[R] Z-test

Rolf Turner rolf.turner at xtra.co.nz
Sat Jul 16 09:05:52 CEST 2011

On 16/07/11 17:49, Joshua Wiley wrote:
> Hi,
> The Z is basically:
> (mean(x) - mean(y))/sqrt(var(x)/length(x) + var(y)/length(y))
> and pnorm will give you a p-value, if you desire it.
> If the n - 1 divisior used in var() is a problem for you, it is
> trivial to work around:

(1) Why on earth should the n - 1 divisor be a problem?  This divisor
yields an unbiased estimator of sigma^2.  Generally speaking,
unbiasedness is a Good Thing.

(2) If a Z-test (rather than a t-test) is being done then this issue simply
does not arise.   In the context of a Z-test, the variances are ***known***
quantities and so do not get estimated.  So there is no divisor to *be* a



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