Re: [Rd] [R] computing the variance

From: Martin Maechler <maechler_at_stat.math.ethz.ch>
Date: Mon 05 Dec 2005 - 18:10:08 GMT

{from R-help, diverted to R-devel}:

    UweL> Wang Tian Hua wrote:

    UweL> hi, when i was computing the variance of a simple
    UweL> vector, i found unexpect result. not sure whether it
    UweL> is a bug.

    UweL> Not a bug! ?var:

    UweL> "The denominator n - 1 is used which gives an unbiased
    UweL>  estimator of the (co)variance for
    UweL>  i.i.d. observations."


    UweL> > var(c(1,2,3))
    UweL> [1] 1  #which should be 2/3.
    UweL> > var(c(1,2,3,4,5))
    UweL> [1] 2.5 #which should be 10/5=2
    UweL> 

    UweL> it seems to me that the program uses (sample size -1) instead of sample     UweL> size at the denominator. how can i rectify this?

    UweL> Simply change it by:

    UweL> x <- c(1,2,3,4,5)
    UweL> n <- length(x)
    UweL> var(x)*(n-1)/n

    UweL> if you really want it.

It seems Insightful at some point in time have given in to this user request, and S-plus nowadays has an argument "unbiased = TRUE"
where the user can choose {to shoot (him/her)self in the leg and} require 'unbiased = FALSE'.
{and there's also 'SumSquraes = FALSE' which allows to not
 require any division (by N or N-1)}

Since in some ``schools of statistics'' people are really still taught to use a 1/N variance, we could envisage to provide such an argument to var() {and cov()} as well. Otherwise, people define their own variance function such as

      VAR <- function(x,....) .. N/(N-1)*var(x,...) Should we?

BTW: S+ even has the 'unbiased' argument for cor() where of course it really doesn't make any difference (!), and actually I think is rather misleading, since the sample correlation is not unbiased in almost all cases AFAICS.

Martin



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