the null hypothesis were true. Clearly, the consequences following a typical hypothesis
test of the effectiveness of, for example, a reading recovery programme would depend
upon whether a Fisherian or a Neyman-Pearson position were adopted. Should the null
hypothesis of no difference between reading recovery intervention and control group not
be rejected then from a Fisherian perspective no action would follow. There is not
sufficient evidence to conclusively reject the null hypothesis and the intervention should
therefore not be discontinued until there was sufficient evidence to reject the null
hypothesis. From a Neyman-Pearson position, the intervention would be discontinued.
This debate presented here, in a somewhat simplified form, is essentially a debate
about different schools of inference. However, it does illustrate the distinction between
scientific and mathematical significance which is part of the long-standing tension in
statistics between mathematics and applications (Efron, 1995).
Since the seminal work on inference in the 1930s by Fisher and Neyman-Pearson
developments in experimental design, multivariate analysis and non-parametric
procedures have advanced and spread into education and psychological research.
However, the Fisherian approach is often not well suited to the analysis of many complex
educational and psychological relationships which can be characterized as dynamic (as
opposed to static) stochastic processes. Complex stochastic (statistical) models are
required to model the complex social phenomena of the real world of schools, classrooms
and learning environments; again advances have been made using approaches such as
LISREL and Multilevel modelling.
More recent computational-intensive statistical techniques such as Logistic
Regression, Gibbs Sampling, Jacknife and Bootstrap estimation procedures, to name a
few, are procedures which are now available given the data handling capabilities of
modern computers. However, these computer-intensive approaches are not well known
and seldom used by educational researchers and have only recently been brought to the
attention of psychologists (Robertson, 1991).
This section has provided the reader with a glimpse over the statistical horizon. Should
one choose to begin this journey, a sound statistical grounding in the fundamentals of
probability and inference is an essential prerequisite. Even if one is not interested in
statistics per se, as social science researchers, basic numeracy and basic statistical
awareness should form part of your tool kit as a competent researcher.
SummaryYou should have by now a good grasp of the ideas of probability, inference and how they
are used in estimation and hypothesis testing. This will equip you to tackle many
statistical procedures. All that you need to determine when considering a statistical test
are the following points:
- Choice of a possible underlying statistical model for the data:
Ask yourself what are the important variables—are they random discrete
or continuous variates?Probability and inference 115