Educational Research - the Ethics and Aesthetics of Statistics
Educational Research - the Ethics and Aesthetics of Statistics
Educational Research - the Ethics and Aesthetics of Statistics
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11 <strong>Statistics</strong> <strong>and</strong> <strong>the</strong> Inference to <strong>the</strong> Best Explanation: Living Without Complexity? 163<br />
Science has conventionally progressed by identifying regularities or invariances; for<br />
instance, planets orbit <strong>the</strong> sun as ellipses. These invariances <strong>the</strong>n serve as <strong>the</strong> phenomenon<br />
to be explained by <strong>the</strong>ory; for instance, elliptical orbits may be explained by <strong>the</strong> Newtonian<br />
<strong>the</strong>ory <strong>of</strong> mechanics. In this mode, <strong>the</strong> search for invariances is a necessary precursor to<br />
<strong>the</strong>oretical development. Though this approach has been fruitful, psychologists, who tend<br />
to focus on verbal explanations <strong>of</strong> differences idiosyncrasies across conditions <strong>and</strong> populations,<br />
have not adopted it. The search for invariances is complicated in many domains by <strong>the</strong><br />
presence <strong>of</strong> unintended or nuisance variability. For instance, in memory research, <strong>the</strong>re is<br />
variability from <strong>the</strong> selection <strong>of</strong> participants <strong>and</strong> items in addition to that from <strong>the</strong> mnemonic<br />
processes at h<strong>and</strong>. The conventional approach is to aggregate across <strong>the</strong>se nuisance sources,<br />
but this aggregation may distort <strong>the</strong> structure <strong>and</strong> mask important invariances in <strong>the</strong> data. To<br />
address this problem, my colleagues <strong>and</strong> I have developed a collection <strong>of</strong> Bayesian hierarchical<br />
models for modelling nuisance variability so that structure in psychological processes<br />
may be explored. I apply <strong>the</strong>se models to recognition memory, where <strong>the</strong>re is a vigorous<br />
debate whe<strong>the</strong>r memory is supported by a single mnemonic process or by multiple distinct<br />
processes. Model analysis reveals that ROC [receiver operating characteristic] curves across<br />
people <strong>and</strong> conditions form an orderly field, much like <strong>the</strong> order in gravitational <strong>of</strong> magnetic<br />
fields. As a consequence, <strong>the</strong> structure <strong>of</strong> recognition memory seems to be one-dimensional<br />
<strong>and</strong> may be accounted for with a single parameter <strong>of</strong> mnemonic strength.<br />
A single parameter <strong>of</strong> mnemonic strength is <strong>the</strong> result <strong>of</strong> a search for invariances<br />
in this area. It is a ‘structural quality’ (a reduction <strong>of</strong> <strong>the</strong> complexity <strong>of</strong> <strong>the</strong><br />
data here as invariance, in o<strong>the</strong>r cases for instance a pattern), which should now be<br />
taken up by <strong>the</strong>ory <strong>and</strong> explained (or ‘given a place’). We might ask what exactly<br />
<strong>the</strong> relationship is between this result <strong>and</strong> <strong>the</strong> particular method that has been used<br />
(in this case, a collection <strong>of</strong> Bayesian hierarchical models). Fur<strong>the</strong>rmore, we might<br />
consider whe<strong>the</strong>r it is in some sense useful. Clearly this is all about reduction, about<br />
‘seeing’ something in a simpler form. For this reason (maybe for this reason alone)<br />
it is something to be strived for.<br />
In educational research as everywhere else in science, academia or even ordinary<br />
life, we are for various reasons interested in trying to underst<strong>and</strong> (some would say,<br />
‘make sense <strong>of</strong>’) <strong>the</strong> phenomena we are surrounded by or subjected to. This underst<strong>and</strong>ing<br />
is supposed to give us a grip on what is happening, bring some order to<br />
<strong>the</strong> chaos. It is not in <strong>the</strong> least bit concerned with how we see ourselves, or what<br />
we aspire to achieve. Some explanations are more attractive to us than o<strong>the</strong>rs, some<br />
are more popular in particular periods, <strong>and</strong> some focus on groups. O<strong>the</strong>rs centre on<br />
<strong>the</strong> individual. Crucial in this endeavour are issues about truth (A) but at <strong>the</strong> same<br />
time a lot will depend on what one is particularly interested in. (B) The latter may<br />
or may not be intertwined with one or o<strong>the</strong>r sort <strong>of</strong> good that is envisaged ei<strong>the</strong>r by<br />
a person or a particular group <strong>and</strong> this opens up <strong>the</strong> sphere <strong>of</strong> manipulation (C) but<br />
also <strong>of</strong> responsibility <strong>and</strong> responsiveness. (D) Thus matters <strong>of</strong> <strong>the</strong> particular concept<br />
that is used when studying a problem come to <strong>the</strong> forefront (E) as crucial factors<br />
concerning <strong>the</strong> characterization <strong>of</strong> that phenomenon. This will have implications<br />
for where one can arrive at in terms <strong>of</strong> solutions for dealing with it.<br />
Let me begin by arguing that whe<strong>the</strong>r something is really explained, or whe<strong>the</strong>r<br />
‘reality’ here is merely <strong>the</strong> opposite <strong>of</strong> fiction, should not necessarily invoke a correspondence<br />
<strong>the</strong>ory <strong>of</strong> truth where sense data are <strong>the</strong> exclusive building blocks.<br />
Instead, as Peter Winch (1958) rightly argued, it is always about ‘what is real for