Week 3: Measurement, Variables, and Unit of Analysis

Measurement and Important Terms

  • Measurement is at the heart of empirical inquiry. It involves talking about abstract ideas and converting these ideas into something objectively measurable (a variable).
  • Objectively measurable means that a system to measure is developed, not that there is universal agreement on the best way to measure the idea.
  • Example: belief that the social class of the person a police officer interacts with during a call for service impacts the outcome of the interaction is a general belief called a “construct.”

Constructs, Concepts, and Operationalization

  • Construct: an idea containing various conceptual elements, typically subjective and not based on empirical evidence.
  • Concept: an abstract element of a notion; not operational (not yet observations).
  • Operationalization: the process of converting a concept to a measurable variable.

Variable and Observation

  • Variable: something that varies and is measurable and can be used by a researcher to collect observations.
  • The movement from abstract concepts to observable data requires operationalization and clear measurement strategies.

From Construct to Concrete Variables (Illustrative Example)

  • Construct: social class impacts police outcomes.
  • Concepts: 1) “social class” 2) “police outcomes.”
  • Variables: 1) how much money a person made last year; 2) whether the person was arrested, ticketed, or given a warning.
  • Note: These variables are concrete and observable, which allows testing the accuracy of the underlying construct.

Unit of Analysis

  • Unit of Analysis (U of A) is the entity that the variable measures or collects information about.
  • Possible UoA: individuals, groups, neighborhoods, counties, cities, states, etc.
  • Important: A variable collected about a neighborhood does not describe any single person or city block within that neighborhood.

Measurement Strategies by Unit of Analysis (Overview)

  • Individual: Surveys; records on the person; observation of the person.
  • Neighborhood: Rates; records or observations about the neighborhood.
  • Cities or Counties: Rates; records or observations about the city or the county.
  • States: Rates; records or observations about the state.

Types of Variables

  • Three types of variables: nominal, ordinal, and interval/ratio.
  • When creating variables, value labels should be collectively exhaustive and mutually exclusive.
  • A good approach is to develop multiple variables to measure a concept (an index).
  • Variables are assessed for validity and reliability.
  • Variables can be independent or dependent; more on these notions later.

3 Types of Variables (and Distinctions)

  • Nominal: Value Labels/Categories = Yes; Rank Ordering = No; Numerical Codes/Values Have Inherent Meaning? = No; Numerical Codes/Values Have Objective Equal Distance? = No
    • Examples: Gender; Race
  • Ordinal: Value Labels/Categories = Yes; Rank Ordering = Yes; Inherent Meaning? = No; Equal Distance? = No
    • Examples: Likert Scales
  • Interval/Ratio: Value Labels/Categories = Yes; Rank Ordering = Yes; Inherent Meaning? = Yes; Equal Distance? = Yes
    • Examples: Rates; Age in Years

Value Labels and the Coding Scheme

  • Determine the Variable Type, then assign Value Labels and a Coding Scheme.
  • Example: Prior Offending
    • Variable: Prior Conviction? Does the person have a prior conviction?
    • Value Labels: No, Yes
    • Coding Scheme: 1 = No, 2 = Yes
    • Type: Nominal

Explanations: Prior Conviction (Nominal)

  • Category/Variable Values: Yes
  • Rank Ordering: No
  • Numerical Codes Have Inherent Meaning? No
  • Numerical Codes Have Objective Distance? No
  • Summary: Prior conviction is a nominal variable with two categories; codes do not carry inherent order or distance.

Explanations: Number Prior Offenses (Ordinal)

  • Variable Type: Ordinal (Categorical)
  • Examples of Coding: 0=0; 1=1; 2=2; 3 or More
  • Rank Ordering: Yes
  • Numerical Codes Have Inherent Meaning? No
  • Numerical Codes Have Objective Distance? No
  • Summary: A variable with ordered categories where the distance between codes is not necessarily equal.

Explanations: Number Prior Offenses (Interval/Ratio - Actual Number)

  • Variable Type: Interval/Ratio (Actual Number)
  • Coding Example: 0=0; 1=1; 2=2; 3=3; 4=4
  • Rank Ordering: Yes
  • Numerical Codes Have Inherent Meaning? Yes
  • Numerical Codes Have Objective Distance? Yes
  • Summary: A true numeric count with equal distances between values.

