Quality & Quantity 33: 185–202, 1999.
© 1999 Kluwer Academic Publishers. Printed in the Netherlands.
Sampling for Possibilities
MICHAEL WOOD and RICHARD CHRISTY
Portsmouth Business School, Locksway Road, Milton, Southsea, Hants, PO4 8JF, England,
e-mail: firstname.lastname@example.org; fax: 44(0)1705-844037
Abstract. This paper views empirical research as a search for illustrations of interesting possibilities
which have occurred, and the exploration of the variety of such possibilities in a sample or universe.
This leads to a deﬁnition of “illustrative inference” (in contrast to statistical inference), which, we
argue, is of considerable importance in many ﬁelds of inquiry – ranging from market research and
qualitative research in social science, to cosmology. Sometimes, it may be helpful to model illustra-
tive inference quantitatively, so that the size of a sample can be linked to its power (for illustrating
possibilities): we outline one model based on probability theory, and another based on a resampling
This paper concerns inferences from data in empirical research in areas where
there is substantial uncertainty, so that precise predictions, exact understanding
and universal laws are not a realistic expectation.
The usual methods for handling this uncertainty are those of statistical infer-
ence. Typically, this involves extrapolating the value of a population parameter,
such as a mean or proportion, from a sample statistic, and then using signiﬁcance
levels, Bayesian posterior probabilities or conﬁdence intervals to indicate a level
of “conﬁdence” – in a sense depending on the statistical formalism adopted – in
these extrapolations. Essentially the same theory can also be used to estimate, in
advance, the sample size required to achieve a given level of conﬁdence in a given
type of result.
Statistical inferences are clearly not the only type of inference which can be
drawn from empirical data. For example, the attempts at universal inferences in
some physical sciences (e.g., Newton’s laws of motion, which were assumed to be
universally valid), and many “qualitative” inferences in the social sciences, do not
ﬁt in any obvious way into the statistical category. Despite this, there is a strong
tradition in many areas of the social sciences that statistical inference is the only
legitimate form of inference from empirical data.
This paper argues that there is an important category of inferences which are not
statistical, but which are of substantial importance, and are at least as rigorous as
statistical inferences. These are inferences about what is possible, as distinct from
statistical inferences about how prevalent each of the possibilities is. Exploratory