HI R-users, I am trying to repeat an example from Rayner and Best "A contingency table approach to nonparametric testing (Chapter 7, Ice cream example). In their book they calculate Durbin's statistic, D1, a dispersion statistics, D2, and a residual. P-values for each statistic is calculated from a chi-square distribution and also Monte Carlo p-values. I have found similar p-values based on the chi-square distribution by using: > pchisq(12, df= 6, lower.tail=F) [1] 0.0619688 > pchisq(5.1, df= 6, lower.tail=F) [1] 0.5310529 Is there a way to calculate the equivalent Monte Carlo p-values? The values were 0.02 and 0.138 respectively. The use of the approximate chi-square probabilities for Durbin's test are considered not good enough according to Van der Laan (The American Statistician 1988,42,165-166). Peter -------------------------------- ESTG-IPVC
Hi, Peter: Please see my reply of a few minutes ago subject: exact goodness-of-fit test. I don't know Rayner and Best, but the same method, I think, should apply. spencer graves Peter Ho wrote:> HI R-users, > > I am trying to repeat an example from Rayner and Best "A contingency > table approach to nonparametric testing (Chapter 7, Ice cream example). > > In their book they calculate Durbin's statistic, D1, a dispersion > statistics, D2, and a residual. P-values for each statistic is > calculated from a chi-square distribution and also Monte Carlo p-values. > > I have found similar p-values based on the chi-square distribution by > using: > > > pchisq(12, df= 6, lower.tail=F) > [1] 0.0619688 > > pchisq(5.1, df= 6, lower.tail=F) > [1] 0.5310529 > > Is there a way to calculate the equivalent Monte Carlo p-values? > > The values were 0.02 and 0.138 respectively. > > The use of the approximate chi-square probabilities for Durbin's test > are considered not good enough according to Van der Laan (The American > Statistician 1988,42,165-166). > > > Peter > -------------------------------- > ESTG-IPVC > > ______________________________________________ > 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-- Spencer Graves, PhD Senior Development Engineer PDF Solutions, Inc. 333 West San Carlos Street Suite 700 San Jose, CA 95110, USA spencer.graves at pdf.com www.pdf.com <http://www.pdf.com> Tel: 408-938-4420 Fax: 408-280-7915
On Thu, 4 Aug 2005, Peter Ho wrote:> HI R-users, > > I am trying to repeat an example from Rayner and Best "A contingency > table approach to nonparametric testing (Chapter 7, Ice cream example). > > In their book they calculate Durbin's statistic, D1, a dispersion > statistics, D2, and a residual. P-values for each statistic is > calculated from a chi-square distribution and also Monte Carlo p-values.Hi Peter, when I understand the example correctly, the main interest is testing independence of the judges' ranking and the ice cream brand, where the judges are interpreted as `blocks' using a chi^2-type statistic based on the rank sums for each ice cream. In R: ice <- data.frame(judge = factor(rep(c(1:7),rep(3,7))), variety = factor(c(1,2,4,2,3,5,3,4,6,4,5,7,1,5,6,2,6,7,1,3,7)), rank = c(2,3,1,3,1,2,2,1,3,1,2,3,3,1,2,3,1,2,3,1,2)) library("coin") it <- independence_test(rank ~ variety | judge, data = ice, teststat = "quadtype") it Asymptotic General Independence Test data: rank by groups 1, 2, 3, 4, 5, 6, 7 stratified by judge T = 12, df = 6, p-value = 0.06197 So without having checked the theory exactly, this looks like being Dubin's D1 statistic with _asymptotic conditional p-value_ (please have a look at coin's vignette which explains what happens here). The Monte-Carlo p-value can now be computed by 99,999 replications: pvalue(independence_test(rank ~ variety | judge, data = ice, teststat = "quadtype", distribution = approximate(B = 99999))) [1] 0.01778018 99 percent confidence interval: 0.01672170 0.01888482 which seems to be a little bit smaller than 0.02. Hope that helps, Torsten> > I have found similar p-values based on the chi-square distribution by > using: > > > pchisq(12, df= 6, lower.tail=F) > [1] 0.0619688 > > pchisq(5.1, df= 6, lower.tail=F) > [1] 0.5310529 > > Is there a way to calculate the equivalent Monte Carlo p-values? > > The values were 0.02 and 0.138 respectively. > > The use of the approximate chi-square probabilities for Durbin's test > are considered not good enough according to Van der Laan (The American > Statistician 1988,42,165-166). > > > Peter > -------------------------------- > ESTG-IPVC > > ______________________________________________ > 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 > >