Statistics in a Nutshell

Chapter 1. Basic Concepts of Measurement

Before you can use statistics to analyze a problem, you must convert the basic materials of the problem to data. That is, you must establish or adopt a system of assigning values, most often numbers, to the objects or concepts that are central to the problem under study. This is not an esoteric process, but something you do every day. For instance, when you buy something at the store, the price you pay is a measurement: it assigns a number to the amount of currency that you have exchanged for the goods received. Similarly, when you step on the bathroom scale in the morning, the number you see is a measurement of your body weight. Depending on where you live, this number may be expressed in either pounds or kilograms, but the principle of assigning a number to a physical quantity (weight) holds true in either case.

Not all data need be numeric. For instance, the categories male and female are commonly used in both science and in everyday life to classify people, and there is nothing inherently numeric in these categories. Similarly, we often speak of the colors of objects in broad classes such as “red” or “blue”: these categories of which represent a great simplification from the infinite variety of colors that exist in the world. This is such a common practice that we hardly give it a second thought.

How specific we want to be with these categories (for instance, is “garnet” a separate color from “red”? Should transgendered individuals be assigned ...