In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, scale analysis is a set of methods to analyse survey data, in which responses to questions are combined to measure a latent variable

Latent variable

In statistics, latent variables , are variables that are not directly observed but are rather inferred from other variables that are observed . Mathematical models that aim to explain observed variables in terms of latent variables are called latent variable models...

. 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

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 individual with others in a given population...

 approach is a way of identifying a group of questions whose responses can be combined together 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
  Likert scale
  A Likert scale 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 is often used interchangeably with rating scale, or more accurately the Likert-type scale, even though...
  
  
• Reliability analysis
  Reliability (statistics)
  In statistics, reliability is the consistency of a set of measurements or of a measuring instrument, often used to describe a test. Reliability is inversely related to random error.-Types:There are several general classes of reliability estimates:...
  
  , see also Classical test theory
  Classical test theory
  Classical test theory is a body of related psychometric theory that predict outcomes of psychological testing such as the difficulty of items or the ability of test-takers. Generally speaking, the aim of classical test theory is to understand and improve the reliability of psychological...
  
   and Cronbach's alpha
  Cronbach's alpha
  Cronbach's \alpha is a coefficient of reliability. It is commonly used as a measure of the internal consistency or reliability of a psychometric test score for a sample of examinees. It was first named alpha by Lee Cronbach in 1951, as he had intended to continue with further coefficients...
  
  
• Factor analysis
  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, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
  
  

Modern models based on Item response theory

Item response theory

In psychometrics, item response theory 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 abilities, attitudes, or other variables. It is based...

 

• Guttman scale
  Guttman scale
  In statistical surveys conducted by means of structured interviews or questionnaires, a subset of the survey items having binary answers forms a Guttman scale if they can be ranked in some order so that, for a rational respondent, the response pattern can be captured by a single index on that...
  
  
• Mokken scale
• Rasch model
  Rasch model
  Rasch models are used for analysing data from assessments to measure variables such as abilities, attitudes, and personality traits. For example, they may be used to estimate a student's reading ability from answers to questions on a reading assessment, or the extremity of a person's attitude to...
  
  
• (Circular) Unfolding analysis
• Circumplex model

Other models

• Latent class analysis
• Multidimensional scaling
  Multidimensional scaling
  Multidimensional scaling is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data. MDS is a special case of ordination. An MDS algorithm starts with a matrix of item–item similarities, then assigns a location to each...
  
  
• NOMINATE (scaling method)
  NOMINATE (scaling method)
  NOMINATE is a multidimensional scaling method developed by political scientists Keith T. Poole and Howard Rosenthal in the early 1980s to analyze...