Educational Research - the Ethics and Aesthetics of Statistics

82 D. Bridges
cases. However, Popper, most notably among philosophers of science, has pointed
out the logical gap that always lies between any number of singular or “particular”
statements, such as accounts of the results of observations or experiments, and “universal”
statements, such as hypotheses or theories or generalisations that are held to
be true for all instances (Popper, 1959, 1963). Instead Popper turns the logic of scientific
method on its head and argues that the task of empirical enquiry is to attempt
to refute conjecture, i.e. such hypotheses or theories, and that the strength of such
hypotheses lies in the measure of their ability to resist such attempts at their refutation
(Popper, 1963). But what then becomes significant is that it takes not a thousand
but just a single case of convincing counter-evidence to achieve this refutation. In
the often quoted example, however many observations of white swans you make,
these will not be enough to demonstrate conclusively that “all swans are white”. On
the other hand, a single observation of a black swan will suffice to refute the same
proposition. This is not just a technical philosophical point, it is a common feature
of scientific experience that it is the occasional aberrational result that signals that
there is something not quite right with the existing theory.
Significantly, Stake situates case study in this Popperian tradition in the sense of
offering the power of the negative example: “Case study is part of scientific method,
but its purpose is not limited to the advance of science. Whereas single or a few cases
are a poor representation of a population of cases and poor grounds for advancing
grand generalization, a single case as a negative example can establish limits to
grand generalization. For example, we lose confidence in the generalization that
a child of separated parents is better off placed with the mother when we find a
single instance of resultant injury. Case studies are of value in refining theory and
suggesting complexities for further investigation, as well as helping to establish the
limits of generalizability” (Stake, 2000, p. 445).
Harvey Goldstein argues, however, that the application of Popperian ideas to
social science can be problematic since many (most?) hypotheses cannot be framed
in terms of a few simple logically distinct states. Stake’s example really needs to be
rephrased along something like the following lines: “Children of separated parents,
on average, are better off placed with the mother”. The counter-example would be
valid only if we could carry out a study that demonstrated that on average they were
not better placed. Of course, it is not that simple, since one would need to specify the
circumstances of the case, the particular features of the situation or context which
might explain the departure from the norm. So Popper’s notions are often fine in
the natural sciences where it may be reasonable to assume universally applicable
relationships so that universal statements or hypotheses make sense. In the social
sciences these ideas have less utility. Of course, finding, for example, that some
families or schools appear to behave differently from others is interesting and leads
to further questions and data collection, and the key role for case studies is to try
and understand why this might be happening. However, in the social sciences a
single case study will rarely refute a generalisation because they are rarely offered
as universally applicable laws. 2
Further, as Elliott and Lukes argue, “case-focussed reasoning” is an intrinsic part
of the development and application of quantitative studies: