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 ...

(

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 ...

), average variance extracted (AVE) is a measure of the amount of variance that is captured by a construct in relation to the amount of variance due to measurement error.Fornell & Larcker (1981), https://www.jstor.org/stable/3151312

History

The average variance extracted was first proposed by Fornell & Larcker (1981).

Calculation

The average variance extracted can be calculated as follows: :

\text = \frac

Here,

k

is the number of items,

\lambda_i

the

factor loading 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 ...

of item

i

and

\operatorname( e_i )

the

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...

of the error of item

i

Role for assessing discriminant validity

The average variance extracted has often been used to assess

discriminant validity In psychology, discriminant validity tests whether concepts or measurements that are not supposed to be related are actually unrelated. Campbell and Fiske (1959) introduced the concept of discriminant validity within their discussion on evaluating ...

based on the following "rule of thumb": the positive square root of the AVE for each of the latent variables should be higher than the highest correlation with any other latent variable. If that is the case, discriminant validity is established at the construct level. This rule is known as Fornell–Larcker criterion. However, in simulation models this criterion did not prove reliable for composite-based

structural equation model Structural equation modeling (SEM) is a label for a diverse set of methods used by scientists in both experimental and observational research across the sciences, business, and other fields. It is used most in the social and behavioral scienc ...

s (e.g., PLS-PM),Henseler, J., Ringle, C. M., Sarstedt, M., 2014. A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science 43 (1), 115–135. but indeed proved to be reliable for factor-based structural equation models (e.g., Amos, PLSF-SEM).Kock, N. (2019). From composites to factors: Bridging the gap between PLS and covariance‐based structural equation modeling. Information Systems Journal, 29(3), 674-706.Voorhees, C. M., Brady, M. K., Calantone, R., Ramirez, E., 2015. Discriminant validity testing in marketing: an analysis, causes for concern, and proposed remedies. Journal of the Academy of Marketing Science 1–16.

Related coefficients

Related coefficients are

tau-equivalent reliability 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 ...

(

\rho_T

; traditionally known as "Cronbach's

\alpha

") and congeneric reliability (

\rho_{C}

; also known as composite reliability) which can be used to evaluate the reliability of tau-equivalent and congeneric

measurement model Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...

s, respectively.

References

Statistical theory