[R] statistics - hypothesis testing question

[Greg Snow]

Is the data paired?  i.e. do you have an A and a B from week 1, then the
same for each following week?

If so, then you could probably do a simple sign test, within each week
see if rsquared B > rsquared A. under the null hypothesis that A and B
are equivalent this should be a binomial with parameter = 0.5.  If you
want something a little  fancier then you could do some type of
permutation test (which the sign test is a special case of).

Hope this helps,

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at intermountainmail.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 Leeds, Mark (IED)
> Sent: Thursday, September 13, 2007 12:18 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] statistics - hypothesis testing question
> 
> I estimate two competing simple regression models, A and B 
> where the LHS is the same in both cases but the predictor is 
> different ( I handle the intercept issue based on other 
> postings I have seen ). I estimate the two models on a weekly 
> basis over 24 weeks. 
> So, I end up with 24 RSquaredAs and 24 RsquaredBs, so 
> essentally 2 time series of Rsquareds. This doesn't have to 
> be necessarily thought of as a time series problem but, is 
> there a usual way, given the Rsquared data, to test 
> 
> H0 : Rsquared B = Rsquared A versus H1 : Rsquared B > Rsquared A 
> 
> so that I can map the 24 R squared numbers into 1 statistic. 
> Maybe that's somehow equivalent to just running 2 big 
> regressions over the whole 24 weeks and then calculating a 
> statistic from those based on those regressions ?
> 
> I broke things up into 24 weeks because I was thinking that 
> the stability of the performance difference of the two models 
> could be examined over time. Essentially these are simple 
> time series regressions X_t = B*X_t-1 + epsilon so I always 
> need to consider whether any type of behavior is stable.  But 
> now I am thinking that,  if I just want one overall number,  
> then maybe I should be considering all the data simultaneously ? 
> 
> In a nutshell,  I am looking for any suggestions on the best 
> way to test whether Model B is better than Model A where
> 
> Model A :  X_t = Beta*X_t-1 + epsilon
> 
> Model B :  X_t = Betastar*Xstar_t-1 + epsilonstar
> 
> 
> Thanks fo your help.
> --------------------------------------------------------
> 
> This is not an offer (or solicitation of an offer) to 
> buy/se...{{dropped}}
> 
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