Incomplete Factorial Design Research Articles

WEXTOR: a Web-based tool for generating and visualizing experimental designs and procedures.

WEXTOR is a Javascript-based experiment generator and teaching tool on the World-Wide Web that can be used to design laboratory and Web experiments in guided step-by-step process. It dynamically creates the customized Web pages and Javascripts needed for the experimental procedure and provides experimenters with a print-ready visual display of their experimental design. WEXTOR flexibly supports complete and incomplete factorial designs with between-subjects, within-subjects, and quasi-experimental factors, as well as mixed designs. The software implements client-side response time measurement and contains a content wizard for creating interactive materials, as well as dependent measures (graphical scales, multiple-choice items, etc.), on the experiment pages. However, it does not aim to replace a full-fledged HTML editor. Several methodological features specifically needed in Web experimental design have been implemented in the Web-based tool and are described in this paper. WEXTOR is platform independent. The created Web pages can be uploaded to any type of Web server in which data may be recorded in logfiles or via a database. The current version of WEXTOR is freely available for educational and noncommercial purposes. Its Web address is http://www.genpsylab.unizh.ch/wextor/index.html.

Setting up a strain-testing design for the seabass, Dicentrarchus labrax: a simulation study

The seabass, Dicentrarchus labrax L., is a leading species in European marine aquaculture, but its genetic characteristics necessary to set up breeding programmes are still unknown. New tools, such as genomic markers, now allow to carry out strain testings and estimations of genetic parameters in reasonable scale experimental facilities. However, because of the high cost of genotyping, the total number of fish to be measured will be limited and mating designs (type of cross, number of sires and dams) must be optimised. An optimisation trial is done in this study by simulation of a quantitative trait for two different strains of fish according to a polygenic model with additive, dominance, maternal and residual effects. The phenotypic coefficient of variation and the difference between crosses means ( D=10%) were also included in the model. For technical limitations due to the species, the mating design chosen was a factorial cross between sires of both strains with dams from one strain (topcross). Different combinations of size of progeny sample (500–4000), number of sires (10–120/strain) and dams (4–16) were studied. Various mixed models (SAS®, proc Mixed, option REML) were used to estimate D, the power for detecting D, heritability ( h 2) and their standard error (S.E.) over 1000 repetitions. Incomplete factorials were also tested as well as the effect of differential survival between dam families. In strictly additive models (no dominance or maternal effects), D and h 2 estimates were unbiased. The number of dams did not noticeably affect the precision of estimates, whatever the number of sires. A joint optimisation of sample size and number of sires led to a consensus value of 40 sires/strain with a sample size of 2000 progenies, which gave good precisions for D and h 2. It was also shown that a mixed model (fixed strain effect+random sire effect) gave more accurate results than a simple fixed model (strain effect only). The inclusion of maternal and dominance effects did not markedly bias nor affect the precision of D and h 2 estimates in a full factorial design, but could lower the precision (up to 40% increase S.E.) in incomplete factorial design. Variance in dam family sizes (due to differential survivals) did not affect the results in full factorials when set at values observed in seabass. It is then concluded that a factorial cross of 40 sires/strain with 8 dams and a sample size of 2000 progenies (on average 1000/strain) is appropriate for comparing seabass strains (power >0.8 for detecting a 20% difference between strains means) and jointly estimating heritability.

Etray: a program for efficient design and recording of crystallization trials

Determination of conditions suitable for crystallizing macromolecules often involves many iterative trials. The current standard procedure of manual design of experiments (including manual calculation of volumes of reagents) and recording observations by hand, is tedious, susceptible to errors, makes organization of records and searches for patterns difficult, and is not suited to automation. We have therefore written Etray, an open-source program that is freely obtainable over the Web, Elkin, C., Hogle, J., http://sbweb.med.harvard.edu/∼hogle/etray (2000), to automate record keeping, most aspects of experimental planning, and to facilitate computational analyses of these results. Etray displays an image of a standard 24 well crystal tray and allows the user to add reagents in appropriate concentrations to the wells, either individually or using tools for grid searches and incomplete factorial design. Etray automatically calculates volumes of stock solutions necessary to achieve the specified concentration, and contains tools for sketching, commenting and scoring the well contents. Speech recognition features allow the observations to be spoken out loud while the investigator looks into the microscope. An example of the use of Etray to design and analyze an incomplete factorial crystallization experiment is presented.

