(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.
firstname.lastname@example.org 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? > > Many thanks in advance of anyone's reply. > > 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