 • May 2009: Observed Confidence Levels reviewed in Technometrics (May 2009, Vol. 51, No. 2, pages 215-225).

• May 9, 2008: While working on some data analysis I found a new (for me anyway) way of returning orderings from an R function. This method uses the rank command. This method shortens the functions that check for every ordering of a mean vector, and makes these functions easier to write. For example, the R function:

perc.fun.all <- function(data,i) {
m <- apply(data[i,],2,mean)
if((m<=m)&&(m<=m)&&(m<=m)) return(1)
if((m<=m)&&(m<=m)&&(m<=m)) return(2)
if((m<=m)&&(m<=m)&&(m<=m)) return(3)
if((m<=m)&&(m<=m)&&(m<=m)) return(4)
if((m<=m)&&(m<=m)&&(m<=m)) return(5)
if((m<=m)&&(m<=m)&&(m<=m)) return(6)
if((m<=m)&&(m<=m)&&(m<=m)) return(7)
if((m<=m)&&(m<=m)&&(m<=m)) return(8)
if((m<=m)&&(m<=m)&&(m<=m)) return(9)
if((m<=m)&&(m<=m)&&(m<=m)) return(10)
if((m<=m)&&(m<=m)&&(m<=m)) return(11)
if((m<=m)&&(m<=m)&&(m<=m)) return(12)
if((m<=m)&&(m<=m)&&(m<=m)) return(13)
if((m<=m)&&(m<=m)&&(m<=m)) return(14)
if((m<=m)&&(m<=m)&&(m<=m)) return(15)
if((m<=m)&&(m<=m)&&(m<=m)) return(16)
if((m<=m)&&(m<=m)&&(m<=m)) return(17)
if((m<=m)&&(m<=m)&&(m<=m)) return(18)
if((m<=m)&&(m<=m)&&(m<=m)) return(19)
if((m<=m)&&(m<=m)&&(m<=m)) return(20)
if((m<=m)&&(m<=m)&&(m<=m)) return(21)
if((m<=m)&&(m<=m)&&(m<=m)) return(22)
if((m<=m)&&(m<=m)&&(m<=m)) return(23)
if((m<=m)&&(m<=m)&&(m<=m)) return(24) }

can be replaced by

perc.fun.all <- function(data,i) {
m <- apply(data[i,],2,mean)
b <- c(1000,100,10,1)
return(t(b)%*%rank(m)) }

The returned value then reflects the ranks of the elements of the mean vector.

• May 9, 2008: Observed Confidence Levels at the Joint Statistical Meetings in Denver Colorado:
 Activity Number: 369 Type: Contributed Date/Time: Wednesday, August 6, 2008 : 8:30 AM to 10:20 AM Sponsor: Section on Nonparametric Statistics Title: Ordered Inference Using Observed Confidence Levels Author(s): Alan M. Polansky*+ Companies: Northern Illinois University Address: Division of Statistics, De Kalb, IL, 60115, Keywords: Bootstrap ; Edgeworth Expansion ; Normal Model ; Restricted Inference ; Multiple Comparisons ; Error Rate Abstract: Statistical inference on the ordering of the elements of a mean vector is an important issue in many applied problems. Many statistical tests of hypotheses to detect these orderings have been developed both within the normal model, and outside the normal model using nonparametric methods. Estimates as well as confidence regions have also been developed for the mean vector under constraints imposed by these ordering models. In order to attempt to distinguish between ordered models, multiple testing procedures are often used to control the overall error rate of the sequence of tests. This paper shows how observed confidence levels allow for the exploration of very general models for the ordering of the elements of a mean vector without the need for specialized asymptotic theory or multiple testing methods. The methods are applied to several well-known examples.        