Do you know NOIR classification of the data? NOIR - nominal ordinal interval ratio.

I want to argue that a line chart can be used with both interval and ratio data whereas area chart should be used only with ratio data. This is because ratio data has a meaningful 0 and in case of an area chart the baseline of the graph is 0 (meaning that the area spans from the curve to the horizontal axis). Therefore it would be unreasonable to use an area chart with interval data. However this is my feeling only and I am not sure. What do you think about it? Do you know any publications that discuss this matter?

  • $\begingroup$ The baseline doesn't have to be zero. It could be e.g. 20°C for an area chart showing heating/cooling degree days. But your argument seems right - there's no sense in emphasizing an area under a curve when the product of the variables on the two axes doesn't have a meaningful interpretation. On the other hand, does it do any positive harm? $\endgroup$ – Scortchi Jun 28 '13 at 10:00

The classification nominal -- ordinal -- interval -- ratio (NOIR) arguably creates as many problems as it solves. This applies to graphics too.

If you look across the overlapping literatures of statistical science, the extent to which people treat NOIR seriously varies enormously: hardly at all in modern mathematical statistics or econometrics, but quite prominently in many elementary or introductory treatments in psychology (where it originated), sociology, biology, and some other disciplines. In some of the latter treatments there is an extraordinary mix of obvious points that no-one disputes and taboos about what you can and can't do, or should or shouldn't do. It's important to grasp that there is much disagreement here between and within communities of statistical people.

To give a concrete example, a variable gender with possible values male and female would presumably be declared nominal by all. But in graphics what is usually being plotted is (say) numbers of males and females or percents of males and females. Such variables are ratio scale, in that ratios make sense (4 males/2 males = 2; 40% males/20% males = 2; 0 or 0% males is a true, not an arbitrary zero). So, the raw data in say spreadsheet form may be nominal (person 42 is female, whatever), but what is plotted is in quite different form.

More generally, most modern categorical data analysis is based on devices to represent categorical data on ratio scales, such as probability or cumulative probability.

So, I suggest that the nub of the matter is not what you call the data in their raw form but what you are actually plotting. To focus on the question, area graphs usually seem to plot fractions in either absolute or relative form. Whether the fractions represent nominal or ordinal categories is no barrier to using area graphs.

In terms of references: there is a massive literature on the relationship (or otherwise) between measurement scales and statistics. My own favourites are as below, partly because I think both are relatively clear and partly because you can read dissenting discussions:

Velleman, P.F. and Wilkinson, L. 1993. Nominal, ordinal, interval, and ratio typologies are misleading. The American Statistician 47: 65-72. See also follow-up under "Letters to the Editor" in 47(4) and 48(1).

[I note incidentally that the comment by David J. Hand is reported as if from "David J. Hand and Milton Keynes". That was a mistake: "Milton Keynes" is not a person, but a place, the town where Hand's then institution, the Open University, is based.]

Hand, D.J. 1996. Statistics and the theory of measurement. Journal of the Royal Statistical Society. Series A (Statistics in Society) 159: 445-492.

(LATER) Two further specific examples may help focus discussion, especially if you disagree with them.

A presentation I saw included bar graphs of sex ratio for various Indian states and territories, the bars drawn with base zero and so to a first approximation all very similar in length. I suggested that base 1 (100%) would be a more effective choice, enabling differences between values to show up much more clearly. This was met with the dogma "But all bar graphs should start at zero because bar lengths encode values!". I see the point, but the point can often just lead to ineffective graphs. Also, bars are just being drawn to encode (value - reference value) and that scale has a zero, the reference value. It is a tough call if the audience is not expected to understand subtraction.

Similarly, bar graphs are often used to show time series (e.g. of monthly averages) in climatology to show temperatures: the bars show temperatures above or below freezing (base at freezing point) or above or below mean temperature. Almost everybody outside the US uses Celsius; in the US people often use Fahrenheit. Both these scales, temperature - freezing point, or temperature - mean, are interval scales, but I have yet to meet a purist who insists on showing bar graphs of climatic data with temperatures in Kelvin and base at 0 K.

  • $\begingroup$ (+1) Treating too seriously amounts to, IMO, (1) thinking of measurement scale as an essential property of data rather than an interpretive decision made by the analyst dependent on the context (2) considering NOIR as the definitive typology, whereas counts, proportions, circular measures, &c. have further constraints on meaningful operations. All the same, I think most people would admit it's a handy starting point for thinking about the issues. $\endgroup$ – Scortchi Jun 28 '13 at 10:41
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    $\begingroup$ @Scortchi I agree: NOIR is not nonsense and would not have survived otherwise. 1 = strongly disagree, 5 = strongly agree are importantly different from 1 sheep, 5 sheep and many points made under the heading of NOIR are serious and practical. $\endgroup$ – Nick Cox Jun 28 '13 at 10:47
  • $\begingroup$ Yes, I think it is important to be aware of what data you are working with and of its limitations. In case of plotting it is also important to use the graphical components (like the area under the curve) properly as they might be misleading otherwise. I agree - NOIR although not perfect certainly is a good starting point. $\endgroup$ – Domajno Jun 30 '13 at 20:37
  • $\begingroup$ I was looking more for a publication which formalize somehow what can/cannot be used for an areachart (or at least good practices). I want to research that topic and I have found another classification which may be usefull in that case. Lenz and Shoshani (1997) classify mesures (come from data warehouse field) into flow, level and unit. Flow measures can be aggregated along time dimension e.g. quantity of sold items so they seem to be a good candidate for an area chart if time plotted on horizontal axis. This would agree with what @Scortchi said what the area should be somehow meaningful. $\endgroup$ – Domajno Jun 30 '13 at 20:38
  • $\begingroup$ If you wonder what is this whole dilemma about I want to suggest best visualization types for given data set. $\endgroup$ – Domajno Jun 30 '13 at 20:39

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