Nonparametric tests are used to test hypotheses when the data at hand violate one or more of the assumptions for parametric tests procedures. The test is an ordered alternative (nondecreasing) when there is prior information about the data. It assumes that the underlying distributions are of the same type and therefore differ in location. For example, in dose-response studies, animals are assigned to k groups corresponding to k doses of an experimental drug. The effect of the drug on the animals is likely to increase or decrease with increasing doses. In this case, the ordered alternative is appropriate for the study. In this paper, we propose eight new nonparametric tests useful for testing against nondecreasing order alternatives for a mixed design involving randomized complete block and balanced incomplete block design. These tests involve various modifications of the Jonckheere-Terpstra test (Jonckheere(1952), Terpstra(1954)) and Alvo and Cabilio’s test (1995). Three, four and five treatments were considered with different location parameters under different scenarios. For three and four treatments, 6,12, and 18 blocks were used for the simulation, while 10, 20, and 30 blocks were used for five treatments. Different tests performed best under different block combinations, but overall the standardized last for Alvo outperformed the other test when the number of treatments and number of missing observations per block increases. A simulation study was conducted comparing the powers of the various modification of Jonckheere-Terpstra (Jonckheere(1952), Terpstra(1954)) and Alvo and Cabilio’s (1995) tests under different scenarios. Recommendations are made.

Ordered alternatives tests are sometimes used in life-testing experiments and drug-screening studies. An ordered alternative test is sometimes used to gain power if the researcher thinks parameters will be ordered in a certain way if they are different. This research proposal focuses on developing new nonparametric tests for the nondecreasing ordered alternative problem for k (k?3) populations when testing for differences in both location and scale. Six nonparametric tests are proposed for the nondecreasing ordered alternative when testing for a difference in either location or scale. The six tests are various combinations of a well-known ordered alternatives test for location and a test based on the Moses test technique for testing differences in scale. A simulation study is conducted to determine how well the proposed tests maintain their significance levels. Powers are estimated for the proposed tests under a variety of conditions for three, four and five populations. Several types of variable parameters are considered: when the location parameters are different and the scale parameters are equal; when the location parameters are equal and the scale parameters are different; when the location and scale parameters are both different. Equal and unequal samples sizes of 18 and 30 are considered. Subgroup sizes of 3 and 6 are both used when applying the Moses test technique. Recommendations are given for which test should be used for various situations.