Graphs and Data Visualization

• A picture is worth a thousand words.
• Graphing skills help you explore data.
• Graphs are a compact form of scientific communication.
• Data visualization can make obvious what would otherwise need complicated statistical tests to confirm.
• Graphics should be true, fair, comprehensible, and useful.

Graphic Representations Can Take Many Forms

Descartes used drawings to explain why the image of the world that is formed on the back of the eye is inverted. The diagram provides a compact summary and explanation of the results of an experiment in which Descartes cut a small window of tissue from the back of an Ox's eye. He then put a paper screen in its place, and saw an inverted image of the world on the screen.

Descartes was an intellectual of the first order and made important contributions to philosophy ('I think therefore I am' etc.), mathematics (Cartesian coordinates etc.) and the natural sciences. He took a robustly mechanistic view of the workings of most of the body and nervous system. Descartes regarded the nervous system as a hydraulic machine filled with 'pneuma' or 'vital spirit'. In this view, movements were caused by vital spirits pumping through the nerves and inflating muscles, in much the same way that a car's brake fluid pushes a piston that squeezes the brake disk. He thought that the 'will' resided in the Pineal Gland at the centre of the brain and was separate from the physical substance of the brain and body (a 'ghost' in the machine). The 'will' would occasionally interact with the physical world by redirecting the flow of 'pneuma' in the nervous system. This kind of view, emphasizing the separateness of mind and brain, is called 'dualism'.

Optical imaging is a modern method that, depending on your point of view, either produces wonderful images of the function organization of the cerebral cortex or else produces totally spurious and artefactual images of random fluctuations in light level (the Jury is still out !). Those who believe in Optical imaging hold that, for some reason, active cerebral cortex is slightly darker in shade than inactive cortex. It is possible to record the minute changes in optical signal from the cortex while presenting a range of sensory stimuli. Thus, differences in local stimulus selectivity in the cortex can be mapped. The image below shows differential activation in a piece of cortex (roughly 2mm by 3mm) in response to moving images of stripes of different orientation. It shows that selectivity to contours of particular orientation is organized in stripes or bands across the cortical sheet.

Legend.Psuedo colour representation of orientation mapping in the cerebral cortex. The colour in the image of a 3mm x 2mm area of cortex is not 'real', but simply represents the orientation of the contour to which the piece of cortex responds. The orientation:colour key is shown at the right margin of the figure. Cortex coloured blue responds to contours sloping from top left to bottom right (unfortunately, the blue lines in the key did not show up very well on this scan). Cortex coloured bright green responds to vertical contours. Orange coloured cortex responds to contours sloping from top right to bottom left. Cortex coloured red responds to horizontal contours.

Dull but Worthy Conventions

The main criteria for judging graphs should be TRUTH, FAIRNESS, CLARITY, and USEFULNESS. There are some dull but worthy conventions that are generally applied and are often useful.

• Name: When presented in your reports, in academic journals and in books, all forms of data visualisation are refereed to as 'figures', whether they are graphs, histograms, diagrams or pictures.
• Number: Figures are numbered ('Figure 1' etc.) so that they can be conveniently referred to in the text of a report, journal article or book (e.g "Figure 1 shows that . . .".)
• Legend: says what the figure shows and is placed below the figure. This is a few lines of text which should explain the figure and make it comprehensible. It is ALWAYS necessary. Don't start the legend with "A graph to show . . ." (as you may have been taught at school). This is too obvious for words (and "don't waste words" is a good basis for scientific writing).
• Label Axes: says what the axes are. State both the name of the measure and the unit of measurement (e.g. "Reaction time (seconds)").

As well as these conventions, there are also different ways of dealing with nominal, ordinal, interval and ratio scales of measurement. These are illustrated in the following histograms.

1) Nominal Scale of Measurement (e.g. type of pet) . The order of categories on the x axis is arbitrary, and the columns usually don't touch.

Legend: Figure 1. Sales of animals at Scannell's Pet Shop. The length of the bars represents average number of animals sold during January, February and March 1996. 'Other' includes all reptiles (except Boa Constrictors), all amphibian species, platyhelmithes and nematodes.

2) Ordinal (e.g. order of finishers in a race, or responses on an attitude scale [Strongly agree/Agree/Neutral/Disagree/Strongly Disagree]). The order of categories on the x axis matters, and the columns usually touch.

3) Interval or Ratio. The scale on the x axis matters, and it is OK to draw lines between points if there is some reason to suppose that they represent data sampled from a continuum. Also, points you join together should be related in some way (e.g. they are all from the same subject, or represent data gathered at successive time periods). For example, you might draw lines between the points on a motion detection curve (because it is sensible to suppose that intervening measurements would have intervening values).

Legend. Figure 2. Motion detection varies with strength of motion signal. The graph shows the percentage of correct responses in a motion detection task in which dots drift either left or right. Data are from 12 subjects who appear to fall into 3 groups. Note the error made with the labeling on the y axis; % correct cannot go above 100!

Fiddling Around With Axes

An old trick in advertising and politics is to fiddle with the scale on the axes to make changes or trends look bigger or smaller. Always check the scale on the axes when you are looking at or drawing graphs.

Legend. Figure 4. Two graphs of exactly the same data. The graphs show that changing the scale on the Y axis can have a major effect on the way the graph looks.