SCALES AND MEASURES
The progress of science, including social science, depends heavily on building on the past. This is particularly so when it comes to the measurement of constructs. Coming to a disciplinary consensus on how to operationalize a construct (ex., "trust in goverment") is itself an exercise which illuminates surrounding issues. Conversely, if each social scientist operationalizes the same construct differently, confusion and "talking past one another" abounds and the state of the art progresses more slowly. While often there is no one perfect way to operationalize a construct, by using the same operationalization, social scientists achieve a far greater level of comparability across varied research than would otherwise be the case. Searching out existing standard scales and measures for constructs is therefore often an important early step in the research process, even if in the end the researcher opts for an original approach.
This volume of the Statistical Associates "Blue Book" series focuses on explanation of the common types of scales, measures of internal consistency and agreement, and standard scales and measures found in the literature. It is not intended to cover multidimensional scaling (subject of a different "Blue Book" volume) or item analysis. Likewise, other statistical methods of measuring constructs are also found in separate "Blue Book" volumes, such as those on factor analysis, structural equation modeling, partial least squares regression, canonical correlation, and latent class analysis.
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Below is the unformatted table of contents.
Table of Contents Overview 7 Key Concepts and Terms 7 Constructs vs. categories and benchmarks 7 Data-gathering techniques 8 Types of techniques 8 Likert survey items 9 Ranking scales 9 Social distance scales 9 Paired comparisons 9 Q-Sorts 10 Fixed resources allocations 10 Other methods 10 Methods of combining items in a scale 10 Overview 10 Indexes 10 Ordinal scales 11 Ordered scales 11 Composite scores 12 Factors and latent variables 12 Multidimensional scales 12 Tau Equivalence 13 Congeneric v. tau-equivalent v. parallel indicators 13 Tau-equivalence in SEM 13 Likert scales 13 Likert items and likert scales 13 "Likert scales" as Likert items in ordinal scales 14 Data level of Likert scales 14 Index of discriminative power (DP) 14 Guttman scales 15 Overview 15 How Guttman scaling works 15 Counting scale errors in Guttman scaling 15 Goodness of fit measures for Guttman scales 17 Minimum marginal reproducibility (MMR) 17 Marginal error (ME) 17 The coefficient of scalability 17 The coefficient of reproducibility 18 Stouffer's H technique 18 Chi-square significance of Guttman scales 18 Proximity scales 19 Overview 19 Example 19 Proximity scales vs. Guttman scales 20 Mokken scales 20 Overview 20 Loevinger's H 21 Measures of Internal Consistency 22 Overview 22 Cronbach's alpha 22 Overview 22 Characteristics of Cronbach's alpha 23 Alpha cut-off criteria 23 Negative alphas 23 Alpha vs. reliability 24 Alpha in SPSS 24 Standardized item alpha 24 Factor analysis 24 Rasch scales 25 Other internal consistency measures 25 Tarkkonen's measure of scale reliability 25 Loevinger's H 25 Kuder-Richardson Formula 20 25 Spearman's rho 25 Intraclass correlation 26 Measures of Agreement 26 Example 27 Measures of Reliability 27 Measures of Item Discrimination 27 Biserial correlation 27 Point-biserial correlation 28 Assumptions 28 Unidimensionality 28 Equality of Means and Standard Deviations 28 Frequently Asked Questions 29 Should I use existing items or create my own? 29 How can I find standard scales and instruments? 29 When may ordinal scale data be used in regression and other interval techniques? 29 Should I standardize my variables before testing for reliability of scale items with Cronbach's alpha? 30 I want to add item scores together to form a scale. How can I test if the items are additive? 30 How can I get my SPSS worksheet into Guttman scaling format? 30 What software programs compute Guttman scaling coefficients of scalability and reliability? 31 What is the 'cluster bloc technique'? 31 Selecting the criteria 32 Computing indices of agreement 32 Establishing non-arbitrary cutoff points 32 Forming the cluster block matrix 32 What are Thurstone equal-appearing interval scales? 33 Q-dispersion 33 Bibliography 34 References 34 Methodology 36 General 38 Business 39 Crime 39 Economic/Financial/Work 39 Education 40 Medical 40 Politics 40 Psychology 41 Public Administration/Organizations 43 Social and Sociology 44