A Two-Sample Adaptive Distribution-Free Test

Hormesis: Biphasic Dose-Responses to Fungicides in Plant Pathogens and Their Potential Threat to Agriculture

“…Buning and Kossler (88) demonstrated that the Mack and Wolfe (87) test with Mann-Whitney counts is appropriate for testing data with symmetric and medium-up to long tailed distributions but they suggested the use of different two-sample statistics, i.e. Hogg et al (89) and Gastwirth (90), for asymmetric and short-tailed distributions respectively.…”

Adaptive Nonparametric Procedures and Applications

“…We now describe the two adaptive schemes. The first resembles that of Hogg et al (1975), while the second is a variation of the first.…”

“…As Q2 is unaffected by the actual value of A, it outperforms Q2 in detecting the tail weight. An indicator of skewness, studied by Fisher and explained in Hogg et al (1975), iS Q = (U0.05 -.5)(M0. 5-LO.5) Mo.5 being the average of the middle 50 the order statistics of the combined sample.…”

“…(a) For hypothesis testing in the two-sample location model, the work of Hogg et al (1975) has shown the supremacy of adaptive procedures over (i) the usual nonparametric procedure of working only with ranks and the resulting statistics such as Wilcoxon and (ii) the parametric normal theory procedure. (b) In addition, the results of Puri (1964Puri ( , 1965, Puri and Sen (1971) and Hajek and Sidak (1967) ensure that these good properties of the adaptive procedures extend to multiple comparisons and testing for ordered alternatives in the one-way ANOVA model.…”

Some Test Procedures and Their Performance Under Umbrella Alternatives

“…Buning and Kossler(1997) generalized the MW-test by replacing the Mann-Whitney statistic in the formula for MW by other two-sample statistics, e.g. by those of Gastwirth(1965) and Hogg et. al.(1975).…”