Collectively Exhaustive and Mutually Exclusive

  • Collectively Exhaustive: All potential value labels are accounted for by the variable. Can be achieved by including an “all others” label.
  • Mutually Exclusive: No observation can be categorized in more than one value label.
  • Requires careful creation of value labels.

Multiple Measures (Indexes)

  • When a concept is difficult to capture with a single variable, researchers use multiple variables.
  • Example: Self-control is a concept; it may involve risk-taking, temper/anger management, and the degree to which a person pursues self-interest.
  • An index combines multiple variables into one score to represent a belief, feeling, or attitude.

Index Components: Sample Scales (Illustrative Items)

  • Impulsivity (Items 11–14)
    • 11: I often act on the spur of the moment without stopping to think.
    • 12: I don't devote much thought and effort to preparing for the future. (reverse coded)
    • 13: I often do whatever brings me pleasure here and now, even at the cost of some distant goal.
    • 14: I'm more concerned with what happens to me in the short run than in the long run.
  • Simple Tasks (Items S1–S4)
    • S1: I frequently try to avoid projects that I know will be difficult.
    • S2: When things get complicated, I tend to quit or withdraw.
    • S3: The things in life that are easiest to do bring me the most pleasure.
    • S4: I dislike really hard tasks that stretch my abilities to the limit.
  • Risk Seeking (R1–R4)
    • R1: I like to test myself every now and then by doing something a little risky.
    • R2: Sometimes I will take a risk just for the fun of it.
    • R3: I sometimes find it exciting to do things for which I might get in trouble.
    • R4: Excitement and adventure are more important to me than security.
  • Physical Activities (P1–P4)
    • P1: If I had a choice, I would almost always rather do something physical than something mental.
    • P2: I almost always feel better when I am on the move than when I am sitting and thinking.
    • P3: I like to get out and do things more than I like to read and contemplate ideas.
    • P4: I seem to have more energy and a greater need for activity than most other people my age.
  • Self-centered (Sc1–Sc4)
    • Sc1: I try to look out for myself first, even if it means making things difficult for other people.
    • Sc2: I'm not very sympathetic to other people when they are having problems.
    • Sc3: If things I do upset people, it's their problem not mine.
    • Sc4: I will try to get the things I want even when I know it's causing problems for other people.
  • Temper (T1–T4)
    • T1: I lose my temper pretty easily.
    • T2: Often, when I'm angry at people I feel more like hurting them than talking to them about why I am angry.
    • T3: When I'm really angry, other people had better stay out of my way.
    • T4: When I have a serious disagreement with someone, it's usually hard for me to talk calmly about it without getting upset.

Criminal Behavior and Indexes

  • Criminal behavior or involvement in crime is also a concept that is often measured with an index.

Independent (IV) and Dependent (DV) Variables

  • When two variables are involved, one is the independent variable (IV) and the other is the dependent variable (DV).
  • Determination is based on the construct: e.g., Level of self-control impacts involvement in criminal behavior.
  • Independent variable: Level of self-control (the “cause” in a cause-and-effect relationship).
  • Dependent variable: Level of involvement in crime (the “effect” or outcome).

Validity and Reliability

  • Validity: The extent to which the variable represents the concept it is intended to measure.
  • Example: Implicit bias tests—some critiques argue the tests measure preferences rather than bias against a target group.
  • Reliability: A reliable variable yields consistent results over time, across researchers (interrater reliability), and across contexts.
  • These are important considerations; this class notes that detailed treatment is in Research Methods.

Appendix: Measurement and Variables – Rates and Neighborhoods

  • A rate is the number of incidents per x population, standardizing differences across population size.
  • Example construct: 'family disruption' impacts crime in a neighborhood. The variable is the rate of single parent households in the neighborhood.
  • Calculation example: The rate of single parent households per 1,000 households is 62.5; this calculation would be done for each neighborhood under study.
  • The same logic applies to crime: crime rate per X population would be calculated for each neighborhood.
  • Example: The crime rate for a particular neighborhood is 116.66 per 1,000 residents; this would be calculated for each neighborhood under study.