R help - Apr 2005 - Stats Question: Single data item versus Sample from Norma l Distribution

Here's one possibility, assuming muhat and sigmahat are estimtes of mu and
sigma from N iid draws of N(mu, sigma^2):

tStat <- abs(x - muhat) / sigmahat
pValue <- pt(tStat, df=N, lower=TRUE)

I'm not quite sure what df tStat should have (exercise for math stat), but
given fairly large N, that should make little difference.

Andy
> From: Ross Clement
> 
> Hi. I have a question that I have asked in other stat forums 
> but do not
> yet have an answer for. I would like to know if there is some way in R
> or otherwise of performing the following hypothesis test.
> 
> I have a single data item x. The null hypothesis is that x 
> was selected
> from a normal distribution N(mu,sigma). The alternate 
> hypothesis is that
> x does not come from this distribution.
> 
> However, I do not know the values of mu and sigma. I have a sample of
> size N from which I can estimate mu and sigma. So, say that I have
> N(m,s,N), and x. I would like to say with some certainty 
> (e.g. 95%) that
> I can, or can't reject the hypothesis that x came from N(mu,sigma). I
> would also like a power test to say how large N should be given the
> degree of accuracy I need when accepting or rejecting individual x
> values.
> 
> What is the name of the hypothesis test I need for this? Is it built
> into R, or are there packages I could use?
> 
> Thanks in anticipation,
> 
> Ross Clement.
> 
> ______________________________________________
> 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
> 
> 
>

> From: Liaw, Andy 
> 
> Here's one possibility, assuming muhat and sigmahat are 
> estimtes of mu and sigma from N iid draws of N(mu, sigma^2):
> 
> tStat <- abs(x - muhat) / sigmahat
> pValue <- pt(tStat, df=N, lower=TRUE)
Oops...  That should be:

pValue <- pt(tStat, df=N, lower=TRUE) / 2

Andy
> 
> I'm not quite sure what df tStat should have (exercise for 
> math stat), but given fairly large N, that should make little 
> difference.
> 
> Andy
> 
> > From: Ross Clement
> > 
> > Hi. I have a question that I have asked in other stat forums 
> > but do not
> > yet have an answer for. I would like to know if there is 
> some way in R
> > or otherwise of performing the following hypothesis test.
> > 
> > I have a single data item x. The null hypothesis is that x 
> > was selected
> > from a normal distribution N(mu,sigma). The alternate 
> > hypothesis is that
> > x does not come from this distribution.
> > 
> > However, I do not know the values of mu and sigma. I have a 
> sample of
> > size N from which I can estimate mu and sigma. So, say that I have
> > N(m,s,N), and x. I would like to say with some certainty 
> > (e.g. 95%) that
> > I can, or can't reject the hypothesis that x came from 
> N(mu,sigma). I
> > would also like a power test to say how large N should be given the
> > degree of accuracy I need when accepting or rejecting individual x
> > values.
> > 
> > What is the name of the hypothesis test I need for this? Is it built
> > into R, or are there packages I could use?
> > 
> > Thanks in anticipation,
> > 
> > Ross Clement.
> > 
> > ______________________________________________
> > 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
> > 
> > 
> > 
>

> From: Liaw, Andy 
> 
> > From: Liaw, Andy 
> > 
> > Here's one possibility, assuming muhat and sigmahat are 
> > estimtes of mu and sigma from N iid draws of N(mu, sigma^2):
> > 
> > tStat <- abs(x - muhat) / sigmahat
> > pValue <- pt(tStat, df=N, lower=TRUE)
> 
> Oops...  That should be:
> 
> pValue <- pt(tStat, df=N, lower=TRUE) / 2
I'm going mad!  That should be:

pValue <- pt(tStat, df=N, lower=FALSE) / 2

Sorry for wasting bw...

Andy
> Andy
> 
> > 
> > I'm not quite sure what df tStat should have (exercise for 
> > math stat), but given fairly large N, that should make little 
> > difference.
> > 
> > Andy
> > 
> > > From: Ross Clement
> > > 
> > > Hi. I have a question that I have asked in other stat forums 
> > > but do not
> > > yet have an answer for. I would like to know if there is 
> > some way in R
> > > or otherwise of performing the following hypothesis test.
> > > 
> > > I have a single data item x. The null hypothesis is that x 
> > > was selected
> > > from a normal distribution N(mu,sigma). The alternate 
> > > hypothesis is that
> > > x does not come from this distribution.
> > > 
> > > However, I do not know the values of mu and sigma. I have a 
> > sample of
> > > size N from which I can estimate mu and sigma. So, say that I
have
> > > N(m,s,N), and x. I would like to say with some certainty 
> > > (e.g. 95%) that
> > > I can, or can't reject the hypothesis that x came from 
> > N(mu,sigma). I
> > > would also like a power test to say how large N should be 
> given the
> > > degree of accuracy I need when accepting or rejecting individual
x
> > > values.
> > > 
> > > What is the name of the hypothesis test I need for this? 
> Is it built
> > > into R, or are there packages I could use?
> > > 
> > > Thanks in anticipation,
> > > 
> > > Ross Clement.
> > > 
> > > ______________________________________________
> > > 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
> > > 
> > > 
> > > 
> > 
>