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Alternative hypotheses for order restrictions, such as umbrella or inverse umbrella (a.k.a tree) orderings, have been studied extensively in the literature, although less so when the studied response for each individual is the presence or absence of the event of interest. Two families of test statistics for solving the problem of testing against an umbrella or a tree ordering when the responses are binomial proportions are studied in this work and their asymptotic distributions are derived. A simulation study is conducted to compare the empirical power of some members of the derived families of test statistics with competing approaches. The methodology developed here was driven by an applied problem arising in stored products research where despite universal mortality in the case of doses of 1000 ppm of the insecticide phosphine, unexpected survival was noted at higher doses.

A series of experiments were carried out between 2007 and 2009 to test the efficacy of selected insecticides against several stored-product psocids. Three series of experiments were conducted against Liposcelis spp. (Psocoptera: Liposcelididae) and Lepinotus reticulatus (Psocoptera: Trogiidae). In the first series of tests, contact insecticides were evaluated in the laboratory as grain protectants. Among these insecticides, diatomaceous earth (DE), natural pyrethrum, and the insect growth regulator methoprene were unable to control psocid populations on wheat, rice, and maize. For the same commodities, spinosad was effective against L. reticulatus, but was effective for Liposcelis entomophila only on maize; spinosad was not effective against Liposcelis bostrychophila and Liposcelis paeta. Chlorpyriphos-methyl + deltamethin and pirimiphos-methyl were very effective for all species tested. In the second series of tests, sulfuryl fluoride (SF) was tested against L. paeta eggs, nymphs, and adults, and Liposcelis decolor eggs and adults. Nymphs and adults were very susceptible; for most species mortality was 100%, after 48 h of exposure to SF doses ranging between 4 and 8 g of SF/m³. In contrast, eggs were less susceptible to SF, and 100% mortality after 48 h of exposure was recorded only at doses ranging between 24 and 96 g of SF/m³. In the third series of experiments, several contact insecticides were evaluated as surface treatments on concrete. In these tests, pyriproxifen and esfenvalerate provided poor control of psocids. The results of the above tests indicate that Liposcelis spp. and L. reticulatus were generally less susceptible than other major stored-product insect species to several insecticides, and susceptibility level is determined by the target species, the insecticide, and the commodity.

DEBBM, an enhanced diatomaceous earth (DE) formulation consisting of a mixture of DE and the plant extract bitterbarkomycin, was applied to seven different grains (wheat, barley, oats, rye, triticale, paddy rice and maize) at two dose rates 50 ppm and 150 ppm. Unsexed, 7d old adults of Sitophilus oryzae (Coleoptera: Curculionidae) and Tribolium confusum (Coleoptera: Tenebrionidae) were exposed to the DEBBM treated commodities and their mortality was assessed after 7d and 14d of exposure at 25°C and 65% r.h. Furthermore, progeny production of the tested species per treated commodity was also assessed. Sitophilus oryzae appeared to be more susceptible than T. confusum to DEBBM. Performance of DEBBM was better in barley, wheat and oats compared to the remainder of the tested commodities. DEBBM performed better in rye and triticale than in paddy rice against both species although in many cases, significant differences among these grains were not recorded. Despite that DEBBM reached its highest efficacy levels on barley, wheat, and oats it did not suppress progeny production of the treated species in any of the grains. A significant reduction in progeny production of the treated species was recorded in the DEBBM treated grains in comparison with the untreated ones. This reduction in progeny production was expressed more vigorously to S. oryzae rather than T. confusum. In commodities with high DEBBM performance such as barley, oats or wheat, > 9-fold less progeny of S. oryzae were recorded at 150 ppm of DEBBM than in the untreated commodities. Although significantly less progeny of T. confusum were recorded in DEBBM treated grains than untreated grains, progeny suppression of this species was neither dose nor commodity dependant.

The combined use of spinosad with deltamethrin against adults of Sitophilus oryzae, Sitophilus granarius and Tribolium confusum was evaluated in a series of laboratory bioassays in two hard wheat varieties (Athos and Sifnos). Two groups of bioassays were carried out. In the first group of bioassays, spinosad or deltamethrin were applied alone at the tested wheat varieties at the doses of 0.01, 0.1 and 0.5 ppm for spinosad and 0.125 ppm for deltamethrin. In the second group of bioassays, the tested wheat varieties were treated with the combination of the above spinosad rates with 0.125 of deltamethrin. In both series of bioassays, mortality of the tested species was evaluated after 7 d of exposure on the treated wheat varieties at 25°C and 65% r.h. Mortality for all species was always significantly higher in Athos than Sifnos. The highest mortality of S. oryzae (73 and 40% for Athos and Sifnos respectively) or S. granarius (88% and 58% for Athos and Sifnos respectively) was recorded in the cases that spinosad was applied alone at 0.5 ppm. On the contrary, in the case of T. confusum, 0.125 ppm of deltamethrin was significantly more effective than any of the application rates of spinosad either when applied alone or in combination with deltamethrin. Despite the fact that the highest mortality of S. granarius adults was recorded after exposure on the wheat varieties treated with 0.1 ppm of spinosad x 0.125 ppm of deltamethrin, in light of the results of the present study, the combination of spinosad with deltmethrin requires further investigation since in most of the tested cases of the present study, single application of spinosad or deltamethrin was more effective or of equal effectiveness than the respective combination of spinosad with deltamethrin.