trying to perform a t.test for each row and count all rows where p-value is less than 0.05

问题

I've been wrecking my head for the past four hours trying to find the solution to an R problem, which is driving me nuts. I've searching everywhere for a decent answer but so far I've been hitting wall after wall. I am now appealing to your good will of this fine community for help.

Consider the following dataset:

set.seed(2112)
DataSample <- matrix(rnorm(24000),nrow=1000)
colnames(DataSample) <- c(paste("Trial",1:12,sep=""),paste("Control",13:24,sep=""))

I need to perform a t-test for every row in DataSample in order to find out if groups TRIAL and CONTROL differ (equal variance applies).

Then I need to count the number of rows with a p-value equal to, or lower than 0.05.

So here is the code I tried, which I know is wrong:

set.seed(2112)
DataSample <- matrix(rnorm(24000),nrow=1000)
colnames(DataSample) <- c(paste("Trial",1:12,sep=""),paste("Control",13:24,sep=""))

pValResults <- apply(
  DataSample[,1:12],1,function(x) t.test(x,DataSample[,13:24], var.equal=T)$p.value
  )

sum(pValResults < 0.05) # Returns the wrong answer (so I was told)

I did try looking at many similar questions around stackoverflow, but I would often end-up with syntax errors or a dimensional mismatch. The code above is the best I could get without returning me an R error -- but I since the code is returning the wrong answer I have nothing to feel proud of.

Any advice will be greatly appreciated! Thanks in advance for your time.

回答1:

One option is to loop over the data set calculating the t test for each row, but it is not as elegant.

set.seed(2112)
DataSample <- matrix(rnorm(24000),nrow=1000)
colnames(DataSample) <- c(paste("Trial",1:12,sep=""),paste("Control",13:24,sep=""))

# initialize vector of stored p-values
pvalue <- rep(0,nrow(DataSample))

for (i in 1:nrow(DataSample)){
   pvalue[i] <- t.test(DataSample[i,1:12],DataSample[i,13:24])$p.value
}
# finding number that are significant
sum(pvalue < 0.05)

回答2:

I converted to a data.table, and the answer I got was 45:

DataSample.dt <- as.data.table(DataSample)
sum(sapply(seq_len(nrow(DataSample.dt)), function(x)
    t.test(DataSample.dt[x, paste0('Trial', 1:12), with=F],
           DataSample.dt[x, paste0('Control', 13:24), with=F],
           var.equal=T)$p.value) < 0.05)

回答3:

To do a paired T test, you need to supply the paired = TRUE parameter. The t.test function isn't vectorised, but it's quite simple to do t tests a whole matrix at a time. Here's three methods (including using apply):

library("genefilter")
library("matrixStats")
library("microbenchmark")
dd <- DataSample[, 1:12] - DataSample[, 13:24]
microbenchmark::microbenchmark(
  manual = {ps1 <- 2 * pt(-abs(rowMeans(dd) / sqrt(rowVars(dd) / ncol(dd))), ncol(dd) - 1)},
  apply = {ps2 <- apply(DataSample, 1, function(x) t.test(x[1:12], x[13:24], paired=TRUE)$p.value)},
  rowttests = {ps3 <- rowttests(dd)[, "p.value"]})
#Unit: milliseconds
#      expr        min         lq       mean     median         uq        max
#    manual   1.611808   1.641783   1.677010   1.663122   1.709401   1.852347
#     apply 390.869635 398.720930 404.391487 401.508382 405.715668 634.932675
# rowttests   2.368823   2.417837   2.639671   2.574320   2.757870   7.207135
# neval
#   100
#   100
#   100

You can see the manual method is over 200x faster than apply.

If you actually meant an unpaired test, here's the equivalent comparison:

microbenchmark::microbenchmark(
  manual = {x <- DataSample[, 1:12]; y <- DataSample[, 13:24]; ps1 <- 2 * pt(-abs((rowMeans(x) - rowMeans(y)) / sqrt((rowVars(x) + rowVars(y)) / ncol(x))), ncol(DataSample) - 2)},
  apply = { ps2 <- apply(DataSample, 1, function(x) t.test(x[1:12], x[13:24], var.equal = TRUE)$p.value)},
  rowttests = {ps3 <- rowttests(DataSample, factor(rep(1:2, each = 12)))[, "p.value"]})

Note the manual method assumes that the two groups are the same sizes.

回答4:

Adding an alternative using an external library.

Performing the test:

library(matrixTests)
res <- row_t_equalvar(DataSample[,1:12], DataSample[,13:24])

Format of the result:

res

   obs.x obs.y obs.tot      mean.x       mean.y    mean.diff     var.x     var.y var.pooled    stderr df    statistic     pvalue   conf.low   conf.high alternative mean.null conf.level
1     12    12      24  0.30569721  0.160622830  0.145074376 0.5034806 1.0769678  0.7902242 0.3629105 22  0.399752487 0.69319351 -0.6075559  0.89770469   two.sided         0       0.95
2     12    12      24 -0.27463354 -0.206396781 -0.068236762 0.8133311 0.2807800  0.5470556 0.3019535 22 -0.225984324 0.82329990 -0.6944500  0.55797651   two.sided         0       0.95
3     12    12      24 -0.19805092 -0.023207888 -0.174843032 0.4278359 0.5604078  0.4941219 0.2869733 22 -0.609265949 0.54858909 -0.7699891  0.42030307   two.sided         0       0.95

Number of rows with p <= 0.05:

> sum(res$pvalue <= 0.05)
[1] 4

来源：https://stackoverflow.com/questions/31596666/trying-to-perform-a-t-test-for-each-row-and-count-all-rows-where-p-value-is-less

标签

statistics

hypothesis-test