# [R] t-test via matrix operations

ripley@stats.ox.ac.uk ripley at stats.ox.ac.uk
Wed Aug 14 18:21:27 CEST 2002

```On Wed, 14 Aug 2002, Kort, Eric wrote:

> I need to calculate a large number of t statistics, and would like to do so via matrix operations.  So far I have figured out a way to calculate the mean of each row of the matrix:
>
> d <- matrix(runif(100000,1,10), 1000, 10) # some test data
> s <- rep(1,ncol(d)) # a sum vector to use for matrix multiplication
> means <- (d%*%s)/ncol(d)
>
> This is at least 1 order of magnitude faster than iterating through the
rows and using the mean function (<1/100th seconds vs. 13/100th seconds
on my computer).
>
> Two questions:
> 1) Do you see a way to further optimize/simplify/elegantize this
calculation of the row means?

function rowMeans

> 2) How do I proceed to calculate the row variances with matrix
operations (specifically, how can I use matrix operations to subtract each
element of each row from the corresponding row mean)?

sweep does the subtraction, but I would make use of rowmeans(d^2) and
rowmeans(d) in the classic hand-calculation formula.

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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```