12.6 Graphing two qualitative variables

The relationship between two qualitative variables can be explored using:

Many variations of these graphs are possible.

As an example, a study of road kill produced the data in Table 12.3. There are two qualitative variables: the season (ordinal, with four levels) and the sex (nominal, with three levels including ‘Unknown’).

TABLE 12.3: The number of possums found as road kill, by sex and season
Unknown M F
Autumn 75 25 21
Winter 74 27 22
Spring 71 10 18
Summer 58 10 12

12.6.1 Stacked bar charts

The data can be graphed by using a bar for each season, stacking the bars by sex on top of each other, within each season (Fig. 12.22).

12.6.2 Side-by-side bar charts

Instead of stacking the bars within each season on top of each other, the bars can be placed side-by-side within each season (Fig. 12.23).

12.6.3 Dot charts

Instead of bars, dots (or other symbols) can be used in place of a side-by-side bar chart (Fig. 12.24).

12.6.4 Other variations

Many variations of these bar charts are possible. We can choose:

• horizontal or vertical bars;
• percentages or counts;
• stacked bar charts, side-by-side bar charts, or dot charts;
• either the sex of the possum or the season as the first division of the data.

Many variations exist; some are shown in Fig. 12.25. Another display is to construct a two-way table, of either counts (Table 12.3) or percentages (Table 12.4).

TABLE 12.4: The percentages of possums found as road kill by sex, within each season (rows sum to 100%)
Unknown M F
Aut. 62.0 20.7 17.4
Wint. 60.2 22.0 17.9
Spr. 71.7 10.1 18.2
Sum. 72.5 12.5 15.0
Think 12.3 (The “best” graph) Of all these displays, which one do you think best communicates the message in the data? (Indeed, what is the main message that you would like to get across?)

References

Russell TC, Herbert CA, Kohen JL. High possum mortality on urban roads: Implications for the population viability of the common brushtail and the common ringtail possum. Australian Journal of Zoology. 2009;57:391–7.