RESEARCH METHOD COHEN ok

24
Quantitative data analysis
Introduction
The prospect of analysing numerical data sends
shivers down the spines of many novice
researchers who not only baulk at the thought
of statistics but also hold fundamental objections
to what they see as ‘the mathematisation of
nature’ (Horkheimer 1972). Most concepts in
education, some will assert, are simply not
reducible to numerical analysis. Statistics, they
will object, combine refinement of process with
crudity of concept.
We do not hold with any of this. Quantitative
data analysis has no greater or lesser importance
than qualitative analysis. Its use is entirely
dependent on fitness for purpose.Arbitrarydismissal
of numerical analysis is mere ideology or prejudice.
Quantitative data analysis is a powerful research
form, emanating in part from the positivist
tradition. It is often associated with largescale
research, but can also serve smaller scale
investigations, with case studies, action research,
correlational research and experiments. In the
following chapters we will show how numerical
data can be reported and introduce some of the
most widely used statistics that can be employed
in their analysis.
Numerical analysis can be performed using software,
for example the Statistical Package for Social
Sciences (SPSS, Minitab, Excel). Software packages
apply statistical formulae and carry out computations.
With this in mind, we avoid extended
outlines of statistical formulae though we do provide
details where considered useful. Our primary
aim is to explain the concepts that underpin statistical
analyses and to do this in as user-friendly
a way as possible. Lest our approach should raise
purist eyebrows, we provide extended treatments
in greater detail, signaled where appropriate by
web site references. Our outline commentary is
closely linked to SPSS, the most widely used statistical
package for social sciences. An introductory
SPSS manual to this volume is located in the accompanying
web site (including printouts of data
analysis) together with comments on what they
show (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file SPSS whole
manual 24.1); the manual is also segmented
into sections, and these are referred to throughout
this chapter. It is often the case that
such outputs can clarify issues more straightforwardly
than extended prose. We also include
a guide to all the SPSS files held on the
web site (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file SPSS files on
the web site).
We begin by identifying some key concepts
in numerical analysis (scales of data, parametric
and non-parametric data, descriptive and
inferential statistics, dependent and independent
variables). We then address the concept
of statistical significance. We finally conclude
with a brief outline of some simple statistics.
Throughout this chapter and the next we indicate
how to report analysis; these are collected
together in a single file on the accompanying
web site (http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file 24.1.doc).
Material in the accompanying web site also
refers to statistical tables (see http://www.
routledge.com/textbooks/9780415368780 –
Chapter 24, file Appendices of Statistical Tables).