RESEARCH METHOD COHEN ok

DESCRIPTIVE AND INFERENTIAL STATISTICS 503
equal interval metric – but adds a fourth, powerful
feature: a true zero. This enables the researcher
to determine proportions easily – ‘twice as many
as’, ‘half as many as’, ‘three times the amount of’
and so on. Because there is an absolute zero, all of
the arithmetical processes of addition, subtraction,
multiplication and division are possible. Measures
of distance, money in the bank, population,
time spent on homework, years teaching, income,
Celsius temperature, marks on a test and so on are
all ratio measures as they are capable of having a
‘true’ zero quantity. If I have one thousand dollars
in the bank then it is twice as much as if I had five
hundred dollars in the bank; if I score 90 per cent
in an examination then it is twice as many as if
Ihadscored45percent.Theopportunitytouse
ratios and all four arithmetical processes renders
this the most powerful level of data. Interval and
ratio data are continuous variables that can take
on any value within a particular, given range.
Interval and ratio data typically use more powerful
statistics than nominal and ordinal data.
The delineation of these four scales of data is
important, as the consideration of which statistical
test to use is dependent on the scale of data: it is
incorrect to apply statistics which can only be used
at a higher scale of data to data at a lower scale. For
example, one should not apply averages (means)
to nominal data, nor use t-tests and analysis of
variances (discussed later) to ordinal data. Which
statistical tests can be used with which data are
set out clearly later. To close this section we
record Wright’s (2003: 127) view that the scale
of measurement is not inherent to a particular
variable, but something that researchers ‘bestow
on it based on our theories of that variable. It is
a belief we hold about a variable’. What is being
suggested here is that we have to justify classifying
avariableasnominal,ordinal,intervalorratio,
and not just assume that it is self-evident.
Parametric and non-parametric data
Non-parametric data are those which make
no assumptions about the population, usually
because the characteristics of the population
are unknown (see http://www.routledge.com/
textbooks/9780415368780 – Chapter 24, file
24.2.ppt). Parametric data assume knowledge of
the characteristics of the population, in order
for inferences to be able to be made securely;
they often assume a normal, Gaussian curve of
distribution, as in reading scores, for example
(though Wright (2003: 128) suggests that normal
distributions are actually rare in psychology). In
practice this distinction means this: nominal and
ordinal data are considered to be non-parametric,
while interval and ratio data are considered to
be parametric data. The distinction, as for the
four scales of data, is important, as the consideration
of which statistical test to use is dependent
on the kinds of data: it is incorrect to apply
parametric statistics to non-parametric data, although
it is possible to apply non-parametric
statistics to parametric data (it is not widely
done, however, as the statistics are usually less
powerful). Non-parametric data are often derived
from questionnaires and surveys (though these
can also gain parametric data), while parametric
data tend to be derived from experiments and
tests (e.g. examination scores). (For the power efficiency
of a statistical test see the accompanying
web site (http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file ‘The power efficiency
of a test’).
Descriptive and inferential statistics
Descriptive statistics do exactly what they say:
they describe and present data, for example,
in terms of summary frequencies (see http://
www.routledge.com/textbooks/9780415368780 –
Chapter 24, file 24.3.ppt). This will include, for
example:
the mode (the score obtained by the greatest
number of people)
the mean (the average score) (see http://www.
routledge.com/textbooks/9780415368780 –
Chapter 24, file 24.4.ppt)
the median (the score obtained by the middle
person in a ranked group of people, i.e. it has an
equal number of scores above it and below it)
minimum and maximum scores
Chapter 24