Using graphs and charts
Words and images
Graphs and charts are used to shows trends or patterns in numerical data. The most common types are line graphs, scatter plots, bar charts, histograms and pie charts (Figures 8.1-8.5). A graph or chart is normally referred to in text nearby, as in the preceding sentence.
Refer to Figures 8.1-8.5 as you examine the various conventions used in constructing graphs or charts:
✵If your document contains more than one graph, chart or other kind of figure, assign each a number in consecutive order and place the number before the title.
✵The title (legend) is placed below the chart or graph and should clearly and concisely describe what is being displayed.
✵Plan the graph or chart so that it fits appropriately on the page, with all features being clearly visible.
✵If the data or information used to create the graph or chart are not your own, the source should be cited (after the title or in a footnote just below the chart or graph).
Use a line graph to display a relationship between two continuous variables (see Figure 8.1). The independent variable (the variable chosen by the investigator) is plotted in relation to the x axis (the horizontal axis). The dependent variable (the variable that is dependent on the independent variable and for which values are not known before the investigation) is normally plotted in relation to the y axis (the vertical axis). In a line graph, each plotted point is described by two numbers, its coordinates, which give its position with respect to the x axis and y axis respectively. Points are normally connected by a hand-drawn line or a statistically computed one. If more than one set of data are plotted on the same graph, the data sets should be clearly distinguished by using different symbols for plotted points and/or a different form of line to connect them. A key is then needed to explain the symbols or forms of line, as in Figure 8.1. Full experimental detail would be included in the method section of the investigation, but might be summarised in the figure legend or in text accompanying the graph. Incidentally, the drop in mean length of the tadpoles at day 24 is due to them beginning
metamorphosis from a tadpole into an adult frog, which is accompanied by the tail being absorbed.
Figure 8.1 The growth of tadpoles of the common British frog, Rana temporaria, at 8°C (n = 25) and 25°C (n = 25). Hypothetical data
The scales for graph axes normally start at zero. If a scale does not start at zero, this should be clearly indicated, and the start point clearly labelled. Each scale is labelled in writing that usually runs parallel to the axis, and any units of measurement are clearly stated. Figure 8.1 is a simple line graph. In your studies you may be plotting graphs from data generated from statistical analyses, in which case a vertical bar showing standard error may be included to indicate distribution about the mean.
Scatter plots are similar to line graphs (see above) in showing a relationship between two continuous variables. However, they plot individual data points, not aggregated ones, and they produce a scatter of points that are not joined by lines. A hand-drawn line of best fit (see Figure 8.2) or a statistically computed regression line may be drawn to highlight or reveal any trend in the data. A lecturer wishing to discover whether students’ success in an exam-preparation module is associated with success in second-year exams might plot a scattergram of their results as in Figure 8.2. In this case, there appears to be a positive association between the two.
Figure 8.2 Marks (as percentages) for students’ results in an exam-preparation module plotted against their value-added scores based on Year 2 exam results compared with Year 1 results. Hypothetical data
Bar charts can be used to plot data where at least one variable is discrete (it falls into distinct categories rather than being on a continuum). In Figure 8.3 the discrete variable is the chemical fertiliser applied to the soil in which the plants are grown. To reflect this characteristic, when numbers of entries are plotted vertically as bars, the bars for different categories are kept separate. If there are two data sets within the same category, as in Figure 8.3, the bars need to be distinguished, often using shading or hatching. As usual, any use of shading or other notation needs to be indicated using a key. Summary details of the growth and treatment conditions could be added to the figure legend or given in the accompanying text.
Figure 8.3 The effects of two types of NPK fertiliser on the growth of maize (Zea mays) and wheat (Triticum aestivum). Hypothetical data
Bar charts follow the usual conventions for graphs and charts that have axes: for example, the independent variable is plotted in relation to the horizontal (x) axis and the dependent variable in relation to the vertical (y) axis.
A histogram is similar to a bar chart but is used where variation in the data is continuous (data do not fall into distinct groups). Histograms are particularly useful for displaying large data sets, where the data are grouped into ranges (Figure 8.4). Like bar charts, histograms follow the normal conventions for graphs and charts that have axes.
Figure 8.4 The height distribution of randomly sampled males (n = 100) and females (n = 100) aged 18/19 in the Psychology Department at University X. Hypothetical data
A pie chart differs from the graphs and charts considered so far, because it does not employ axes. A pie chart is an impressionistic device for making comparison between several categories of data. It is most effective when used to display strong distinctions between just a few categories, such as population statistics or responses to a question that might be displayed in an essay, report or presentation (see Figure 8.5).
Pie charts can be readily drawn using computer software such as Microsoft Word or Microsoft Excel. If the charts are drawn by hand, percentages can be readily converted to degrees by multiplying by 3.6 (100% represents 360 degrees). The different ’slices’ of a pie chart are called ’sectors’ and they are commonly displayed anticlockwise in order of increasing size, or otherwise in a logical order (see Figure 8.5). It is difficult to distinguish sectors of similar size and so a pie chart is best used when the categories differ markedly in size. If they do not, a table or bar chart may be a better way to display differences between categories.
Figure 8.5 Students’ responses (n = 90) to the question ’Overall, do you consider the teaching on the exam-preparation module to have been effective?’ Hypothetical data
In some cases your assessor may print your work in black and white even if it has been submitted as an electronic file and you have included colour in your tables, graphs or charts. So, any colour you have used to distinguish between items will print out as black or grey and distinctions could be lost. Check with your assessor, but it is normal practice to use different symbols, shading or conventions other than colour to clearly distinguish between different data sets in a table or figure.
Improving a chart
Below is a simple bar chart comparing the exam marks of male (n = 45) and female (n = 48) students on a module from a History of Art course. Assuming further information about how the data was gathered is given in accompanying text, suggest two ways in which this bar chart could be improved.
Compare your answers with those at the end of the chapter.
Figure 8.6 A comparison of the mean exam marks of male (n = 45) and female (n = 48) students on an Art and Protest module. Hypothetical data
American Edward R. Tufte is a visionary statistician and artist who wrote four classic books about the visual presentation of data, including his highly influential The Visual Display of Quantitative Information. Among Tufte’s principles are:
-show the data
-tell the truth
-let the viewer think about the information rather than the design
-encourage the eye to compare data.
In other words, he was concerned with simplicity and elegance - how to show data in such a way that meaning and importance becomes clear. You would do well to do the same.