1.1 Statistical Inference: Making the Most of Your Data

Statistics is a tool for scientific research. It offers a range of techniques to check whether statements about the observable world are supported by data collected from that world. Scientific theories strive for general statements, that is, statements that apply to many situations. Checking these statements requires lots of data covering all situations addressed by theory.

Collecting data, however, is expensive, so we would like to collect as little data as possible and still be able to draw conclusions about a much larger set. The cost and time involved in collecting large sets of data are also relevant to applied research, such as market research. In this context we also like to collect as little data as necessary.

Inferential statistics offers techniques for making statements about a larger set of observations from data collected for a smaller set of observations. The large set of observations about which we want to make a statement is called the population. The smaller set is called a sample. We want to generalize a statement about the sample to a statement about the population from which the sample was drawn.

Traditionally, statistical inference is generalization from the data collected in a random sample to the population from which the sample was drawn. This approach is the focus of the present book because it is currently the most widely used type of statistical inference in the social sciences. We will, however, point out other approaches in Chapter 4.

Statistical inference is conceptually complicated and for that reason quite often used incorrectly. We will therefore spend quite some time on the principles of statistical inference. Good understanding of the principles should help you to recognize and avoid incorrect use of statistical inference. In addition, it should help you to understand the controversies surrounding statistical inference and developments in the practice of applying statistical inference that are taking place. Investing time and energy in fully understanding the principles of statistical inference really pays off later.