the data of most other clinical scales, are not properly measured but assessed in some way, by the clinician working with the patient.6 This is a characteristic of all ordinal data.

Because ordinal data are not real numbers, it is not appropriate to apply any of the rules of basic arithmetic to this sort of data. You should not add, subtract, multiply or divide ordinal values. This limitation has marked implications for the sorts of analyses we can do with such data – as you will see later in this book.

Exercise 1.2 Suggest a few more scales with which you may be familiar from your clinical work.

Exercise 1.3 Explain why it wouldn’t really make sense to calculate an average Glasgow Coma Scale for a group of head injury patients.

Metric variables

Continuous metric variables

Look at Table 1.4, which shows the weight in kg (rounded to two decimal places) of six individuals.

6There are some scales that may involve some degree of proper measurement, but these will still produce ordinal values if even one part of the score is determined by a non-measured element.

The variable ‘weight’ is a metric continuous variable. With metric variables, proper measurement is possible. For example, if we want to know someone’s weight, we can use a weighing machine, we don’t have to look at the patient and make a guess (which would be approximate), or ask them how heavy they are (very unreliable). Similarly, if we want to know their diastolic blood pressure we can use a sphygmometer.7 Guessing, or asking, is not necessary.

Because they can be properly measured, these variables produce data that are real numbers, and so can be placed on the number line. Some common examples of metric continuous variables include: birthweight (g), blood pressure (mmHg), blood cholesterol (μg/ml), waiting time (minutes), body mass index (kg/m2), peak expiry flow (l per min), and so on. Notice that all of these variables have units of measurement attached to them. This is a characteristic of all metric continuous variables.

In contrast to ordinal values, the difference between any pair of adjacent values is exactly the same. The difference between birthweights of 4000 g and 4001 g is the same as the difference between 4001 g and 4002 g, and so on. This property of real numbers is known as the interval property (and as we have seen, it’s not a property possessed by ordinal values). Moreover, a blood cholesterol score, for example, of 8.4 μg/ml is exactly twice a blood cholesterol of 4.2 μg/ml. This property is known as the ratio property (again not shared by ordinal values).8 In summary:

Metric continuous variables can be properly measured and have units of measurement.

They produce data that are real numbers (located on the number line).

These properties are in marked contrast to the characteristics of nominal and ordinal variables. Because metric data values are real numbers, you can apply all of the usual mathematical operations to them. This opens up a much wider range of analytical possibilities than is possible

with either nominal or ordinal data – as you will see.

Exercise 1.4 Suggest a few continuous metric variables with which you are familiar. What is the difference between, and consequences of, assessing the value of something and measuring it?

7We call the device we use to obtain the measured value, e.g. a weighing scale, or a sphygmometer, or tape measure, etc., a measuring instrument.

8It is for these two reasons that metric data is also known as ‘interval/ratio’ data – but ‘metric’ data is shorter!

Discrete metric variables

Consider the data in Table 1.5. This shows the number of times in the past 24 hours that each of six children with asthma used their inhalers.

Continuous metric data usually comes from measuring. Discrete metric data, such as that in Table 1.5, usually comes from counting. For example, number of deaths, number of pressure sores, number of angina attacks, and so on, are all discrete metric variables. The data produced are real numbers, and are invariably integer (i.e. whole number). They can be placed on the number line, and have the same interval and ratio properties as continuous metric data:

Metric discrete variables can be properly counted and have units of measurement – ‘numbers of things’.

They produce data which are real numbers located on the number line.

Exercise 1.5 Suggest a few discrete metric variables with which you are familiar.

Exercise 1.6 What is the difference between a continuous and a discrete metric variable? Somebody shows you a six-pack egg carton. List (a) the possible number of eggs that the carton could contain; (b) the number of possible values for the weight of the empty carton. What do you conclude?

How can I tell what type of variable I am dealing with?

The easiest way to tell whether data is metric is to check whether it has units attached to it, such as: g, mm, ◦C, μg/cm3, number of pressure sores, number of deaths, and so on. If not, it may be ordinal or nominal – the former if the values can be put in any meaningful order. Figure 1.2 is an aid to variable type recognition.

Table 1.6 Characteristics of cases and controls from a case-control study into stressful life events and breast cancer in women. Values are mean (SD) unless stated otherwise. Reproduced from BMJ, 319, 1027–30, courtesy of BMJ Publishing Group

Two sample t test.

†Data for one case missing.

‡χ 2 test for trend. §χ 2 test.

¶No data for one control.

Table 1.7 Patient characteristics from a cross-section study of thrombotic risk during pregnancy. Reproduced with permission from Elsevier (Obstetrics and Gynaecology, 1999, Vol. 94, pages 595–599.

OR = odds ratio; CI = confidence interval.

Data presented as n (%).

Table 1.8 Basic characteristics of two groups of children in a study to compare two lotions in the treatment of head lice. One group (95 children) were given Malathion lotion, the second group (98 children), d-phenothrin. Reprinted courtesy of Elsevier (The Lancet, 1994, 344, 1724–26)

The 2 groups were similar at baseline except for a significant difference for the length of hair (p = 0.02; chi-square).One value missing in the d -phenothrin group.

Baseline characteristics of the P Humanus capitis-infested schoolchildren assigned to receive malathion or d - phenothrin lotion

II

Descriptive Statistics