Class 4 - Measurement

8/7/2019 Class 4 - Measurement

http://slidepdf.com/reader/full/class-4-measurement 1/26

Measurement Note: Chapter 4 workbook exercises dueTuesday, February 15



Measurement

• Def: Systematic observation and representation by scores or

numerals, of the variables we have decided to investigate

(JRM)

• Conceptual definition vs. Operational Definition

• Concepts vs. Indicators



MEASUREMENT

Examples• Hypothesis: The level of democracy in a country is negatively

related to the level of political violence

Key Question: How do we operationalize the dependent and

independent variables in this hypothesis?



Operational Definitions

• Operationalize Democracy:

• Turnout – The percentage of eligible citizens voting in the last

national election

• Operationalize Political Violence:

• Riots – any act of spontaneous collective violence (rock throwing,vandalism, arson, sniping, beatings) involving 30 or more people

that can be interpreted as politically motivated



Levels of Measurement

• Orderable (Ordinal, Interval, Ratio)

vs.

• Non-orderable Variables (Nominal)

• Orderable Variable: Values of an orderable variable represent

quantities of that variable, such that any value of a variable X

must be either >, <, or = to any other value of X



Ordinal Variables

• Ordinal: Assume there exists a variable X with

values X1, X2, and X3, where X1 < X2 < X3 (i.e. it

is orderable).•

This variable is said to be measured at the ordinal level if it is notcertain that the quantity of X represented by |X1 - X2| is equal to

the quantity of X represented by |X2 - X3|

• Example: X=Olympic Performance,

• where 1=Bronze, 2=Silver, 3=Gold



Ordinal Variables

X1 X2

X

X3

the quantity of X represented by |X1 - X2| is notknown to be equal to the quantity of X representedby |X2-X3|

Example: Olympic Performance(Bronze, Silver, Gold)



Interval Variables

• Interval: Assume there exists a variable X withvalues X1, X2, and X3, where X1 < X2 < X3 (i.e. itis orderable).

• This variable is said to be measured at the intervallevel if we know that the quantity of X represented by|X1 - X2| IS equal to the quantity of X represented by|X2-X3|;

• AND the measurement scale does not contain at TRUE

zero

• Example: Temperature



Interval Variables

X1

X2

X

X3

the quantity of X represented by |X1 - X2| IS equal to the quantity of X represented by |X2-X3|

Example: Temperature



Ratio Variables

• Ratio: A variable measured at the ratio level is

simply an interval level variable with a "true"

zero (i.e. where a value of zero represents a

complete absence of that variable)

• Example: Prize money for a golf tournament (in thousands of

$)



Nominal Variables

• Nominal – Classification of observations into a set of

categories that do not have direction (i.e. do not represent

quantities of that variable)

• Example: Race, where 1= White, 2=Black, 3=Asian, 4=NativeAmerican



Other Types of Variables

• Dichotomous Variable:

• Variables that take on only two values

• Can be orderable or nominal

• Discrete Variable:

• Orderable variable that can take on limited values

• Examples:

• 1, 2, 3, 4….

• 1979, 1980, 1981…

•

Continuous Variable:• Orderable variable variable that can take on a limitless set of

values

• Example: decimals



Examples

• Determine whether the following variables are (i) discrete or continuous,

• and (ii) measured at the nominal, ordinal, interval or ratio levels.

• Academic Department Size (number of faculty)

• Region of Nation (North, South, East, West)

• TV watching (avg. hours spent watching TV per week)

• Crime Rate (crimes per 100,000 population)

• Hometown (city of residence)

• Partisanship (% voting Republican by precinct)

• Partisanship (party that individual is registered as)

• Ideology (7-point scale from Extremely Liberal to Extremely Conservative)

•

Percentage of state population that is Hispanic• Year of birth

• Weight of contestant

• Size of drink (small, medium, large, biggie)



Measurement Quality

• Measurement Error – Lack of correspondence between

observed indicator and underlying concept

• Validity

• Reliability



Measurement Quality - Validity

• Validity - The extent to which a measurement procedure

measures what it intends to measure



Measurement Quality - Validity

• Determine if the following indicators are valid measures of the

underlying concept

• Party registration (Dem, Rep or Ind) as a measure of political

ideology• Number of riots as a measure of political violence

• GPA as a measure of academic aptitude



Assessing Validity

• Face validity – does the measure appear valid?

• Content validity – does the measure encompass

the entire domain of the concept?

• Construct validity – is this measure related to

other variables that would be suggested bytheory?



Assessing Validity

• Content validity – does the measure encompass

the entire domain of the concept?

• Example: An individual’s ideology (liberal-conservative) as measured by the following

question:

• “Do you support a woman’s right to have an

abortion?”



Assessing Validity

• Construct validity – is this measure related to

other variables that would be suggested by

theory?

• Example – GRE or LSAT scores



Measurement Quality - Reliability

• Reliability – the extent to which a measuring instrument

consistently measures whatever it is that it is measuring



Measurement Quality - Reliability

• Determine if the following measures are reliable

• Level of racial stereotyping (based on interviewer by phone)

• Gender of an individual (based on interviewer observation in

face-to-face survey)• Weight of an individual (on a scale) as a measure of ideology



Improving Measurement

Quality• Creating multi-item measures

• Reduce errors in measurement that occur by using a single

variable

• Different types



Original CPS Political Efficacy Index [agree-disagree]

• 1. People like me don't have any say about what the government does.

• 2. Sometimes politics and government seem so complicated that a personlike me can't really understand what's gong on.

•

3. Voting is the only way that people like me can have any say about howthe government runs things.

• 4. I don't think public officials care much what people like me think.

• 5. Generally speaking, those we elect to Congress in Washington lose

touch with the people pretty quickly.

• 6. Parties are only interested in people's votes but not in their opinions.





Class Exercise…

Devise a measure of political ideology



Example: Judicial Ideology

Documents

Class 4 - Measurement