Educational Research - the Ethics and Aesthetics of Statistics

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146 J.P. Van Bendegem et al. quite philosophically minded, we will also take this issue seriously. Formula and figure are not the same kind of thing. Here, we are saying something quite similar to the distinction that is made between (mathematical) proofs and diagrams, a topic that will be developed during this chapter. Does not the figure contain additional elements that have nothing to do with the formula, such as the thickness of the curve or its colour? And, at the same time, does the figure not erase crucial information? After all, from the drawing one cannot conclude that the elusive number π plays a part in it. We do not want to focus on ontological matters here. Rather, our interest is in the ethics and aesthetics of the matter (along with epistemology concerns when they become relevant). However, this is a complex matter. A first-order approximation whereby statistics is seen as either a part of pure mathematics or a part of applied mathematics 1 and where ‘only’ the ethical and aesthetical dimension are considered, leads to a first-order four-case classification, illustrating the complexities of the issue as follows: ‘Pure’ statistics ‘Applied’ statistics Ethics What are the (often hidden) assumptions internal to thinking ‘in a statistical way’? What are the conditions and requirements that allow for the use of statistics in a given setting? Aesthetics What are the aesthetic values that mathematicians foster in relation to statistics? How is the information represented to those who need it? Some comments relating to each of these possibilities are as follows: • Pure statistics and ethics: it is clear that (formalised) statistics cannot exist without an underlying theory or conception of probability. Without such a theory, it is, for example, impossible to prove the central limit theorem – given a set of independent random measurements of a population with any distribution, the sum of these measurements will be distributed according to the normal distribution – and similar theorems that form the basis of deductive, statistical thinking. Probabilities, however, presuppose a set of conditions. What are the cases about which a probability statement is made (individual cases, samples or populations)? How are these cases weighted amongst one another (think of the concept of an ‘honest’ die)? How are probabilities calculated? The mere fact that, mathematically speaking, the cases could be virtually anything carries ethical implications. What I mean by this is that, in terms of applications, hardly any cases are ruled out. It is precisely that generality, or dare we say universality, that mathematicians so famously and continuously search for that strengthens the ethical dimension. • Pure statistics and aesthetics: this in itself is really interesting territory to explore. Mathematicians do have aesthetic ideals that their practice aspires to, but these relate mainly, though not exclusively, to proofs. Now, it is often argued that statistics does not ‘favour’ proofs and is more ‘empirically’ focused. Hence, it does not appeal to the same kind of aesthetics. In fact, many mathematicians
10 The Good, the Beautiful and the Literate: Making Statistics Accessible for Action 147 regard statistics as the ugly sibling of the mathematical family. But, as mentioned above, there is a clear connection between statistics and deductive, formalised mathematics. Even after Kolmogorov really changed the subject through his axiomatic-algebraic approach (which made it possible to calculate probabilities in cases that were previously excluded) statistics does not seem to share in the aesthetic standards of ‘pure’ mathematics. 2 • Applied statistics and ethics: Undoubtedly, is the area where most of us have immediate ideas about what the problems are. Surely each time we apply statistical methods to some real-life problem, the first question must be whether the application is, in some sense, acceptable. Probability theory and statistics really took off in the seventeenth century once international sea trade bloomed (e.g. Hacking, 1975). Insurances became acceptable up to and including not merely a ship’s load but its crew as well. From that moment onwards, bets could be made with human life as its literal stake. In that sense it is obvious that ethics enter into the discussion. • Applied statistics and aesthetics: at first sight, this combination might seem rather odd. It would seem that we are talking here about applications and what could be the aesthetic value of an application? However, we take a different tack. When applied, the tool that is being used has to become very concrete. It cannot remain on an abstract plane, but must be ‘translated’ or ‘transformed’ into something concrete. Anything concrete has a specific form and where specific forms are present, aesthetic considerations must come into play. A comparison with architecture (or perhaps music as well?) seems apt in this context. On the one hand, the plans surely have an aesthetic value of their own. On the other hand, once the plan has been implemented through the construction of a concrete building, the building has aesthetic qualities of its own that are lacking in the plans. Think of the aesthetic value a building has for those either living in it or looking at it from the outside. In addition, it must be clear that the four cases are not independent from one another. Thus, even if it is our aim to focus on the third and fourth case, it is obvious that the two other cases will intervene time and again to provide important insights or to support the claims made. To avoid dividing this chapter up into two separate sections on ethics and aesthetics, we propose to introduce a common element that will allow us to keep both dimensions in view. More specifically, in order to make connections with the philosophy of educational theory, we will focus on the representation of statistics or, if you like, its visualisation. We believe that visualisation is directly connected with an important concept, in terms of education and educational views, namely, accessibility or, as it is sometimes expressed, literacy. When statistical data are presented to a particular audience, how many of its members have ‘true’ access to the data presented? By this we mean how many effectively understand what is presented to them and can thus be considered literate about the subject? Note that, once again, different levels can (and should) be distinguished: problems of access can occur in the collecting of data to support a (quantitatively
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Educational Research: The Ethics an
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Paul Smeyers · Marc Depaepe Editor
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Earlier Volumes in this Series Educ
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viii Contents 10 The Good, the Beau
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2 P. Smeyers and M. Depaepe their a
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Chapter 2 The Lure of Statistics fo
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2 The Lure of Statistics for Educat
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28 M. Depaepe of the Leuven Catholi
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30 M. Depaepe Tan’s final verdict
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32 M. Depaepe of methodological bot
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34 M. Depaepe tapping other sources
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36 M. Depaepe In the context of dem
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38 M. Depaepe combination. Moreover
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40 M. Depaepe 4. See Pelleriaux (19
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42 M. Depaepe Schneider, J. (2010).
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44 J.J.H. Dekker (see Section 4.4).
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46 J.J.H. Dekker from their own par
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48 J.J.H. Dekker a cohort study tha
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50 J.J.H. Dekker child” (Van IJze
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52 J.J.H. Dekker USA resulted in ev
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54 J.J.H. Dekker of the problem”.
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56 J.J.H. Dekker Dekker. J. J. H.,
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198 R. Smith 7 www.equalitytrust.or
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200 R. Smith It is an interesting q
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202 R. Smith self-esteem, happiness
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204 R. Smith Reeves, R. (2009, Apri
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206 P. Standish Some students’ no
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212 P. Standish research none of us
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216 About the Authors co-editor-in-
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218 About the Authors voor Wetensch
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220 Author Index Elkins, G. R., 190
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222 Author Index Silverman, J. G.,
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224 Subject Index I Inequality, 29-
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