7.4 Reasoning with statistics 269
7.4 Reasoning with statistics
so on. If someone said to you: ‘Prison works
because it reduces crime,’ you would be
entitled to ask for some proof of this, or at least
some indication that locking people up does
bring down the crime figures.
You would also be entitled to ask whether
some observed reduction in crime would be a
sufficient condition for claiming that prison
works. (Necessary and sufficient conditions
were discussed in Chapter 7.1.) For a start, we
would need to be sure that it is prison that is
responsible for the reduction. It would be
wrong to assume that because crime numbers
were falling, and prison policy getting
tougher, that one was the cause or the
consequence of the other. And even if we were
satisfied that prison sentences do reduce
crime, we might still want to know by how
much they reduce it. If it turned out that a
very large increase in the number and severity
of prison sentences was needed to achieve a
small reduction in crime, we might well
question whether this showed that prison was
really as effective as the author of [1] would
have people believe.Interpreting statistical data
In Chapter 4.3 the distinction was made
between raw data and processed data. Raw
statistics are just numbers, or quantities. If we
want to use them we have to interpret them,
and draw inferences from them. They do not
come with inferences and interpretations
attached. Statistics on their own don’t make
points or support arguments or answer
questions. They are used by people to do these
things, and for that purpose they usually need
to be processed in some way: for example,
combined or contrasted with other statistics;A leading politician once summed up his
approach to law and order with the now
famous slogan:
[1] ‘Prison works.’But does it? Does it, for example, reduce
crime? Do the authorities make law-abiding
citizens safer by locking up criminals? Does
prison deter people from committing crimes
in the first place, or from reoffending after
serving a sentence?
In this chapter we shall be considering ways
in which questions like these can be answered:
what sort of evidence is required to support or
to challenge the claim expressed by [1]? We
shall be looking in particular at the use of
statistical evidence, and statistical reasoning.
As well as considering ways in which statistics
can legitimately be used to support claims, we
will also be looking at ways in which they can
give false or misleading impressions. It is fairly
obvious why statistical evidence is needed in a
context such as this. It would be hard to see
how any grounds could be given either for or
against [1] without producing facts and
figures: numbers of prisoners, levels of crime,
lengths of sentence, rates of reoffending and