503 Effect of Source and Timing of Potassium Fertilizer on `Empire' Apple Tree Growth, Yield, and Fruit Quality

A field experiment was established in 1993 in a 3-year-old `Empire'/M.9 apple orchard. An incomplete factorial treatment design compared nitrogen only fertilization with nitrogen plus potassium fertilizer applied either on the ground with and without trickle irrigation or through the trickle irrigation system. Timing of potassium fertigation treatments compared season-long K fertigation to early season or late-season K fertigation. Results of main effects showed that K fertilization reduced trunk cross-sectional area increase, but increased yield, fruit size, and fruit red color. There was no benefit of fertigation compared to ground application of fertilizers plus trickle irrigation. There was no effect of source of K fertilizer (KCl vs KNO3) on tree growth, yield, fruit size, or color. Time of K fertigation showed that late-season K fertigation resulted in greater trunk cross-sectional area increase compared to early season fertigation or season-long fertigation. Fruit size was greatest when K fertigation was done in the early season. There was no effect of time of fertigation on yield or fruit red color. Potassium fertilization increased leaf K levels and reduced leaf Mg levels. Time of fertigation did not affect leaf K levels, but early season fertigation resulted in higher leaf N levels.

Effects of selected process parameters in extrusion of yam flour (Dioscorea rotundata) on physicochemical properties of the extrudates.

Raw yam (Dioscorea rotundata) flour was cooked and extruded in a Brabender single-screw laboratory scale extruder. Response surface methodology using an incomplete factorial design was applied with various combinations of barrel temperature [100, 125, 150 degrees C], feed moisture content [18, 22, 26%] and screw speed [100, 150, 200 rpm]. Initial viscosity at 30 degrees C, water solubility index, expansion and hardness were determined. The highest values of initial viscosity were at the highest barrel temperatures and the highest moisture contents. At high feed moisture content and high barrel temperatures the yam extrudate flour showed the greatest values of water solubility index. The physical properties of the extruded product showed that at high temperature the lower the moisture content the greater the expansion index. Hardness was influenced directly by moisture content and inversely by extrusion temperature. The extrusion of yam flour led to the production of snacks and pre-gelatinized flours of diverse properties. Also extruded yam flour can be successfully used in the preparation of 'futu' (pre-cooked compact dough), a yam-based food, popular in Western Africa.

Effects of dietary carnitine and lipid on growth and body composition of hybrid striped bass (Morone chrysops × M. saxatilis).

A study was undertaken to investigate the effects of graded dietary levels and different types of carnitine on hybrid striped bass (Morone chrysops ♀ × M. saxatilis ♂ %) fed different levels of lipid. An incomplete factorial design was utilized in which diets containing lipid at either 5 or 10% were supplemented with l-carnitine at 0, 500, or 1000 mg kg−1 diet, dl-carnitine at 1000 mg kg−1 diet, or carnitine chloride to provide 1000 mg carnitine kg−1 diet. Juvenile hybrid striped bass (3.3 g fish−1) were stocked into individual 38-l aquaria connected as a brackish water (6‰), recirculating system and fed each diet in triplicate for 9 weeks.

Effect of Dietary Carbohydrate on Growth, Glucose Tolerance, and Liver Composition of Juvenile Striped Bass

Abstract Dietary carbohydrate utilization by juvenile striped bass was evaluated in two studies. An incomplete factorial design was employed to determine the effect of carbohydrate complexity and dietary level on glucose tolerance. Five diets were formulated to contain 0, 12.5, or 25% of glucose or cornstarch, respectively. After 4 weeks, fish were fasted and administered an oral glucose challenge of 167 mg glucose/100 g body weight. Blood samples were collected at 0, 1, 2, 3, 4, 5, and 6 h after administration. Fasting plasma glucose concentrations (7.2 ± 0.8 mM/L) were similar among all treatments. Plasma glucose concentrations peaked higher at 4 and 5 h after administration in fish fed diets containing 25% glucose (23.9 ± 3.6 and 23.3 ± 3.2 mM/L, respectively) and 25% cornstarch (26.1 ± 2.0 and 23.9 ± 4.0 mM/L, respectively) when compared with plasma values for fish fed 0 and 12.5% carbohydrate (P < 0.05). There was neither a significant effect of carbohydrate type nor a significant interaction between...

