Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 202P(X (j) ≤M≤X (n+1−j) )≥1−α. In terms of T, this becomes the largest j so that P(j≤T≤n−j)>1−α,which in turn becomes a search for the largest j with P(T n = length(x)> pbinom(0:n,n,1/2) # P(T sort(x)[c(j,n+1−j)][1] 4.3 540.07.6.2 Confidence intervals based on signed-rank statisticThe Wilcoxon signed-rank statistic allows for an improvement on the confidence intervalgiven by counting the number of data points above the median. Its usage is valid whenthe X i are assumed to be symmetric about their median. If this is so, then a data point isequally likely to be on the left or right of the median, and the distance from the median isindependent of what side of the median the data point is on. If we know the median thenwe can rank the data by distance to the median. Add up the ranks for the values where the