"Why
all analysis is quantitative"
 My title
is meant to be provocative; to state the matter
strongly
 Measurement
is often problematic in the social
sciences
 Some
people say, "you can't quantify that"
 Measurement
of complex concepts offers the greatest challenge for
social research
 Creativity
often comes in the form of new measurement
techniques
 Indeed,
virtually all empirical analysis involves
measurement
 By
implication, all empirical analysis is
quantitative
 Basic
distinctions in quantitative analysis
 CONSTANTS:
values of observations do not vary
 VARIABLES:
observations vary from case to case, trial to
trial
 Relationship
of variables to
concepts
 variables
are concrete manifestations, or
operationalizations of concepts
 variables
are to concepts as hypotheses are to
propositions
 Two
conventional views of
variables
 QUANTITATIVE:
vary in magnitude
 QUALITATIVE:
vary in kind but not in
degree
 Sex
and religion are standard
examples
 But
the distinction is not
ironclad
 Sex
may be viewed as a continuous variable for
some analyses
 Death
is the classic example, but not always
foolproof
 Reinterpreting
quantitative and qualitative variables
 Quantitative
variables as CONTINUOUS
variables
 Observations
can assume any of countless values on a
line
 Examples
from physical sciences: time, distance,
etc.
 Examples
from social sciences: age, mortality rate,
liberalism
 Qualitative
variables as DISCRETE
variables
 Observations
can assume only a countable number of
values
 DICHOTOMOUS
values: male, female
 POLYCHOTOMOUS
values: Protestant, Catholic, Jew, Hindu,
etc.
 The
categories may or may not be
orderable
 NONORDERABLE
discrete categories: Religion
 ORDERABLE
discrete categories: Attitude toward things
quantitative in the class survey
 The
orderability of discrete categories becomes a major issue
in execution of research
 Problem
areas in classifying variables as discrete or
continuous
 There
is the problem of a great many valuesbut not an
infinite number.
 Family
income as an example  increments are in
cents
 Become
more complex when mean family income is
computed, and fractional cents can be computed
for a group.
 The
practice in social research is to regard a scale
with many observational values as continuous,
even though in concept the measurement is
discrete
 The
problem of a few categories but an underlying
seamless continuum
 Attitude
toward things quantitative
 Political
liberalism
 Note
that is a problem only for ORDERABLE discrete
variables
 Thus in
practice, social measurement deals with these
situations
 NONORDERABLE
DISCRETE CATEGORIES: sex, religion
 FEW
ORDERABLE AND DISCRETE CATEGORIES: attitudes
towards statistics or Ronald Reagan
 MANY
ORDERABLE DISCRETE CATEGORIES: income, votes,
missiles
 PRACTICAL
OR INFINITE CONTINUOUS MEASUREMENT: country size,
birth rate
 Conventional
"levels" of measurement according to S.S.
Stevens
 NOMINAL
level
 Arbitrary
numbers are pinned to classes: the mathematical
"operator" is the equal sign, =
 Note
that this "level" of measurement conforms to
nonorderable discrete categories
 ORDINAL
level
 Numbers
pinned to classes now have values: operations of =,
>, and <
 Note
that this conforms to orderable discrete categories
with limited number of categories
 INTERVAL
 Numbers
pinned to classes have values and the distances
between the values is known, involves =, <,
>, +, and 
 This
overlaps greatly with the many orderable discrete
categories but not completely  for Stevens says
that an interval scale has no zero
point
 Note
that income, votes, and missiles HAVE a zero
point
 The
most common example of an interval scale is a
Celsius or Fahrenheit thermometer
 Unfortunately,
it is probably also the only common
example
 RATIO
Involves
all the above mathematical functions plus / and x 
due to the presence of an absolute zero
 Applies
to income, votes, and missiles  but not to
temperature
 Evaluation
of the continuous/discrete and the "levels" distinctions
in measurement theory:
 How the
two approaches fit
together
 NOMINAL
= non orderable discrete categories
 ORDINAL
= few orderable discrete categories
 INTERVAL
= many orderable discrete EXCEPT no zero
point
 RATIO
= infinite categories (like temperature) but with a
zero point
 Relevance
of all this for social
research
 Stevens'
levels of measurement has been the dominant
approach in the statistical literature
 Which
type of statistics apply to which level of
measurement has become a matter of faith to some
social analysts
 The
issue, as we will see, hinges on the treatment of
ORDINAL data.
 Are
ordinal data to be treated as interval  i.e.,
many ordered discrete categories and analyzed with
more powerful statistical tools?
 Or
are ordinal data to be treated strictly as
"ordered" categories with no knowledge of distance
between categories and analyzed with weaker
statistics?
 One
position: since most ordinal scales are assumed to
reflect an underlying concept which is continuous,
their measures will often be treated as if they were
continuous as well
 I agree
with this position and will urge us to ASSUME that we
know the distance between scale positions, when we
really don't .
 Why all
social analysis is quantitative
 Note
the complexity involved in this discussion of
measurement
 To
some, this may seem to be unnecessarily
complex
 These
people may also be those who think that
quantitative analysis cannot deal with the
complexities of life
 Can't
on the one hand dismiss attempts to investigate
fine and complex issues and then complain that
quantitative concepts are too "simple" to capture
complexities
 But the
basic argument rests on the "lowest" level of
measurement
 Nominal
measurement involves pinning numbers to
categories
 I
don't know of any social analysis that does not
involve categorization
 Anything
that one can categorize, can be
numbered
 Anything
that can be numbered, can be counted  and thereby
be analyzed with statistics
 Therefore,
all social analysis involves
quantification.
Creating a measure of partisanship to study voting
behavior
 Consider
the psychological state of "partisanship" as different
from the behavioral act of "voting"
 Usually,
citizens will vote for candidates of their "preferred"
parties.
 Yet,
citizens may think of themselves as "Democrats" and
yet vote Republican.
 In
essence, partisanship is a psychological attachment to
a party that's separate from voting
behavior.
 Can we
develop a separate measure of partisanship to help
explain voting behavior?
 The "party
identification" scale
 Developed
at the University of Michigan's Survey Research Center
(SRC) in the late 1940s.
 Used in
all National Election Studies since 1952.
 It
arrays people along a sevenpoint scale from Strong
Democrat to Strong Republican.
 See how
scholars at the SRC "operationalized"
the concept of "party identification."
