statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, scale analysis is a set of methods to analyze

survey data Survey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey dat ...

, in which responses to questions are combined to measure a

latent variable In statistics, latent variables (from Latin: present participle of ''lateo'', “lie hidden”) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or me ...

. These items can be dichotomous (e.g. yes/no, agree/disagree, correct/incorrect) or polytomous (e.g. disagree strongly/disagree/neutral/agree/agree strongly). Any measurement for such data is required to be reliable, valid, and homogeneous with comparable results over different studies.

Constructing scales

The

item-total correlation The item-total correlation test arises in psychometrics in contexts where a number of tests or questions are given to an individual and where the problem is to construct a useful single quantity for each individual that can be used to compare that i ...

approach is a way of identifying a group of questions whose responses can be combined into a single measure or scale. This is a simple approach that works by ensuring that, when considered across a whole population, responses to the questions in the group tend to vary together and, in particular, that responses to no individual question are poorly related to an average calculated from the others.

Measurement models

Measurement is the assignment of numbers to subjects in such a way that the relations between the objects are represented by the relations between the numbers (Michell, 1990).

Traditional models

Likert scale A Likert scale ( , commonly mispronounced as ) is a psychometric scale commonly involved in research that employs questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term (or more fully the ...

* Semantic differential (Osgood) scale *

Reliability analysis Reliability, reliable, or unreliable may refer to: Science, technology, and mathematics Computing * Data reliability (disambiguation), a property of some disk arrays in computer storage * High availability * Reliability (computer networking), a ...

, see also

Classical test theory Classical test theory (CTT) is a body of related psychometric theory that predicts outcomes of psychological testing such as the difficulty of items or the ability of test-takers. It is a theory of testing based on the idea that a person's observe ...

and

Cronbach's alpha Cronbach's alpha (Cronbach's \alpha), also known as tau-equivalent reliability (\rho_T) or coefficient alpha (coefficient \alpha), is a reliability coefficient that provides a method of measuring internal consistency of tests and measures. Numero ...

Factor analysis Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed ...

Modern models based on
Item response theory In psychometrics, item response theory (IRT) (also known as latent trait theory, strong true score theory, or modern mental test theory) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring ...

Guttman scale In the analysis of multivariate observations designed to assess subjects with respect to an attribute, a Guttman scale (named after Louis Guttman) is a single (unidimensional) ordinal scale for the assessment of the attribute, from which the orig ...

Mokken scale The Mokken scale is a psychometric method of data reduction. A Mokken scale is a unidimensional scale that consists of hierarchically-ordered items that measure the same underlying, latent concept. This method is named after the political scientist ...

Rasch model The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between the respondent's abilities, at ...

* (Circular) Unfolding analysis * Circumplex model

Other models

Latent class analysis In statistics, a latent class model (LCM) relates a set of observed (usually discrete) multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a latent class model because the latent variable is disc ...

Multidimensional scaling Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configurati ...

NOMINATE (scaling method) NOMINATE (an acronym for Nominal Three-Step Estimation) is a multidimensional scaling application developed by US political scientists Keith T. Poole and Howard Rosenthal in the early 1980s to analyze preferential and choice data, such as legis ...

References