R help - Nov 2006 - 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

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 op 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 op stat.math.ethz.ch
[mailto:r-help-bounces op stat.math.ethz.ch] Namens Robin Hankin
Verzonden: donderdag 23 november 2006 14:12
Aan: R-help op 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

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Robin Hankin <r.hankin at noc.soton.ac.uk> writes:
> 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?

You can't. Shouldn't be too much of a problem to modify t.test.default
to stop it complaining. (It's not quite enough to remove the check for
nx < 2, though. You also need to deal with var(x) being NA if x has
length one.)

Alternatively, just write up the formula for the t statistic:
> x <- c(23,25,29,27,30,30)
> (x[1]-mean(x[-1]))/sqrt(var(x[-1])*(1+1/(length(x)-1)))
[1] -2.189595
> 2*pt(-2.1896,4)
[1] 0.09373392


-- 
   O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907