## 12.8 Other types of graphs

Many types of graphs have been studied, for specific types of data. But sometimes, other plots are useful. Usually the best plot is one of those just described, but sometimes the best plot is something different, perhaps even unique. Always remember the driving principle:

The purpose of a graph is to display the information in the clearest, simplest possible way, to help us understand the data.

Importantly, a graphs needed that helps answer the research question. In this section, graphs for some other situations are discussed:

**Geographic plots**: Useful when the RQ is about comparing geographical regions.**Case-profile plots**: Useful when the same units are measured over a small number of time points, or are otherwise connected.**Histogram of differences**: Useful when the same units are measured over*two*time points, or are otherwise connected.**Time plots**: Useful when the units are measured over a large number of time points.

### 12.8.1 Geographic plots

When data are summarised over a geographic area, plotting accordingly can be useful.

**Example 12.18 (Geographics plots) **A study examining lower-limb amputation incidence in Australia
(based on Dillon et al. (2017))
produced the graphs in
Figs. 12.28 and 12.29.

### 12.8.2 Case-profile plots

Sometimes the same variable is measured on each
unit of analysis more than once
(i.e. many observations per unit of analysis) but only a small number of times.
Then a *case-profile plots* can be used:
plots that show how the response variable
changes for each unit of analysis.
Examples of this type of data include:

- Measurements of household water consumption before and after installing water-saving devices, for many households.
- Blood pressure measurements taken from left arms and right arms, for many people.

In both cases,
the data are *paired* (*two* observations per unit of analysis)
as each unit of analysis gets a pair of similar measurements.

**Example 12.19 (Case-profile plots) **A study of children with atopic asthma
(Lothian et al. 2006)
included
the graph in
Fig. 12.30.
Each line on the graph represents one person.

### 12.8.3 Histogram of differences

An alternative way to present paired data
(two observations made for each unit of analysis)
is to produce a histogram of the *changes* for each individual.
This may be easier to produce in software than a case-profile plot.

Consider the person in the case-profile plot
whose line is at the top of the plot in Fig. 12.30.
Their ‘pre’ IgE level is about 5500 micrograms/L,
and their ‘post’ IgE level is about 4500 micrograms/L,
which is a *change*
(or more descriptively, a *reduction*)
of about 1000 micrograms/L.
These reductions could be computed for each person
(Table 12.5).

IgE (before) | IgE (after) | IgE reduction |
---|---|---|

83 | 83 | 0 |

292 | 292 | 0 |

293 | 292 | 1 |

623 | 542 | 81 |

792 | 709 | 83 |

1543 | 1000 | 543 |

1668 | 1000 | 668 |

1960 | 1626 | 334 |

2877 | 2502 | 375 |

2961 | 2711 | 250 |

5504 | 4504 | 1000 |

Then a histogram can be constructed based on these
*reductions* in IgE,
with one reduction for each person
(Fig. 12.31).

**Example 12.20 (Graphing paired data) **The Electricity Council in Bristol
wanted to determine if a certain type of wall-cavity insulation
was effective in reducing energy consumption in winter
(The Open University 1983).
Their RQ was:

Is there an

average reductionin energy consumption due to adding insulation?

The data collected,
shown below,
can be graphed using a case-profile plot
(Fig. 12.32, top panel):
A dashed line has been used to show an *increase* in energy usage,
and a solid line for houses where energy was *saved* after installing insulation.
(Again, this is *encoding*
extra information.)

For these data,
finding the difference in energy consumption for each house seems sensible.
The same unit of analysis is measured twice on the same variable:
energy consumption *before* adding insulation and then *after* adding insulation.
The difference in energy consumption
(or the energy *saving* more specifically)
for each house can be computed,
then graphed
using a histogram, bar chart, stemplot, or dot chart
(Fig. 12.32, bottom panel).

**Example 12.21 (Graphing paired data) **A study (Dawson et al. 2017)
examined the average number of bacteria on birthday cakes
*before* and *after* blowing out the candles.

*change*in the number of bacteria could be computed for each cake, and a histogram of the differences plotted.

### 12.8.4 Time plots

Sometimes,
a variable is measured over many time points.
A *time plot* can be used,
which show how the variable changes over time.

**Example 12.22 (Time plots)**The baby-birth data (in Sect. 12.2.1) recorded the time of each birth. A time plot shows how the weights varied over time (Fig. 12.33).

**Example 12.23 (Time plots)**A study of the number of lynx trapped in the Mackenzie River area of Canada (Elton and Nicholson 1942) each year from 1821 to 1934 produced the data shown in Fig. 12.34. A regular cycle is apparent, where the number trapped is very large.