Quantitatitive Analysis in Political Research: Lecture 3:

"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 iron-clad 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 values--but 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 seven-point scale from Strong Democrat to Strong Republican. See how scholars at the SRC "operationalized" the concept of "party identification."