), it is only numerical data that will be discussed here.

We also focus primarily on questions of the interpretation of data and do not attempt to discuss points of experimental design. This is actually a rather artificial distinction, since when designing an experiment, a scientist must be sure that once data are obtained they will be amenable to analysis. Thus, what may appear as an after-the-fact analysis of data in this discussion should really be an analysis that the experimenter intended to do from the start.