Environmental factors controlling NO 3− leaching, N 2O emissions and numbers of NH 4+ oxidisers in a coniferous forest soil

Main and interactive effects of temperature, throughfall volume and NH 4 + deposition on soil solution NO 3 − concentrations, N 2O emissions and numbers of NH 4 + oxidisers were investigated in a controlled laboratory experiment. Large intact soil cores from a Picea abies (L.) Karst. stand were incubated according to an `incomplete factorial design' at 4, 12 or 20°C and watered every 2 weeks with 300, 500 or 700 ml (442, 737 and 1032 mm yr −1) of a natural throughfall solution enriched with 0, 37.5 or 75 kg NH 4 +–N ha −1 yr −1. Watering and sampling were performed every 2 weeks, during a 112 d period. At d 112, a temperature optimum for NO 3 −–N concentrations in the leachate, NO 3 −–N fluxes and numbers of NH 4 + oxidisers in the mineral soil layer was determined at ca. 11°C. NO 3 −–N concentrations also decreased with throughfall volume, towards a minimum at 590 ml, with temperature however contributing most to modelling NO 3 −–N concentrations and the two factors acting independently. The model explained 59% of the variability in the data, and the regression between observed and predicted concentrations was highly significant ( P<0.0001, r 2=0.93). NO 3 −–N fluxes increased quadratically with throughfall volume, and throughfall volume and NH 4 + deposition interacted significantly in determining the numbers of NH 4 + oxidisers in the mineral soil layer. Numbers of NH 4 + oxidisers were higher in the humus layer and decreased with increasing temperatures. N 2O fluxes increased quadratically with temperature, and the linear and quadratic effects of throughfall volume (maximum at 500 ml). Results suggest that optimum temperatures for net nitrification may have been overestimated in previous studies by the use of disturbed soils.

Response of juvenile red drum (Sciaenops ocellatus) to practical diets supplemented with medium chain triglycerides.

Medium chain triglycerides (MCT), mostly C6–C12, are physiologically active compounds which are readily absorbed, transported and appear to be preferentially utilized as an energy source but are not deposited in lipid stores in a variety of terrestrial animals. Consequently, the incorporation of MCT in feeds may allow the utilization of higher levels of lipids, possibly increasing protein sparing, without affecting the proximate composition of the fish. To evaluate the response of red drum to varying levels of menhaden fish oil (MFO) and MCT's supplements, two growth trials were conducted utilizing a basal diet containing 44% protein and 5.7% lipid. The first growth trial utilized an incomplete factorial design to evaluate the general response of red drum to MCT's and MFO. The final weights and feed utilization of the fish was significantly affected by lipid source and level of supplementation as well as their interaction. In general, final weights of the fish and feed utilization were significantly higher for fish receiving diets supplemented with 0,4 or 8% MFO and lowest in fish offered the basal diets supplemented with 4% MCT. The performance of fish receiving diets supplemented with 8% MCT or a combination of 4% MFO and 4% MCT was intermediate. In the second experiment, low levels of MCT (0–4%) were evaluated in conjunction with low (3%) and high (8%) lipid supplement to the basal diet. Although, not significantly different from the high lipid basal diet, the largest fish and best feed utilization were found in fish offered the high lipid diet containing 1% MCT. However, as the level of MCT supplement was increased performance of the fish in terms of growth and feed utilization was reduced. Increasing the levels of MCT in the diet resulted in a reduction of intraperitoneal fat deposition. The fatty acid profiles of the intraperitoneal fat as well as the polar and neutral lipid fractions from the liver were determined. In general lipid content of the selected tissues reflected the FA profile of the diet. Based on FA profiles of the intraperitoneal fat, it appears that MCT are incorporated into fat stores of red drum. Based on the observed results, the response of red drum to MCT appear similar to other vertebrates but that MCT are incorporated into lipid stores. The incorporation of MCT in diets appears to be a suitable mechanism to reduce excessive lipid deposition in fish; however, with the exception of high lipid diet supplements may result in poor performance of the fish.

