Chapter 6

Indexes, Scales, and Typologies

Index and Scale Index

Constructed by accumulating scores assigned to individual attributes.

Scale Constructed by assigning scores to patterns

of responses, recognizing that some items reflect a weak degree of the variable while others reflect something stronger.

Index and Scale: Similarities Both are ordinal measures of variables. Both rank order units of analysis in terms

of specific variables. Both are measurements based on more

than one data item.

Index and Scale:Scoring Differences Index

Accumulate scores assigned to individual attributes.

Scale Assign scores to patterns of responses.

Index-Construction Logic Below are political actions with similar degrees

of activism. To create an index we might give people 1 point for each of the actions they’ve taken.

Scale-Construction Logic Below are political actions with different

degrees of activism. To construct a scale we might score people according to which of the ideal patterns most closely describes them.

Constructing an Index Select items for a composite index. Examine empirical relationships. Assign scores for responses. Handle missing data. Validate the index.

Selecting Items

Criteria Face (logical) validity Unidimensionality General or specific Variance

Bivariate Relationships Among Scientific Orientation Items

Trivariate Relationships Among Scientific Orientation Items

Hypothetical Trivariate Relationship Among Scientific Orientation Items

Empirical Relationships Established when respondents’ answers

to one question help predict how they will answer other questions.

If two items are empirically related, we can argue that each reflects the same variable, and both can be included in the same index.

Assign Scores for Responses

Two basic decisions: Decide the desirable range of the index

scores. Decide whether to give each item in the

index equal weight or different weights.

Ways to Handle Missing Data Exclude cases with missing data from the

construction of the index and the analysis. Treat missing data as one of the available

responses. Analyze missing data to interpret the

meaning.

Validate the Index Item Analysis - internal validation. External validation - ranking of groups on

the index should predict the ranking of groups in answering similar or related questions.

Techniques of Scale Construction Bogardus social distance scale -

measures the willingness of people to participate in social relations.

Thurstone scales - judges determine the intensity of different indicators.

Techniques of Scale Construction Likert scaling - uses standardized

response categories. Semantic differential -asks respondents

to rank answers between two extremes. Guttman scaling - uses an empirical

intensity structure (most common).

Semantic Differential: Feelings about Musical Selections

The semantic differential asks respondents to describe something or someone in terms of opposing adjectives.

Scaling Support for Choice of Abortion

Women’s Health

Result of Rape

Woman Unmarried

Number of Cases

+ + + 677

+ + - 607

Scale Types

+ - - 165

- - - 147

Total = 1,596

Scaling Support for Choice of Abortion

Women’s Health

Result of Rape

Woman Unmarried

Number of Cases

- + - 42

+ - + 5

Mixed Types

- - + 2

- + + 4

Total = 53

Index and Scale ScoresResponse

PatternNumber of Cases

Index Scores

Scale Scores

Total Errors

Scale Types

+ + + 677 3 3 0

+ + - 607 2 2 0

+ - - 165 1 1 0

- - - 147 0 0 0

Mixed Types

- + - 42 1 2 42

+ - + 5 2 3 5

- - + 2 1 0 2

- + + 4 2 3 4

Index and Scale Scores

Response Pattern

Number of

Cases

Index Scores

Scale Scores

Total Errors

Total Scale Errors = 53

Coefficient of reproducibility = 1 -

Number of errorsnumber of guesses

Typologies The classification (typically nominal) of

observations in terms of their attributes on two or more variables.

The classification of newspapers as liberal-urban, liberal-rural, conservative-urban, or conservative-rural would be an example.

A Political Typology of Newspapers

Foreign Policy

Conservative Liberal

Domestic Policy

Conservative A B

Liberal C D