1986 Volume 13 Issue 19 Pages 1-15
Recently several graphs for analysis of ranked observation have been proposed. Among them there exists rank graph proposed by Baba et al.. In this paper a graphical rank test method by using the rank graph is proposed and some merits of the rank graph are mainly discussed.
Suppose that k items are ordered by n judges. The rank graph was proposed originally as a descriptive one in which the average rank and the degree of concordance of ranks assigned to each item are represented by the vector called item vector. It is shown that under the assumption of random rankings, the distribution of the final point of an item vector can be asymtotically approximated by a 2-dimensional normal distribution. This is applied to graphical test of null hypothesis that ranks are given at random to each item. It is shown that in the case of large sample, the null hypothesis for each item can be tested visually by the rank graph with a critical ellipse without the bother of using a table.