bands of the APACHE II score. Quite clearly, for those less severely ill, percentage mortality among the medical emergency group is noticeably higher than among the post-operative group. For those patients classified as the most severely ill (scores of 35+), the situation is reversed.

Figure 3.6 A stacked bar chart of hair colour by sex

The stacked bar chart

Figure 3.6 shows a stacked bar chart for the same hair colour and sex data shown in Table 3.1. Instead of appearing side by side, as in the clustered bar chart of Figure 3.5, the bars are now stacked on top of each other.1 Stacked bar charts are appropriate if you want to compare the total number of subjects in each group (total number of boys and girls for example), but not so good if you want to compare category sizes between groups, e.g. redheaded girls with redheaded boys.

Exercise 3.6 Draw a stacked bar chart showing the same data as in Figure 3.6, but grouped by hair colour (i.e. hair colour on the horizontal axis).

Charting discrete metric data

We can use bar charts to graph discrete metric data in the same way as with ordinal data.2

1We could, alternatively, have used four columns for the four colour categories, with two groups per column (boys and girls). As with the clustered bar chart, the most appropriate arrangement depends on what aspects of the data you want to compare.

2In theory we should represent the discrete metric values with vertical lines and not bars, since they are ‘point’ values, but most common computer statistics packages don’t offer this facility.

(prescribed for hypertension) and the risk of suicide (Lindberg et al. 1998). So for example, in year 4 the suicide rate per 1000 of the population was (7 − 5.2) = 1.8 (the approximate height of the step). And over the course of the first four years, the suicide rate had risen to seven per thousand. You can produce step charts for numeric ordinal data, such as cumulative Apgar scores in exactly the same way, although not, as far as I am aware, with Word or Excel, or with SPSS or Minitab.

Table 3.3 Cumulative and relative cumulative frequency for the grouped birthweight from the data in Table 2.6

Exercise 3.10 Draw a step chart for the percentage cumulative Apgar scores in Table 3.3.

The cumulative frequency curve or ogive

With continuous metric data, there is assumed to be a smooth continuum of values, so you can chart cumulative frequency with a correspondingly smooth curve, known as a cumulative frequency curve, or ogive.4 If you add columns for cumulative and relative cumulative frequency to the grouped birthweight data in Table 2.6, you get Table 3.3.

If you want to draw an ogive by hand, you plot, for each group or class, the group cumulative frequency value against the lower limit of the next higher group. So, for example, 16.67 is plotted against 3300, 46.67 against 3600, and so on. The points should be joined with a smooth curve.5 The result is shown in Figure 3.11. Notice that I have put a percentage cumulative frequency of zero in the imaginary group 2400–2699 g. This enables me to close the ogive at the left-hand end.

The ogive can be very useful if you want to estimate the cumulative frequency for any value on the horizontal axis, which is not one of the original group values. For example, suppose you want to know what percentage of infants had a birthweight of 3650g or less. By drawing a line vertically upwards from a value of 3750 g on the horizontal axis to the ogive, and then horizontally to the vertical axis, you can see that about 63 per cent of the infants weighed 3750 g or less. You can of course ask such questions in reverse, for example, what birthweight marks the lowest 50 per cent of birthweights? This time you would start with a value of 50 per cent

4The ‘g’ in ogive is pronounced as the j in ‘jive’.

5Unfortunately, I couldn’t find a program that would allow me to join the points with a smooth curve.

Birthweight (g)

Figure 3.11 The relative cumulative frequency curve (or ogive) for the percentage cumulative birthweight data in Table 3.3

on the vertical axis, move right to the ogive, then down to the value of about 3700 g on the horizontal axis.

An example from practice

Figure 3.12 shows two per cent ogives for total cholesterol concentration in two groups taken from a study into the effectiveness of health checks conducted by nurses in primary care (Imperial Cancer Fund OXCHECK Study Group 1995)

Total cholesterol (mmol/l)

Figure 3.12 Percentage cumulative frequency curves for total cholesterol concentration in two groups. Reproduced from BMJ, 310, 1099–104, courtesy of BMJ

An example from practice

Figure 3.13 shows the suicide rates (number of suicides per one million of population), for males and females aged 15–29 years in England and Wales, between 1974 and 1999. The contrasting patterns in the male/female rates are noticeable, more perhaps in this chart form than if shown in a table.

There is one other useful chart, the boxplot, but that will have to wait until we meet some new ideas in the next two chapters. Meanwhile Table 3.4 may help you to decide on the most appropriate chart for any given set of data.