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Checking How Good A Correlation Is

I'm working with a set of data and I've obtained a certain correlations (using pearson's correlation coefficient). Is there a R function or package that would determine how good a correlation is by permutation tests? Or is there any other way to do this?

The example data:

data A

  structure(list(A = c(4.7671948292, 5.057230067, 5.3789958351, 
  6.1564088085, 4.8594252454, 5.8761895664, 4.4854758124, 4.7528916483, 
  4.4210848845, 3.9850111524), B = c(4.5852526479, 4.9673151031, 
  5.1601803995, 6.3082498288, 4.5796519129, 5.665788171, 4.2886052774, 
  4.4678455852, 4.4444468354, 3.8911975809)), .Names = c("A", 
  "B"), row.names = c("901_at", "902_at", "903_at", 
   "904_at", "905_at", "906_at", "907_at", "908_at", 
   "909_at", "910_s_at"), class = "data.frame")

data B

      structure(list(A = c(5.5552465406, 5.8527484565, 8.3272537274, 
      6.4436035152, 5.597121724, 7.7741738479, 4.9931115346, 5.3852788212, 
      6.0292060458, 4.8351702985),B = c(5.6748698406, 6.8504588796, 
      9.4375062219, 7.6984745916, 5.7246927142, 9.0156741296, 4.8601744963, 
     5.4403609238, 6.842929093, 5.474543968)), .Names = c("A", "B"
     ), row.names = c("901_at", "902_at", "903_at", "904_at", 
    "905_at", "906_at", "907_at", "908_at", "909_at", 
    "910_s_at"), class = "data.frame")

The correlation was calculated as :

   cor1<-cor(data A, data B)

How to do the permutation tests to validate the same?

r correlation
• 3,451 views • link
updated by Sean Davis Sean Davis • written by deschisandy • deschisandy

What exactly do you have in mind? You want to remove some data 1000 times and verify if the correlation still holds? You want to permute data between A and B randomly 1000 times? You want to permute all the data, some of the data? Why do you want to accomplish this? In order to see if the correlation is robust to small changes in the data? Otherwise, a correlation coefficient already tells you how good the correlation is.

• 113 views • link
written by Eric Normandeau Eric Normandeau

Yes, I would like to permute all of the data to see if the correlation still holds and how good a correlation is when compared to a correlation between random permutations of the data

• 0 views • link
written by deschisandy • deschisandy

2 answers

You could start with something like:

corperm = function(x,y,n) {
  # n is the number of permutations
  # x and y are the vectors to correlate
  obs = abs(cor(x,y))
  tmp = sapply(1:n,function(z) {abs(cor(sample(x,replace=TRUE),y))})
  return(1-sum(obs>tmp)/n)
}

Usage is like corperm(A$A,B$B,1000). Note that this will likely give results very similar to cor.test and will be slower.

• 61 views • link
written by Sean Davis Sean Davis

Hello!

I think you can use the function cor.test.

Example:

cor.test(A$A, B$A)
• 156 views • link
written by Leandro Lima Leandro Lima

This just associates a significance value with your correlation coefficient, i.e. is it significantly different from 0 given the sample size

• 76 views • link
written by Ben Ben

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