Archive 2025

Dealing with correlation in designed field experiments: part II

Published at February 10, 2025 ·  11 min read

With field experiments, studying the correlation between the observed traits may not be an easy task. For example, we can consider a genotype experiment, laid out in randomised complete blocks, with 27 wheat genotypes and three replicates, where several traits were recorded, including yield (Yield) and weight of thousand kernels (TKW). We might be interested in studying the correlation between those two traits, but we would need to face two fundamental problems:

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A trip from variance-covariance to correlation and back

Published at January 24, 2025 ·  6 min read

The variance-covariance and the correlation matrices are two entities that describe the association between the columns of a two-way data matrix. They are very much used, e.g., in agriculture, biology and ecology and they can be easily calculated with base R, as shown in the box below.

data(mtcars)
matr <- mtcars[,1:4]

# Covariances
Sigma <- cov(matr)

# Correlations
R <- cor(matr)

Sigma
##              mpg        cyl       disp        hp
## mpg    36.324103  -9.172379  -633.0972 -320.7321
## cyl    -9.172379   3.189516   199.6603  101.9315
## disp -633.097208 199.660282 15360.7998 6721.1587
## hp   -320.732056 101.931452  6721.1587 4700.8669
R
##             mpg        cyl       disp         hp
## mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684
## cyl  -0.8521620  1.0000000  0.9020329  0.8324475
## disp -0.8475514  0.9020329  1.0000000  0.7909486
## hp   -0.7761684  0.8324475  0.7909486  1.0000000

It is useful to be able to go back and forth from variance-covariance to correlation, without going back to the original data matrix. Let’s consider that the variance-covariance of the two variables X and Y is:

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