Phosphorus and potassium soil test and nitrogen leaf analysis as a base for citrus fertilization

A network of six NPK long-term field trials was carried out on different soils of citrus-producing regions of Sao Paulo state, Brazil, in order to estimate quantitative relations of fruit yield to NPK fertilization and to determine parameters for fertilizer recommendation based on soil testing and leaf analysis. The experiments were set up in an incomplete factorial design 1/2 43 with 32 treatments, with four yearly rates of N (30, 100, 170 and 240 kg N/ha), P (9, 27, 45 and 63 kg P/ha) and K (25, 91, 157 and 223 kg K/ha). Four to seven harvests were recorded for the six experiments. Response surfaces of the type y = bo + b1N + b11N2 + b2P + b22P2 + b3K + b33K2 + b12NP + b13NK + b23PK were adjusted to the average yields of each trial. Correlation were established for yield increases, expressed as relative yields, and results of soil analysis of P and K, and leaf analysis of N. Soil samples taken at 0-20 cm depth in the beginning of each experiment were analyzed for resin extractable P and exchangeable K using an ion-exchange resin procedure. Yield responses for phosphorus and potassium applications were observed respectively in soils with less than 20 mg dm-3 of P and 20 mmolc dm-3 of K+. Yield responses to nitrogen were related to the total content of nitrogen in leaves, being largest for N values of 23 g kg-1 and smallest for N of 28 kg-1. With these field information, a practical approach for fertilizer recommendation for citrus, based on soil analysis for P and K and leaf analysis for N, was developed.

Efeito do tempo de incubação de termofosfato magnesiano no solo e inoculação com fungos micorrízicos na recuperação de fósforo pelo capim-pensacola

Com os objetivos de avaliar os efeitos da incubação no solo de termofosfato magnesiano de granulometria grosseira por períodos de tempo antecedentes a semeadura na disponibilidade de fósforo para o capim pensacola (Paspaium notatum Flugge var. saurae) e avaliar o efeito de fungos micorrízicos arbusculares (fMA) nativos na recuperação do fósforo deste fertilizante, foi conduzido o experimento em casa de vegetação da Universidade Federal de Santa Maria no Centro de Ciências Rurais. O experimento foi conduzido num delineamento inteiramente casualizado com quatro repetições e os tratamentos formaram fatorial incom pleto 3X2X2 + 8: três tempos de incubação do termofosfato de antecedência a semeadura (0, 100 e 200 dias); dois valores de pH (4,8 e calagem para 6,0); e com e sem inoculação de fMA. Mais tratamentos testemunha sem a adição de fósforo e com adição de superfosfato triplo, ambos com e sem inoculação e/ou calagem. A dose de fósforo usada foi de l00mg kg-1 P2O5. Verificou-se que a antecipação da aplicação do termofosfato à semeadura do capim pensacola quando incrementa a sua solubitização no solo não aumenta substancialmente a disponibilidade de fósforo comparado ao superfosfato e, a inoculação com fMA nativos no capim pensacola aumentou a produção de massa seca e a absorção de fósforo somente nas condições em que a planta estava sob estresse nutricional, apesar da baixa colonização micorrizica.

The influence of system of production on the performance and meat quality of entire, castrated and female lambs

The purpose of this experiment was to quantify the seasonal variations in lamb meat quality and identify the contributory factors associated with the various production systems used in the UK. The approach taken was therefore largely a systems one, with the various production systems used in the project mimicking those typical of the British sheep industry supplying lambs onto the market from April to January.Material and methods 504 spring-born lambs [equal numbers of entire male (E), castrated male (C) and female (F)] which were the twin-reared progeny of Mule ewes (Bluefaced Leicester x Swaledale) and Suffolk rams were allocated to one of 7 finishing systems (n=72 per system). These were combinations of 4 diets and 4 slaughter periods (at 2 monthly intervals between June 1992 and January 1993) in an incomplete factorial design: concentrates (CS1), grass (GRI, GR2), silage (SL2, SL3) and roots (RT3, RT4); all but the grass diet were fed indoors.

