T test for two lists of matrices

I have two lists of matrices (list A and list B, each matrix is of dimension 14x14, and list A contains 10 matrices and list B 11) and I would like to do a t test for each coordinate to compare the means of each coordinate of group A and group B. As a result I would like to have a matrix of dimension 14x14 which contains the p value associated with each t test.

Thank you in advance for your answers.

Solution

Here's a method using a for loop and then applying the lm() function.

First we'll generate some fake data as described in the question.

#generating fake matrices described by OP
listA <- vector(mode = "list", length = 10)
listB <- vector(mode = "list", length = 10)
for (i in 1:10) {
   listA[[i]] <-  matrix(rnorm(196),14,14,byrow = TRUE)
}
for (i in 1:11) {
  listB[[i]] <-  matrix(rnorm(196),14,14,byrow = TRUE)
}

Then we'll unwrap each matrix as described by dcarlson in a for loop.

Unwrapped.Mats <- NULL
for (ID in 1:10) {
  unwrapped <- as.vector(as.matrix(listA[[ID]])) #Unwrapping each matrix into a vector
  withID <- c(ID, "GroupA", unwrapped) #labeling it with ID# and which group it belongs to 
  UnwrappedCorMats <- rbind(Unwrapped.Mats, withID)
}
for (ID in 1:11) {
  unwrapped <- as.vector(as.matrix(listB[[ID]]))
  withID <- c(PID, "GroupB", unwrapped)
  UnwrappedCorMats <- rbind(UnwrappedCorMats, withID)
}

Then write and apply a function to run lm(). lm() is statistically equivalent to an unpaired t-test in this context but I'm using it to be more easily adapted into a mixed effect model if anyone wants to add mixed effects.

UnwrappedDF <- as.data.frame(UnwrappedCorMats)
lmPixel2Pixel <- function(i) { #defining function to run lm
  lmoutput <-   summary(lm(i ~ V2, data= UnwrappedDF)) 
  lmoutputJustP <- lmoutput$coefficients[2,4] #Comment out this line to return full lm output rather than just p value
}

Vector_pvals <- sapply(UnwrappedDF[3:length(UnwrappedDF)], lmPixel2Pixel)

Finally we will reform the vector into the same shape as the original matrix for more easily interpreting results

LM_mat.again <- as.data.frame(matrix(Vector_pvals, nrow = nrow(listA[[1]]), ncol = ncol(listA[[1]]), byrow = T)) 
colnames(LM_mat.again) <- colnames(listA[[1]]) #if your matrix has row or column names then restoring them is helpful for interpretation
rownames(LM_mat.again) <- colnames(listB[[1]])

head(LM_mat.again)

I'm sure there are faster methods but this one is pretty straight forward and I was surprised there weren't answers for this type of operation yet