Experiment!: Planning, Implementing and Interpreting

7

Basic Statistics

There is nothing permanent except change.

—Heraclitus

Knowledge in statistics is crucial when analyzing data. Most students in the natural and engineering sciences therefore take a course that covers descriptive statistics and some more advanced topics, such as confidence intervals, hypothesis tests and so on. Since these concepts are rarely used in courses other than statistics, students tend to forget about them. As a result, many Ph.D. students never venture beyond using purely descriptive statistical methods such as calculating means and standard deviations of data sets. My personal experience is that statistics courses are often taught outside of a practical context. Instead of teaching how to use statistics to solve real problems, the courses tend to focus on statistical theory and textbook problems. This could explain why knowledge often seems to decay so rapidly after the statistics exam. The best way to forget theoretical knowledge is, after all, to never apply it.

The purpose of this chapter is to lay a foundation for the next few chapters. Statistical concepts are introduced that will be important when analyzing experimental data. Since the readers probably have varying degrees of mathematical training I have tried to use less mathematics than many books on statistics do. Many readers will be familiar with much of the contents, especially the first few sections. They might feel tempted to skip the entire chapter but there are probably a few topics ...