Raising the bar

Chapter 2. Describing Data: Graphical

Unit 2.1. Classification of variables

An important part of working with definitions consists in comparing related definitions. This is the right time to discuss the choice from among different definitions of the same object. An intuitive definition gives you the main idea and often helps you come up with the formal definition, which is mostly a formula. Formal definitions may have different forms. The one which is easier to apply is called a working definition. Some complex definitions may be difficult to understand on the first push. In this case it is better to start with simplified definitions. They usually are also shorter. We also distinguish between descriptive definitions (when properties of an object are described) and complementary definitions (instead of saying what an object is we can say what it is not).

In the figure below you see a summary of part of Chapter 1 from Newbold, Carlson, and Thorne (NCT) on classification of variables. Those definitions that are not essential for the subsequent chapters are skipped. For the remaining ones I give short, working and simplified definitions.

Figure 2.1. Classification of variables.

NCT usually gives several motivating examples. I recommend remembering and thinking about just one motivating example for each definition (or statement, or method).

Problem with categorical variables. Categorical variables have been defined as complementary to numerical ones. Most statistical measures use arithmetic operations. Therefore they are not applicable to categorical variables. The workaround is to associate numerical variables with categorical variables. For example, instead of working with responses "Yes" and "No" we can work with the variable that takes two values: 1 for "Yes" and 0 for "No".

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