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poisson mean hypothesis

5 messages · Jan Wijffels, Dimitris Rizopoulos, Thomas Lumley +1 more

Original
Dimitris Rizopoulos
# 
you could use something like the following (in case of two-group 
comparisons make the proper adjustements):

pois.test <- function(x, alternative = c("two.sided", "less", 
"greater"), mu){
    alternative <- match.arg(alternative)
    if (missing(mu) || (length(mu) != 1 || is.na(mu)))
        stop("'mu' must be a single number")
    nx <- length(x)
    mu.x <- mean(x)
    stat <- (mu.x - mu) / sqrt(mu.x/nx)
    p.value <- switch(alternative,
        "two.sided" = 2 * pnorm(-abs(stat)),
        "less" = pnorm(stat),
        "greater" = pnorm(stat, lower = FALSE))
    list("sample mean" = mu.x, "null mean" = mu, "alternative" = 
alternative,
            statistic = stat, p.value = p.value)
}
################

y <- rpois(50, 5)
pois.test(y, alt = "g", mu = 4)

y <- rpois(30, 15)
pois.test(y, alt = "l", mu = 16)


I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Jan Wijffels" <Jan.Wijffels at ucs.kuleuven.be>
To: <r-help at stat.math.ethz.ch>
Sent: Monday, September 12, 2005 10:01 AM
Subject: [R] poisson mean hypothesis
Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
Jan Wijffels
# 
Dimitris,
Thanks for the test. But you are using a normal approximation to the
poisson distribution. This is not applicable in my case. I was more
looking for an exact test. Probably based on Garwood's (1936) confidence
interval. If there is already an R implementation available, than this
would be helpful for me.

Jan

-----Original Message-----
From: Dimitris Rizopoulos [mailto:dimitris.rizopoulos at med.kuleuven.be] 
Sent: maandag 12 september 2005 11:33
To: Jan Wijffels
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] poisson mean hypothesis

you could use something like the following (in case of two-group 
comparisons make the proper adjustements):

pois.test <- function(x, alternative = c("two.sided", "less", 
"greater"), mu){
    alternative <- match.arg(alternative)
    if (missing(mu) || (length(mu) != 1 || is.na(mu)))
        stop("'mu' must be a single number")
    nx <- length(x)
    mu.x <- mean(x)
    stat <- (mu.x - mu) / sqrt(mu.x/nx)
    p.value <- switch(alternative,
        "two.sided" = 2 * pnorm(-abs(stat)),
        "less" = pnorm(stat),
        "greater" = pnorm(stat, lower = FALSE))
    list("sample mean" = mu.x, "null mean" = mu, "alternative" = 
alternative,
            statistic = stat, p.value = p.value)
}
################

y <- rpois(50, 5)
pois.test(y, alt = "g", mu = 4)

y <- rpois(30, 15)
pois.test(y, alt = "l", mu = 16)


I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Jan Wijffels" <Jan.Wijffels at ucs.kuleuven.be>
To: <r-help at stat.math.ethz.ch>
Sent: Monday, September 12, 2005 10:01 AM
Subject: [R] poisson mean hypothesis
Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm



Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
Thomas Lumley
# 
Use ppois(x,lambda), which gives P(X<=x) for mean=lambda.

Eg: lower one-sided test for observing no events with mean of 3.4
[1] 0.03337327

upper one-sided test for observing 8 events with a mean of 3.4 (need the 
-1 to include 8 in the rejection region)
[1] 0.02307394

If you want an exact confidence interval there is a formula involving the 
quantiles of the gamma distribution (ie the qgamma() function) that I 
can't remember off hand. It might even be Garwood's formula.


 	-thomas
On Mon, 12 Sep 2005, Jan Wijffels wrote:

            

      
      
      
    

        

      
      
    

            
        

      
      
    

        
Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

  
  


  


      

    

    

      
      

        


  

        

      Peter Dalgaard
    

    

      
      #
    

  


  

      
Thomas Lumley <tlumley at u.washington.edu> writes:

            

      
      
      
    

        
Or you can clone the procedure in binom.test. In fact, using
binom.test with a sufficiently large n is a rather decent "cheat":

            

      
      
      
    

        
[1]  1.623488 11.668293
attr(,"conf.level")
[1] 0.95

            

      
      
      
    

        
[1] 0.975

            

      
      
      
    

        
[1] 0.02500060

The qgamma-based interval would seem to be from

            

      
      
      
    

        
[1] 1.623486

to

            

      
      
      
    

        
[1] 11.66833


Notice that this is obtained as the intersection of the two one-sided
intervals, each at half the nominal alpha level. There are other
possible definitions (e.g. invert the two sided test), but this one
has the advantage of being computable.