Differences Between Pearson'S Correlation And Pca Biplots

Question

[deschisandy]

I have a scaled PCA biplot (i.e. based on correlation matrix, not covariance matrix) of the first two PCs of a data set with 400 individuals and 26 variables (phenotypes).

The biplot indicates certain relationships between variables, based on the angles between the vectors. Some variables are positively correlated, others are negatively or not correlated at all. Why then, if I calculate and plot a Pearson's correlation between two columns in my data set, would the relationship be different from what's indicated on the biplot? (i.e. Pearson indicates a strong and significant negative correlation, but biplot shows vectors with an angle less than 90 degrees?)

[Josh Herr]

This is not a bioinformatics question and is a straight statistics question. What have you tried to understand this? I'm not sure what your question is other than "my PCA and Pearson's correlation show different associations" and the short answer to that is they are different tests.

[Manu Prestat]

Josh is right, you could try Cross Validated http://stats.stackexchange.com/

Answer 1

[Neilfws]

As Josh said in the comments: the short answer to that is they are different tests.

Principal components are linear combinations of the original variables - not the original variables themselves. So the angle between vectors on the biplot does not tell you about correlations between the original variables. I suggest you spend some time making sure that you understand how PCA works.