The influence of system of production on the performance and meat quality of entire, castrated and female lambs

The purpose of this experiment was to quantify the seasonal variations in lamb meat quality and identify the contributory factors associated with the various production systems used in the UK. The approach taken was therefore largely a systems one, with the various production systems used in the project mimicking those typical of the British sheep industry supplying lambs onto the market from April to January.Material and methods 504 spring-born lambs [equal numbers of entire male (E), castrated male (C) and female (F)] which were the twin-reared progeny of Mule ewes (Bluefaced Leicester x Swaledale) and Suffolk rams were allocated to one of 7 finishing systems (n=72 per system). These were combinations of 4 diets and 4 slaughter periods (at 2 monthly intervals between June 1992 and January 1993) in an incomplete factorial design: concentrates (CS1), grass (GRI, GR2), silage (SL2, SL3) and roots (RT3, RT4); all but the grass diet were fed indoors.

GLOBAL TESTS FOR COMBINATION DRUG STUDIES IN FACTORIAL TRIALS

To test the hypothesis that there are some studied dose combinations more effective in treating a disease than their respective component doses of two drugs, Hung, Chi and Lipicky proposed two alpha-level tests for normally distributed data. This paper extends the utilities of these tests to the outcome variable that has variance as a function of its mean, such as with a binomially distributed outcome, and to incomplete factorial design settings where some cells are not studied. I explore the impacts of excluding cells from study on the power performances of these tests.

Preliminary characterization of EcoRI-DNA co-crystals: incomplete factorial design of oligonucleotide sequences.

A full understanding of the sequence specificity of EcoRI endonuclease requires structural information on complexes where the DNA contains one 'incorrect' base pair; historically, these sites are referred to as EcoRI* sites. They are inherently asymmetric, unlike the canonical EcoRI site, GAATTC, which possesses a twofold axis of rotational symmetry. All previously determined DNA-EcoRI complexes incorporated this symmetry axis into the space group, requiring the design of 'new' oligonucleotides to produce an asymmetric unit appropriate to an EcoRI* complex. The incomplete factorial approach of Carter & Carter [Carter & Carter (1979). J. Biol. Chem. 254, 12219-12223.] was used to design the DNA sequence. Factors included the location and type of EcoRI* substitution and the length and AT richness of the sequences on both sides of the RI site. Co-crystals were obtained with several sequences, including one with TCGTGGACTTCGTG. Diffraction data were collected from one crystal of this complex to 3.2 A resolution; the unit-cell parameters are a = b = 123.8 and c = 148.9 A and the space group is P3(2)21. Unit-cell and space-group information was also obtained for the EcoRI* sites AAATTC, GGATTC and GAGTTC. These experiments demonstrated the need for a rapid, economical method that would distinguish DNA-protein co-crystals from crystals of protein only. This can be readily achieved with a single small crystal and a staining method based on methylene blue and methyl violet, which stain DNA and protein, respectively.

Nutrient management in a Pinusradiata plantation after thinning: the effect of nitrogen fertilizer on soil nitrogen fluxes and tree growth

The influence of N fertilizer on soil mineral N fluxes, canopy development, and tree growth was studied in a thinned 11-year-old Pinusradiata D. Don plantation. Ammonium sulphate and single superphosphate were applied in an incomplete factorial design, but only the main effects of N application at 0 (control) or 200 kg N•ha−1 are considered here. Spring application of fertilizer increased the quantity of mineral N in the forest floor plus surface soil (0–0.30 m) from 1.2 to 194 kg•ha−1. Within 51 weeks this had fallen to 8.3 kg•ha−1, and after 89 weeks had returned to prefertilizer levels. In the unfertilized soil, rates of net mineralization were low with little seasonal variation. Nitrogen fertilizer increased N mineralization; over the 2 years of measurement fertilized and unfertilized soils mineralized 155 and 77 kg N•ha−1, respectively. There was no net immobilization of fertilizer N. There was no leaching of mineral N from the unfertilized soil whereas 149 kg N•ha−1 was leached below 0.30 m during the 2 years after fertilizer application. Nitrogen uptake increased from 71 kg•ha−1 in the control to 203 kg•ha−1 in the fertilized treatment. Fifty-one percent (103 kg•ha−1) of N uptake by trees in the fertilized treatment occurred within 20 weeks of fertilizer application. Fertilized trees took up 58% of the available N (N added as fertilizer plus N mineralized), while 42% was leached. Ammonium dominated the soil mineral N pool and mineral N fluxes, with nitrate generally accounting for less than 10% of mineral N in both fertilized and unfertilized soils. Leaching of mineral N from the fertilized soil (Nleach, kg•ha−1•week−1) was highly correlated (r2 = 0.92) with soil mineral N content (Nstart, kg•ha−1) and effective rainfall (rainfall minus evaporation, Reff, mm•week−1) according to the relationship Nleach = aNstart + bReff, while N uptake (kg•ha−1•week−1) was highly correlated (r2 = 0.91) with soil mineral N content and N mineralization (Nmin, kg•ha−1•week−1) according to the relationship Nuptake = aNstart + bNmin. Fertilizer increased needle N concentrations and content by 52 and 87%, respectively, after 58 weeks, and resulted in a 17% increase in leaf area index after 71 weeks. These differences were reflected by an increase in basal area increment of 23% during the 2 years since fertilizer application. The rapid uptake of N fertilizer was associated with storage in existing biomass. Uptake of fertilizer N should, therefore, increase with plantation biomass. Consequently, it should be possible to increase the uptake of N fertilizer, and minimize leaching, by applying fertilizer before, rather than after, thinning. Such a strategy may be particularly appropriate for soils that have a low capacity to retain applied N.

