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Topic: Question about use of 1-Sample Sign test
Replies: 1   Last Post: Apr 21, 2005 7:51 PM

 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Question about use of 1-Sample Sign test
Posted: Apr 21, 2005 7:51 PM

(nA - nB) +- 1
To test the hypothesis p(A) = p(B), use z = --------------,
sqrt(nA + nB)

where the +- is taken opposite to the sign of (nA - nB),
so as to reduce the magnitude of the numerator.

If nA + nB >= 10 and the hypothesis is true
then z will be approximately standard normal.
Large |z| allow the hypothesis to be rejected.

Splitting the "No Preference" count 50-50 between the As & Bs
will lower the power of the test.

edd@mredd.co.uk wrote:
> Hi,
>
> I have collected some data and am trying to find a method of

attaching
> a statistical significance to a hypothesis about the data. This is
the
> first time I have collected data for analysis and I think my data
> (questionnaire) design
> may have been flawed so I am now trying to salvage what I can from

the
> final data.
>
> The data:
> Consists of 50 responses indicating preference for the design of a
> website. Possible responses include:
>
> Prefer Website A (+1)
> Have No Preference (0)
> Prefer Website B (-1)
>
>
> What I'm trying to do:
>
> I "think" that by attaching numerical values (in brackets above) to
> each response I can perform a 1-Sample Sign test. What I want to do
> with this test is to test the hypothesis that the median of the data

is
> >0 (i.e. more people preferred Website A). I am doing this by testing
a
> null hypothesis that the median is equal to 0 with an alternate
hypothesis
> that the median is greater than 0. If that p value generated
> from this test is less than 0.05 I accept the alternate hypothesis,
> otherwise I must accept the null hypothesis.
>
> What I would like to know:
>
> I have got this far by reading various text books but I am still
> unclear about certain aspects, these are:
>
> Can I viably perform this test (i.e. is it ok to associate numbers

with
> each response? I think it is as it results in non-parametric data
which
> is what the 1-Sign sample test is designed for)
>
> Why is the accept / reject level for the null hypothesis set at 0.05?
> This is something I have come across in every example in books and on
> the internet but it has never been explained. Is it something to do
> with a 95% confidence interval?
>
> If this is not a suitable test to perform, does anyone have any
> suggestions of tests which might be suitable?
>
> Lastly, if this is a suitable test to be performing, does anyone have
> any references towards good books or websites that I can use to

further
> understand the test mechanism?
>
>
> Cheers,
>
> Edd
>
> Disclaimer. Last time I posted I was pretty much flamed for

attempting
> to perform statistics without having the required knowledge!! I am
> doing this out of necessity as it for my degree dissertation. I
> acknowledge there may be many
> things I am not doing correctly but I am a Software Engineer and not

a
> statistician, this is why I have posted this request for info. So
> please go easy on me!
>
> http://www.mredd.co.uk