[R] Z-test

[Joshua Wiley]

On Sat, Jul 16, 2011 at 12:05 AM, Rolf Turner <rolf.turner at xtra.co.nz> wrote:
> (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.

Yes, it is an unbiased estimator of sigma^2 for a sample.  My response
was predicated on the assumption the OP was choosing a Z-test because
data on the entire population was available hence no need to use an
estimate.

>
> (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
> problem.

But if raw data from the entire population is all that is available,
then the "known" variances still need to be calculated though not
estimated.  var() does not do this directly which is why I offered an
alternative.

Josh

>
>    cheers,
>
>        Rolf