Re: st: Bootstrap sampling for evaluating hypothesis tests

[Margaret MacDougall <Margaret.MacDougall@ed.ac.uk>]

Hello

I refer to the recommendation from Maarten below, which was sent in 
response to a query I raised about testing the robustness of a new 
hypothesis test to Type I errors.

I have a very large sample to work from and I am expecting the null 
hypothesis (involving a comparison of two correlation coefficients) to 
be refuted for these data. My question is as follows: are there 
recommended approaches, other than crude trial and error, to adapting 
experimental data which naturally refute a null hypothesis so that the 
null hypothesis is satisfied? In this particular case, there are three 
variables to consider and therefore the data for each would need to be 
modified so that one correlation coefficient was equal to the other.  I 
have a gut feeling that there are possibly bog-standard versus 
statistically sound approaches to fixing the data to meet the null 
hypothesis and would welcome some advice.

Many thanks

Best wishes

Margaret

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr Margaret MacDougall
Medical Statistician and Researcher in Education
Centre for Population Health Sciences
University of Edinburgh Medical School
Teviot Place
Edinburgh EH8 9AG

Tel:  +44 (0) 131 650 3211
Fax:  +44 (0) 131 650 6909
E-mail: Margaret.MacDougall@ed.ac.uk
http://www.chs.med.ed.ac.uk/cphs/people/staffProfile.php?profile=mmacdoug

On 13/03/2013 15:45, Maarten Buis wrote:
> On Wed, Mar 13, 2013 at 4:04 PM, Margaret MacDougall wrote:
> > I would value receiving recommendations on literature explaining the
> > application of bootstrap sampling to assess robustness to Type I errors of a
> > proposed new hypothesis test. Better still, if the recommended references
> > contain corresponding computer syntax!
>
> Rich Williams and I are currently working on such a project. In
> general I would not say that a test is "robust" against Type I errors
> but that the Type I error rate corresponds to your prespecified level
> of significance. Type I errors will occur, but the chance of it
> occuring should be the same as the level of significance you have
> chosen. This means that if we change the data such that the null
> hypothesis is true and bootstrap from that changed dataset the
> p-values should follow a uniform distribution. This changing the data
> is inevitable when assessing the Type I error rate: in order to assess
> the probability of rejecting a true null hypothesis you first need to
> make sure that the null hypothesis is true.
>
> Here are two examples of how to do this in Stata:
>
> *------------------ begin example ------------------
> clear all
> sysuse auto
> recode rep78 1/2=3
> logit foreign price
> predict double pr
> gen byte ysim = .
> keep foreign price rep78 pr ysim
> keep if !missing(foreign,price,rep78)
> program define sim
> 	replace ysim = runiform()<  pr
> 	logit ysim  price ib3.rep78
> 	test 4.rep78 = 5.rep78 = 0
> end
> simulate chi2=r(chi2) p=r(p), reps(1000) : sim
> simpplot p
> qchi chi2, df(2) name(q)
> *------------------- end example -------------------
> (For more on examples I sent to the Statalist see:
> http://www.maartenbuis.nl/example_faq )
>
> *------------------ begin example ------------------
> clear all
> sysuse auto
> gen lnprice = ln(price)
> reg turn mpg i.rep78 foreign
> predict double mu1
>
> reg turn mpg i.rep78 foreign weight lnprice
> predict double mu2
> gen double ysim = turn - mu2 + mu1
>
> keep ysim mpg rep78 foreign weight lnprice
> keep if !missing(ysim, lnprice, mpg, rep78, foreign, weight)
> tempfile temp
> save `temp'
>
>   program define qenv_sim_F
>      use `1', clear
>      bsample
>      reg ysim mpg i.rep78 foreign weight lnprice
>      test weight lnprice
> end
>
> simulate F=r(F) p=r(p), reps(1000): qenv_sim_F `temp'
>
> simpplot p
> *------------------- end example -------------------
> (For more on examples I sent to the Statalist see:
> http://www.maartenbuis.nl/example_faq )
>
> Hope this helps,
> Maarten
>
> ---------------------------------
> Maarten L. Buis
> WZB
> Reichpietschufer 50
> 10785 Berlin
> Germany
>
> http://www.maartenbuis.nl
> ---------------------------------
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