Definition

Noun: 1. A statistical method for data reduction: Factor analysis is a family of techniques used to analyze the interrelationships among a large number of observed variables (e.g., test scores, survey responses) and to explain them in terms of a smaller number of underlying, unobserved variables called factors. It aims to identify the latent structures or dimensions that account for the patterns of correlation in the observed data.

Examples of Usage

• Noun:
  • The researcher used factor analysis to identify the key personality traits measured by the lengthy questionnaire.
  • Factor analysis of the customer satisfaction survey revealed three primary factors: product quality, customer service, and value.
  • Before building the scale, they performed factor analysis to verify that all questions loaded onto a single construct.

Advanced Usage

• Exploratory Factor Analysis (EFA): Used when the researcher does not have a pre-defined hypothesis about the number or nature of the underlying factors. It is a data-driven approach to discover the latent structure.
  • We conducted an exploratory factor analysis to see how the variables naturally grouped together.
• Confirmatory Factor Analysis (CFA): Used to test a specific hypothesis or theory about the factor structure. The researcher specifies the expected number of factors and which observed variables are related to which latent factor before analysis.
  • The model was validated using confirmatory factor analysis, which supported the proposed three-factor structure.

Variants and Related Words

• Factor (n): In this context, an underlying, unobserved variable or dimension that is inferred from the correlations among observed variables.
  • The analysis extracted two main factors: verbal ability and spatial reasoning.
• Factor loading (n): A statistic (typically a correlation coefficient) that indicates the strength and direction of the relationship between an observed variable and a latent factor.
  • Questions with a factor loading below 0.4 were removed from the scale.
• Factor rotation (n): A step in factor analysis that adjusts the factor axes to achieve a simpler, more interpretable structure, often making clear which variables align with which factor.
  • Varimax rotation was applied to clarify the meaning of the extracted factors.

Synonyms

• Data reduction technique: A broader term for statistical methods, including factor analysis, that simplify complex datasets.
• Latent variable analysis: A category of techniques, including factor analysis, that aim to measure constructs that are not directly observed.

Related Phrases

• To run a factor analysis: To perform or execute a factor analysis.
  • The next step is to run a factor analysis on the collected data.
• To extract factors: The statistical process of identifying the latent factors from the correlation matrix.
  • The software was used to extract four factors from the 20 survey items.
• To load on a factor: Describes when an observed variable has a strong statistical relationship with a specific latent factor.
  • All items designed to measure anxiety loaded highly on the same factor.

Noun

1. any of several methods for reducing correlational data to a smaller number of dimensions or factors; beginning with a correlation matrix a small number of components or factors are extracted that are regarded as the basic variables that account for the interrelations observed in the data