Educational Research - the Ethics and Aesthetics of Statistics

11 Statistics and the Inference to the Best Explanation: Living Without Complexity? 167
statistically relevant. The statistical-relevance relations must be explained in terms
of two causal processes in which C is causally relevant to A and C is causally relevant
to B. This is the heart of matters where it is claimed that a statistical explanation
is based on causality. Now the question is, why should we prefer, for explanatory
purposes, the relevance of C to A and C to B over the relevance of A to B, which we
had in the first place? The answer is that we can trace a spatiotemporally continuous
causal connection from C to A and from C to B (while the relation between A and B
cannot be accounted for by any such direct continuous causal relation). Recall that,
according to Hume, causal explanations present us with a problem. As deductive
logic cannot provide the answer (that explains why ball number 2 is set in motion
after being hit by ball number 1), Hume turns to empirical investigations. On the
basis of his observations he concludes that in situations where we believe that there
is a causal relation, there is a temporal priority of the cause to the effect. There is
furthermore a spatiotemporal contiguity of the cause to the effect and finally, on
every occasion on which the cause occurs, the effect follows – there is constant
conjunction. As there is, in his opinion, no physical connection between the cause
and the effect (the connection does not exist outside of our own minds), the relation
between cause and effect is to be found in custom and habit. We may want to qualify
the latter and argue for a more robust interpretation of causality (see for instance,
Salmon, 1998), but for our purposes little depends on this. It does not affect either
the use of cause or our interest in causes. As indicated, it is important to realize that
when statistics are used to explain the occurrence of events, a model that uses causes
is operative. Hempel’s position, often referred to in this context, makes this clear.
In an explanation one may cite specific conditions obtaining prior to the event
(initial conditions) and invoke general laws. It is held that the occurrence of
the event to be explained follows logically from those premises, i.e. those initial
conditions and laws. One can distinguish between deductive explanations that incorporate
universal laws (which hold without exceptions) and inductive explanations,
which employ statistical laws (which hold for most or many cases). According to
Hempel (1965) scientific explanation consists in deductive or inductive subsumption
of that which is to be explained under one or more laws of nature. This
is referred to as the deductive-nomological model (D–N). For Hempel, however,
inductive-statistical explanations are essentially relativized to knowledge situations
– he suggested the requirement of total evidence that took the form of the
requirement of maximal specificity, where all possibly relevant knowledge is available.
If there were an inductive-statistical explanation whose law-like statistical
premise involved a genuinely homogenous reference class then we would have an
instance of an inductive-statistical explanation simpliciter, not merely an inductivestatistical
explanation relative to a specific knowledge situation. However, as there
are, according to Hempel, no inductive-statistical explanations simpliciter, ideally
inductive-statistical explanation would have no place in his account. There is a
striking similarity between this kind of explanation and Laplace’s formulation of
determinism. In view of this close relationship it is tempting to conclude that events
that are causally determined can be explained, and those that can be explained are
causally determined. We have set aside above the problems of determinism versus