Statistical Methods in Medical Research 4ed

22 Describing data
cannot be less than zero, and there is presumably some lower limit above zero
and some upper limit, but it would be difficult to say exactly what these limits
are. The distinction between discrete and continuous variables is not always
clear, because all continuous measurements are in practice rounded off; for
instance, a series of heights might be recorded to the nearest centimetre and so
appear discrete. Any ambiguity rarely matters, since the same statistical methods
can often be safely applied to both continuous and discrete variables, particularly
if the scale used for the latter is fairly finely subdivided. On the other hand,
there are some special methods applicable to counts, which as we have seen must
be positive whole numbers. The problems of summarizing quantitative data are
much more complex than those for qualitative data, and the remainder of this
chapter will be devoted almost entirely to them.
Sometimes a continuous or a discrete quantitative variable may be summarized
by dividing the range of values into a number of categories, or grouping
intervals, and producing a table of frequencies. For example, for age a number of
age groups could be created and each individual put into one of the groups. The
variable, age, has then been transformed into a new variable, age group, which
has all the characteristics of an ordered categorical variable. Such a variable may
be called an interval variable.
A useful first step in summarizing a fairly large collection of quantitative data
is the formation of a frequency distribution. This is a table showing the number of
observations, or frequency, at different values or within certain ranges of values
of the variable. For a discrete variable with a few categories the frequency may
be tabulated at each value, but, if there is a wide range of possible values, it will be
convenient to subdivide the range into categories. An example is shown in Table
2.3. (In this example the reader should note the distinction between two types of
countÐthe variable, which is the number of lesions on an individual chorioallantoic
membrane, and the frequency, which is the number of membranes on which
the variable falls within a specified range.) With continuous measurements one
must form grouping intervals (Table 2.4). In Table 2.4 the cumulative relative
Table 2.4 Frequency distribution of age for 1357 male patients with lung cancer.
Age (years)
Frequency
(number of patients)
Relative
frequency (%)
Cumulative relative
frequency (%)
25± 17 1 3 1 3
35± 116 8 5 9 8
45± 493 36 3 46 1
55± 545 40 2 86 3
65±74 186 13 7 100 0
Total 1357 100 0