Reciprocal differences for forage traits in single and three‐way crosses of maize

Eleven flint inbreds of maize were crossed with 11 dent inbreds according to a balanced incomplete factorial mating design to produce 66 single crosses (2W) in both reciprocal forms. Additionally, six three‐way crosses (3W) were also produced in both reciprocal forms. These hybrids were evaluated for 11 forage yield and quality traits in 1983 and 1984 at three sites in Germany. Highly significant reciprocal differences were observed for nine traits in the 2W. The respective variance component estimates amounted to 2–33% of the variance component due to crosses. On average, flint × dent 2W had lower dry‐matter content (DMC) than dent × flint 2W and a 1 % greater dry‐matter yield (DMY) of forage. Three‐way crosses produced on singles exhibited greater DMC (3%) and DMY (5%) of the ear, metabolizable energy content (MEC) of stover (1%), and DMC and DMY of forage (2%) than their reciprocal forms produced on lines. Based on this study, because of their minor importance, routine testing for reciprocal differences among 2W hybrids is not recommended.

Entropy, likelihood and phase determination.

Entropy, likelihood and phase determination.

Identifying Which Sets of Parameters are Simultaneously Estimable in an Incomplete Factorial Design

Incomplete factorial designs are fractional or complete factorials with some cells missing. In clinical trials or laboratory experiments that use these designs, not all the main effects and interactions can be estimated. By inspecting the null space of the design matrix one may identify the sets of parameters that can be estimated. Some examples are presented.

Intercrop Performance of Pearl Millet, Amaranth, Cowpea, Soybean, and Guar in Response to Planting Pattern and Nitrogen Fertilization

AbstractIntercropping is a common practice in developing countries because it may produce higher total yields than monocropping. The objective of this study was to apply intercropping principles to alternative and traditional crops in the USA under mechanized conditions. Although these crops have been examined in intercropping systems, in most cases studies were not conducted with improved varieties found in the USA or in strip widths that can accommodate machinery. A field study was conducted at two central Missouri locations in 1991 and 1992 to determine the effect of intercropping on grain yields of pearl millet [Pennisetum glaucum (L.) R. Br.], amaranth (Amaranthus hypochondriacus L. × A. hybridus L.), cowpea [Vigna unguiculata (L.) Walp.], guar [Cyamopsis tetragonoloba (L.) Taub.], and soybean [Glycine max (L.) Merrill]. Treatments were assigned in an incomplete factorial design and consisted of planting pattern (monocrops, narrow and wide row strips, and alternate row intercrops), N fertilizer (0, 56, or 112 kg N ha−1), and component crop combination. Each intercrop consisted of a legume (cowpea, soybean, or guar) and a nonlegume (pearl millet or amaranth). In the strip intercrops, only cowpea showed a consistent yield response to planting pattern, with the narrow strip arrangement with amaranth yielding 53 and 39% lower than its monocrop in two environments. Land equivalent ratios of amaranth and pearl millet grown in alternate rows with cowpea were not significantly different from their monocrops. At the Columbia site, yields of alternate row intercrops generally did not increase upon addition of N and in 1992, amaranth yield at 0 kg N ha−1 was 25% higher in the alternate row intercrop than it was at the same N rate in the monocrop. In general, grain yields were similar in the various intercrops compared with monocrops.