[R] t.test()

[Robin Hankin]

Hello everybody


thanks for your advice here.

I think I'm getting tangled up.

If I use Thierry's test on iid Gaussian data,
the returned p-value should be uniform(0,1),
right?

OK,


R> f <- function(x){t.test(x=x[-1],mu=x[1])$p.value}
R> hist(replicate(1000,f(rnorm(5))))


This is very skewed towards zero.  Why isn't the
histogram showing a uniform distribution?







On 23 Nov 2006, at 13:32, ONKELINX, Thierry wrote:

> There is no such thing as an unpaired t-test. A t-test can be a  
> paired,
> one sample or two sample t-test. Since you want to compare the sample
> against a given mean, you need a one sample t-test. You tried to do a
> two sample test. That didn't work because you need at least two
> observations in each group.
>
> x <- c(23,25,29,27,30,30)
> t.test(x[-1], mu = x[1])
>
>         One Sample t-test
>
> data:  x[-1]
> t = 5.3634, df = 4, p-value = 0.005833
> alternative hypothesis: true mean is not equal to 23
> 95 percent confidence interval:
>  25.50814 30.89186
> sample estimates:
> mean of x
>      28.2
>
>
> Cheers,
>
> Thierry
>
> ---------------------------------------------------------------------- 
> --
> ----
>
> ir. Thierry Onkelinx
>
> Instituut voor natuur- en bosonderzoek / Reseach Institute for Nature
> and Forest
>
> Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
> methodology and quality assurance
>
> Gaverstraat 4
>
> 9500 Geraardsbergen
>
> Belgium
>
> tel. + 32 54/436 185
>
> Thierry.Onkelinx at inbo.be
>
> www.inbo.be
>
>
>
> Do not put your faith in what statistics say until you have carefully
> considered what they do not say.  ~William W. Watt
>
> A statistical analysis, properly conducted, is a delicate  
> dissection of
> uncertainties, a surgery of suppositions. ~M.J.Moroney
>
> -----Oorspronkelijk bericht-----
> Van: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] Namens Robin Hankin
> Verzonden: donderdag 23 november 2006 14:12
> Aan: R-help at r-project.org
> Onderwerp: [R] t.test()
>
> Hi
>
> I have a vector x of length n.   I am interested in x[1]
> being different from the other observations (ie x[-1]).
>
> My null hypothesis  is that x[1]
> is drawn from a Gaussian distribution of the same
> mean as observations x[-1], which are assumed
> to be iid Gaussian.   The (unknown) variance
> of x[1] is assumed to be the same as the
> variance of x[-1].
>
>
> This should be an unpaired t-test.
>
> But
>
>
>> x <- c(23,25,29,27,30,30)
>> t.test(x=x[1] , y=x[-1])
> Error in t.test.default(x = x[1], y = x[-1]) :
>          not enough 'x' observations
>>
>
>
>
> What arguments do I need to send to t.test() to test my null?
>
>
>
>
>
>
>
> --
> Robin Hankin
> Uncertainty Analyst
> National Oceanography Centre, Southampton
> European Way, Southampton SO14 3ZH, UK
>   tel  023-8059-7743
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743