measurement

measurement Measurement raises four main issues for the sociologist: representation (how many properties of the empirical world can best be modelled?); uniqueness (how unique are the resulting measurement numbers?); appropriate statistics (what indices may legitimately be used to summarize the measures?); and meaningfulness (what do the measurement numbers signify?).

Measurement itself is concerned with the exact relationship between the ‘Empirical Relational System’ and the ‘Formal (or Numerical) Relational System’ chosen to represent it. Thus, a strict status relationship between individuals or positions can be shown to have the same properties as the operators ‘>, <’ (greater than, less than) in the set of numbers, and may be thus represented. Most social and psychological attributes do not strictly have numerical properties, and so are often termed ‘qualitative’ or ‘non-metric’ variables, whereas properties such as wealth or (arguably) measured intelligence or cardinal utility are termed quantitative or metric.

For any given domain of interest, a measurement representation or model states how empirical data are to be interpreted formally; for example, a judgement that x is preferred to y may be interpreted as saying that x is less distant from my ideal point than is y. Once represented numerically, uniqueness issues arise. S. S. Stevens (among others) postulates a hierarchy of levels of measurement of increasing complexity, defined in terms of what transformations can be made to the original measurement numbers, whilst keeping the properties they represent (see, for example, his essay ‘On the Theory of Scales of Measurement’, Science, 1946
). The simplest version distinguishes four such levels. At the nominal level, things are categorized and labelled (or numbered), so that each belongs to one and only one category (for example, male = 0, female = 1). Any one-to-one re-assignment of numbers preserves information about a categorization. At the level of ordinal measurement, the categories also have a (strict) order (such as a perfect Guttman scale), and any order-preserving transformation is legitimate. Interval-level measurement requires that equal differences between the objects correspond to equal intervals on the scale (as in temperature) and that any linear transformation preserves the differences. At the ratio level, the ratio of one distance to another is preserved, as in moving from (say) miles to kilometres.

Clyde H. Coombs (‘A Theory of Psychological Scaling’, Engineering Research Institute Bulletin, 1946)
has shown that there are many other such scales (such as partial orderings) which are useful in the social sciences, and urges keeping to lower levels, rather than quantifying by fiat. Procedures for transforming data into higher levels of measurement are known as ‘scaling’ or ‘quantification’. If the representation can be made on a straight line it is unidimensional scaling (as in Guttman and Likert scales), but if it needs two or more dimensions it is multidimensional scaling.

Most textbooks on survey research explain the different levels of measurement, with examples, and describe the statistics and techniques that are appropriate to the different levels (see, for example, D. A. de Vaus , Surveys in Social Research, 1985, 1991
).