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 Scale Types Total = 1,596

Scaling Support for Choice of Abortion Women’s Health Result of Rape Woman Unmarried Number of Cases Mixed Types Total = 53

Index and Scale Scores Response Pattern Number of Cases Index Scores Scale Scores Total Errors Scale Types Mixed Types

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 errors number 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 ConservativeLiberal Domestic Policy ConservativeAB LiberalCD