# Coeficiente RV

RV coefficients that measure the proximity between two data matrices. Compute them on your data in Excel using the XLSTAT statistical software.

## What is the RV coefficient?

The RV coefficient depicts the similarity between two matrices of quantitative variables or two configurations resulting from multivariate analysis.

## RV coefficient: definition

This tool allows computing the RV coefficient between two matrices of quantitative variables. The RV coefficient is defined as (Robert and Escoufier, 1976; Schlich, 1996):

RV(Wi,Wj) = trace(Wi,Wj) / [trace(Wi,Wi).trace(Wj,Wj)]1/2

Where trace(Wi,Wj) = Σl,mwil,mwjl,m is a generalized covariance coefficient between matrices between matrices Wi and Wj, trace(Wi,Wi) = Σl,mwil,m2 is a generalized variance of matrix Wi and wil,m is the (l,m) element of matrix Wi.

The RV coefficient is a generalization of the squared Pearson correlation coefficient. The RV coeffcient lays between 0 and 1. The closer to 1 the RV is, the more similar the two matrices Wi and Wj are. XLSTAT offers the possibility:

• To compute the RV coefficient between two matrices, including all variables form both matrices;
• To choose the k first variables from both matrices and compute the RV coefficient between the two resulting matrices.

XLSTAT allows testing if the obtained RV coefficient is significantly different from 0 or not.

Two methods to compute the p-value are proposed by XLSTAT. The user can choose between a p-value computed using on an approximation of the exact distribution of the RV statistic with the Pearson type III approximation (Kazi-Aoual et al., 1995), and a p-value computed usingMonte Carlo resamplings.

## Results

RV coefficients: A table including the RV coefficient(s), standardized RV coefficient(s), and mean(s) and variance(s) of the RV coefficient distribution; and the adjusted RV coefficient(s) and p-value(s) if requested by the user.

RV bar chart: A bar chart showing the RV coefficient(s) (with color codes to show significance of the associated p-value(s) if requested).

## References

Kazi-Aoual F., Hitier S., Sabatier R., Lebreton J.-D., (1995) Refined approximations to permutations tests for multivariate inference. Computational Statistics and Data Analysis20, 643–656.

Robert P. and Escoufier Y. (1976) A unifying tool for linear multivariate statistical methods: the RV-coefficient. Applied Statistics25, 257–265.

Schlich P. (1996). Defining and validating assossor compromises about product distances and attribute correlations. In T, Næs, & E. Risvik (Eds.), Multivariate analysis of data in sensory sciences. New York: Elsevier.

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