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

[Greg Snow]

Rolf, 

	I no longer claim to be young, the naïve part is still up for debate, but I find that restricting the null to only include = to be more confusing than to have it include the inequality.  To have the alternative be > and the null be = implies that we are working on the assumption that < is impossible, a stronger assumption than = of the null hypothesis.

I prefer to have all three possibilities explicitly stated between the 2 hypotheses to cover all possibilities.  An analogy that can be used to explain why we do the computation using the = value instead of any or all of the < values in the <= null is:  If you wanted to prove that you are smarter/stronger/richer/etc. than a group of people, then all you would need to do is prove that you are smarter/stronger/richer/etc. than the smartest/strongest/richest/etc.est of the group, not every individual.  Using the equality value of the null does the same, if you can find evidence against that, then you have found evidence against all other possible values (within the null) as well.

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Rolf Turner
> Sent: Wednesday, September 16, 2009 2:31 PM
> To: Bert Gunter
> Cc: 'r-help'
> Subject: Re: [R] T-test to check equality, unable to interpret the
> results.
> 
> 
> 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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