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Hi I would a appreciate the help of anyone who can offer some help with "The Method of Normal Scores", a methodology for the multiple comparison of means originally illustrated by Dr J. A. Nelder in the paper "The Present State of Multiple Comparison Methods", R. O' Neill, G. B. Wetherill (1971) (pp.244-245). This method can be outlined as follows: Suppose we want to compare k means from k normally distributed rvs. We plot the ordered mean scores x(i) against the expected valued of the ordered statistics in a sample of the same size n from a standard normal distribution (i.e. the normal score). The null hypothesis (under H0) is that the code means are sampled from a normal distribution with mean mu and variance sigma^2 . If this hypothesis is true the expected value for the code means are given by : E[x(i)] =mu + sigma/sqrt(n) *r(i) So if a line of slope sigma/sqrt(n) is drawn through the means, the points on the plot x(i) against r(i) should lie roughly along this line. If they don't and there is a discontinuity in the plot, it may be argued that the code means divide into more than one group. More precisely Nelder used, q(i) =(x(i) - x(i-1)) / (r(i)-r(i-1)) to divide the means into more than one group. My main question is what the are the properties of the q(i) statistic , in particular its distribution and any other properties would be useful . It would also be useful to know any other ways to group means using this methodology or others, but I guess the difficulty is in working out the theoretical misclassification rate for more than one mean. Thanks in advance Siva