MEASUREMENT

Operational Definitions
Variables are first defined by conceptual definitions.  These are definitions that explain the concept the variable is attempting to capture.

Second, variables are defined by operational definitions.  These are definitions of how the variable will be measured in practice.

For example, the variable "work effort" can be defined conceptually as the amount of effort required to do the work, including speed, hardness, effort, dexterity, and repetitiveness.  Each of these aspects must have an operational definition if it is to be measured.

 
 
 
 
 

Variable	Conceptual Definition	Operational Definition
Work Effort	Speed	My job requires me to work fast  for ___ hours per day (1-2, 3-5, 6+)
	Hardness	My job requires me to work hard  for ___ hours per day (1-2, 3-5, 6+)
	Effort	My job requires a lot of effort  for ___ hours per day (1-2, 3-5, 6+)
	Dexterity	My job requires a lot of dexterity for ___ hours per day (1-2, 3-5, 6+)
	Repetitiveness	My job is doing repetitive things  for ___ hours per day (1-2, 3-5, 6+)

 

In doing research in public policy and administration, it is important to involve key decision-makers in the formulation of operational definitions in order to:

MEASUREMENT

Measurement is a procedure for assigning symbols, letters, or numbers to empirical properties of variables according to rules.

Numerals are labels that have no inherent meaning, for example, in drivers' license numbers, zip codes, or social security numbers.

Numbers are numerals that have quantitative meaning and are amenable to statistical analysis, for example, age, height, or weight.

Rules for assigning labels to properties of variables are the most important component of measurement, because poor rules can make the outcome meaningless.

It is difficult to measure concepts directly, e.g., "work effort," so what are usually measured are indicators of concepts, such as speed, repetitiveness, etc.

LEVELS OF MEASUREMENT

There are different levels of measurement.  These levels differ as to how closely they approach the structure of the number system we use.  It is important to understand the level of measurement of variables in research, because the level of measurement determines the type of statistical analysis that can be conducted, and, therefore, the type of conclusions that can be drawn from the research.

Nominal Level
A nominal level of measurement uses symbols to classify observations into categories that must be both mutually exclusive and exhaustive.  Exhaustive means that there must be enough categories that all the observations will fall into some category.  Mutually exclusive means that the categories must be distinct enough that no observations will fall into more than one category.  This is the most basic level of measurement; it is essentially labeling.  It can only establish whether two observations are alike or different, for example, sorting a deck of cards into two piles:  red cards and black cards.

In a survey of boaters, one variable of interest was place of residence.  It was measured by a question on a questionnaire asking for the zip code of the boater's principal place of residence.  The observations were divided into zip code categories.  These categories are mutually exclusive and exhaustive.  All respondents live in one zip code category (exhaustive) but no boater lives in more than one zip code category (mutually exclusive).

Similarly, the sex of the boater was determined by a question on the questionnaire.  Observations were sorted into two mutually exclusive and exhaustive categories, male and female.  Observations could be labeled with the letters M and F, or the numerals 0 and 1.

The variable of marital status may be measured by two categories, married and unmarried.  But these must each be defined so that all possible observations will fit into one category but no more than one:  legally married, common-law marriage, religious marriage, civil marriage, living together, never married, divorced, informally separated, legally separated, widowed, abandoned, annulled, etc.

In nominal measurement, all observations in one category are alike on some property, and they differ from the objects in the other category (or categories) on that property (e.g., zip code, sex).  There is no ordering of categories (no category is better or worse, or more or less than another).

Ordinal Level
An ordinal level of measurement uses symbols to classify observations into categories that are not only mutually exclusive and exhaustive; in addition, the categories have some explicit relationship among them.

For example, observations may be classified into categories such as taller and shorter, greater and lesser, faster and slower, harder and easier, and so forth.  However, each observation must still fall into one of the categories (the categories are exhaustive) but no more than one (the categories are mutually exclusive).  Meats are categorized as regular, choice, or prime; the military uses ranks to distinguish categories of soldiers.

Most of the commonly used questions which ask about job satisfaction use the ordinal level of measurement.  For example, asking whether one is very satisfied, satisfied, neutral, dissatisfied, or very dissatisfied with one's job is using an ordinal scale of measurement.

Interval Level
An interval level of measurement classifies observations into categories that are not only mutually exclusive and exhaustive, and have some explicit relationship among them, but the relationship between the categories is known and exact.  This is the first quantitative application of numbers.

In the interval level, a common and constant unit of measurement has been established between the categories.  For example, the commonly used measures of temperature are interval level scales.  We know that a temperature of 75 degrees is one degree warmer than a temperature of 74 degrees, just as a temperature of 42 degrees is one degree warmer than a temperature of 41 degrees.

Numbers may be assigned to the observations because the relationship between the categories is assumed to be the same as the relationship between numbers in the number system.  For example, 74+1=75 and 41+1=42.

The intervals between categories are equal, but they originate from some arbitrary origin.  that is, there is no meaningful zero point on an interval scale.

Ratio Level
The ratio level of measurement is the same as the interval level, with the addition of a meaningful zero point.  There is a meaningful and non-arbitrary zero point from which the equal intervals between categories originate.

For example, weight, area, speed, and velocity are measured on a ratio level scale.  In public policy and administration, budgets and the number of program participants are measured on ratio scales.

In many cases, interval and ratio scales are treated alike in terms of the statistical tests that are applied.

Variables measured at a higher level can always be converted to a lower level, but not vice versa.  For example, observations of actual age (ratio scale) can be converted to categories of older and younger (ordinal scale), but age measured as simply older or younger cannot be converted to measures of actual age.

Measurement Problems
Commonly encountered problems include a misplaced belief in precision.  It is not usually necessary, for example, to measure annual income in dollars and cents.

Another problem is measures that go against social conventions.  It is often easier to ask people to check of categories than to supply specific information, for example, with regard to age, income, education, etc.  It is a trade-off between gathering higher-level (interval or ratio) data and having a higher questionnaire completion rate (less missing data).

A third problem is when the operational definition does not correspond to the conceptual definition.  It may be easier to measure the number of students suspended from school than to measure the concept of school violence.

A fourth problem is when the researcher becomes addicted to certain statistics, and gathers only data measured at the level appropriate for those statistical formulas.