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A letter to the Editor revisiting misleading graphs, published in Electronics Australia, June 1991, pp.4-5

Thank you for publishing my letter in your February 1991 edition. Thank you also for the comment.

I must confess to error in respect of the second graph, that with the decibel scale. Please accept my apologies.

In relation to the first graph, you point out that it was supplied by Kodak. That is no more than I assumed to be the case. I would expect a commercial enterprise to endeavour to present its products in the best light, as indeed is its right. For this reason I exercise caution with regard to claims published in advertisements or glossy handouts. I do not expect magazines, however, which perform a valuable advisory role for consumers (not that the particular product in question is actually a consumer item) to present products in their best light on behalf of manufacturers. I rely on publications such as yours to provide information about products in a clear and informative way.

The use of an 'offset zero' is not the ideal way to present graphs -- not if you are trying to convey an accurate representation of fact at any rate. Graphs are useful for one specific purpose (otherwise tables of figures would suffice): they give the viewer a feel for figures, trends and relationships. They do this by appealing to an 'older' part of humanity than our reasoning brains -- they appeal to that part of us that allows us to judge spatial relationships, an ability much older in evolutionary terms than the ability to manipulate numbers. This atavistic appeal breaks through the defences of even those who reject mathematics as `too hard' while those who understand the subject are also grateful, for the supporting figures would in any case have to be converted into the psychological equivalent of a graph to be actually understood.

The graph you reproduced very effectively allows the reader to grasp a relationship: a wrong one! To notice the error the reader has to re-engage his or her cortex and discover, in perhaps five point print, the scaling problems I complained about.

In some cases the ideal graphing techniques have to be dispensed with for practical reasons. This is typically because the variation between the items being shown in the graphs is small compared to the magnitude of those items. In such cases it is wise to clearly mark the break in the scale, not only on the scaling line but also, in this case, on the bars of the graph itself. This graph not only fails to show that, it actually uses equal physical intervals on the vertical scale along with a zero at its base in such a manner that it was either intended to deceive or was assembled by someone who has little knowledge of proper graphing techniques.

The combination of a linear scaling of the top part and the near infinite scaling of the bottom part means that one octave (and, being the highest frequency octave, arguably the least musically significant) is spread across five sixths of the vertical scale compared to the nine other audible octaves (along with an undefined number of infrasonic octaves) compressed into one sixth of the scale.

You point out that it is 'not unusual' to use such graphs. Indeed it isn't. That is one reason why Scientific American has in recent months in its 'Mathematical Recreations' column been conducting a campaign against all forms of misleading 'mathematics', including what it refers to as 'chart abuse'.

A truly informative graph by Kodak would have been to show three superimposed generalised frequency response graphs with a logarithmic horizontal frequency scale. Of course, you could not publish a graph with which you had not been supplied. Perhaps then you should simply have refrained from publishing the graph that you were supplied with.

© 1991 - Stephen Dawson