1

First things first – the nature of data

Learning objectives

When you have finished this chapter, you should be able to:

Explain the difference between nominal, ordinal, and metric discrete and metric continuous variables.

Identify the type of a variable.

Explain the non-numeric nature of ordinal data.

Variables and data

A variable is something whose value can vary. For example, age, sex and blood type are variables. Data are the values you get when you measure1 a variable. For example, 32 years (for the variable age), or female (for the variable sex). I have illustrated the idea in Table 1.1.

1I am using ‘measure’ in the broadest sense here. We wouldn’t measure the sex or the ethnicity of someone, for example. We would instead usually observe it or ask the person or get the value from a questionnaire. But we would measure their height or their blood pressure. More on this shortly.

Medical Statistics from Scratch, Second Edition David Bowers

C 2008 John Wiley & Sons, Ltd

Table 1.2 Blood types of 100 patients (fictitious data)

By the way, a table like Table 1.2 is called a frequency table, or a contingency table. It shows how the number, or frequency, of the different blood types is distributed across the four categories. So 65 patients have a blood type O, 15 blood type A, and so on. We’ll look at frequency tables in more detail in the next chapter.

The variable ‘blood type’ is a nominal categorical variable. Notice two things about this variable, which is typical of all nominal variables:

The data do not have any units of measurement.3

The ordering of the categories is completely arbitrary. In other words, the categories cannot be ordered in any meaningful way.4

In other words we could just as easily write the blood type categories as A/B, B, O, A or B, O, A, A/B, or B, A, A/B, O, or whatever. We can’t say that being in any particular category is better, or shorter, or quicker, or longer, than being in any other category.

Exercise 1.1 Suggest a few other nominal variables.

Ordinal categorical variables

Let’s now consider another variable some of you may be familiar with – the Glasgow Coma Scale, or GCS for short. As the name suggests, this scale measures the degree of brain injury following head trauma. A patient’s Glasgow Coma Scale score is judged by their responsiveness, as observed by a clinician, in three areas: eye opening response, verbal response and motor response. The GCS score can vary from 3 (death or severe injury) to 15 (mild or no injury). In other words, there are 13 possible values or categories of brain injury.

Imagine that we determine the Glasgow Coma Scale scores of the last 90 patients admitted to an Emergency Department with head trauma, and we allocate the score of each patient to one of the 13 categories. The results might look like the frequency table shown in Table 1.3.

3For example, cm, or seconds, or ccs, or kg, etc.

4We are excluding trivial arrangements such as alphabetic.