Statistical Methods in Medical Research 4ed

2.3 Summarizing numerical data 23
frequencies are also tabulated. These give the percentages of the total who are
younger than the lower limit of the following interval, that is, 9 8% of the
subjects are in the age groups 25±34 and 35±44 and so are younger than 45.
The advantages in presenting numerical data in the form of a frequency
distribution rather than a long list of individual observations are too obvious to
need stressing. On the other hand, if there are only a few observations, a frequency
distribution will be of little value since the number of readings falling into each
group will be too small to permit any meaningful pattern to emerge.
We now consider in more detail the practical task of forming a frequency
distribution. If the variable is to be grouped, a decision will have to be taken
about the end-points of the groups. For convenience these should be chosen, as
far as possible, to be `round' numbers. For distributions of age, for example, it is
customary to use multiples of 5 or 10 as the boundaries of the groups. Care
should be taken in deciding in which group to place an observation falling on one
of the group boundaries, and the decision must be made clear to the reader.
Usually such an observation is placed in the group of which the observation is
the lower limit. For example, in Table 2.3 a count of 20 lesions would be placed
in the group 20±, which includes all counts between 20 and 29, and this convention
is indicated by the notation used for the groups.
How many groups should there be? No clear-cut rule can be given. To
provide a useful, concise indication of the nature of the distribution, fewer
than five groups will usually be too few and more than 20 will usually be too
many. Again, if too large a number of groups is chosen, the investigator may find
that many of the groups contain frequencies which are too small to provide any
regularity in the shape of the distribution. For a given size of grouping interval
this difficulty will become more acute as the total number of observations is
reduced, and the choice of grouping interval may, therefore, depend on this
number. If in doubt, the grouping interval may be chosen smaller than that to
be finally used, and groups may be amalgamated in the most appropriate way
after the distribution has been formed.
If the original data are contained in a computer file, a frequency distribution
can readily be formed by use of a statistical package. If the measurements are
available only as a list on paper, the counts should be made by going systematically
through the list, `tallying' each measurement into its appropriate group.
The whole process should be repeated as a check. The alternative method of
taking each group in turn and counting the observations falling into that group is
not to be recommended, as it requires the scanning of the list of observations
once for each group (or more than once if a check is required) and thus
encourages mistakes.
If the number of observations is not too great (say, fewer than about 50), a
frequency distribution can be depicted graphically by a diagram such as Fig. 2.5.
Here each individual observation is represented by a dot or some other mark