A new test for stochastic order of k[greater-or-equal, slanted]3 ordered multinomial populations

A new one-sided test for stochastic order of k[greater-or-equal, slanted]3 ordered multinomial populations is offered. The test has desirable monotonicity properties in the sense that it is monotone in practical directions and admissible directions. A practical direction is one for which stochastic order is more readily convincing. An admissible direction is a requirement for a test to be admissible. The test is based on a directed chi-square statistic. In addition to the monotonicity properties the test is exact (nonasymptotic), readily calculated (a program is offered), and has favorable power properties when compared with competitors. The test can also be used when some data are censored.