[R] T-test to check equality, unable to interpret the results.

[Rolf Turner]

On 17/09/2009, at 8:06 AM, Bert Gunter wrote:

	<snip>

> Furthermore, the null can be other than equality -- e.g. that the  
> mean  of
> the first population is less than the second.

	<snip>

QUIBBLE:  Some elementary texts will indeed state the null hypothesis as
``mu_1 <= mu_2'' when the alternative hypothesis is ``mu_1 > mu_2''.

However it seems to me more perspicuous to keep the null hypothesis as
``='' and allow only the alternative to change (i.e. to be one of ``! 
='',
``<'', or ``>'').

One calculates one's *test statistic* using the ``='' (which is the
``most extreme'' point of the null hypothesis, the point ``closest'' to
the alternative, i.e. the point least likely to lead one to reject  
the null.

Thus confusion amongst the young and naive is minimized if one  
insists that
the null hypothesis is always ``=''.

	cheers,

		Rolf Turner

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