Experimental Unit Size Research Articles

185 Opportunities and Challenges of Conducting Grazing Experiments in Pasturelands

Abstract Grasslands cover approximately 30% of the world area and research conducted in pasturelands has been crucial to realize the benefits of grassland contributions to livestock production and ecosystem services. The Forage and Grazing Terminology Task Force has developed a list of recommended nomenclature for grazing lands research and this effort has been a landmark to avoid misleading terms in research reports. Other challenges remain. The intrinsic variability of pastureland research data limits the capacity of researchers to detect differences among treatments. In addition, the quantity of resources and labor required by pastureland experiments may lead researchers to decrease the size of experimental units and/or number of replicates, exacerbating the limitations in detecting differences among treatments. In general, experimental units in grazing studies encompass relatively large areas, which may pose a challenge to identifying representative sampling units that reflect the experimental area. The use of indirect measurements to estimate forage mass is a feasible approach to increase the representativeness of forage quantity evaluations. The nutritive value determination of forage samples from grazing studies also has many limitations. The collection of samples representing the animal diet and the methods of nutritive value determination, primarily digestibility, are major areas of concern. For animal performance evaluations, determination of the correct experimental unit has been a frequent issue. Among animal measures, forage intake is one of the most influential factors affecting animal performance and the existent methodology to estimate forage intake by grazing animals has limitations, reducing the accuracy of the results. Development and validation of mathematical models to estimate the benefits of grasslands on livestock performance and ecosystem services are important steps in the evolution of grassland science, but in some cases additional data are needed to support this effort.

Biomass Yield Evaluation for Switchgrass Breeding: Seeded Swards vs. Transplanted Plots Yield Different Results

Switchgrass (Panicum virgatum L.) is undergoing intensive development as a biomass crop to support the production of energy from perennial grasslands. Plant breeding and selection represent a significant component of this development effort, requiring breeders to evaluate large numbers of genotypes and families for performance under real-world field conditions. Experimental unit size, shape, and interplant spacing can vary widely both within and across breeding programs, and there is some evidence that experimental units established from seedling transplants are poorly predictive of biomass yield in seeded swards. The purpose of this study was to determine the relationships among five types of experimental units, three based on transplanted seedlings (spaced plants, row plots, and simulated sward plots) and two based on seeded rows (bordered and unbordered sward plots). Nine switchgrass populations were evaluated with or without nitrogen fertilizer under all five plot types. Simulated sward plots had the lowest predictive value for biomass yield of sward plots. Spaced plants and row plots had greater predictive ability than simulated swards, but they accounted for less than 50% of the variability, suggesting that biomass measurements on these types of plots should not be considered as the same trait measured on seeded sward plots, especially considering the fact that the conditions of interplant competition are drastically different between these groups of plot types. Whereas biomass yield on a per-hectare basis would be an appropriate trait name for seeded swards, plot-specific terms such as “plant biomass” or “row biomass” are more appropriate for biomass measured on spaced plant plots or row plots. These terms would clearly indicate that measurements on seeded plots where there is intensive interplant competition are not the same trait as those made on plants without competition.

Do Spatial Designs Outperform Classic Experimental Designs?

Controlling spatial variation in agricultural field trials is the most important step to compare treatments efficiently and accurately. Spatial variability can be controlled at the experimental design level with the assignment of treatments to experimental units and at the modeling level with the use of spatial corrections and other modeling strategies. The goal of this study was to compare the efficiency of methods used to control spatial variation in a wide range of scenarios using a simulation approach based on real wheat data. Specifically, classic and spatial experimental designs with and without a two-dimensional autoregressive spatial correction were evaluated in scenarios that include differing experimental unit sizes, experiment sizes, relationships among genotypes, genotype by environment interaction levels, and trait heritabilities. Fully replicated designs outperformed partially and unreplicated designs in terms of accuracy; the alpha-lattice incomplete block design was best in all scenarios of the medium-sized experiments. However, in terms of response to selection, partially replicated experiments that evaluate large population sizes were superior in most scenarios. The AR1 times AR1 spatial correction had little benefit in most scenarios except for the medium-sized experiments with the largest experimental unit size and low GE. Overall, the results from this study provide a guide to researchers designing and analyzing large field experiments.Supplementary materials accompanying this paper appear online.

Desarrollo de yogur tipo III con zapallo y ajonjolí como aporte de fibra y antioxidantes

La presente investigación se llevó a cabo en la Planta de Producción de Alimentos de la Facultad de Ciencias Pecuarias de la ESPOCH, se desarrolló un yogur tipo III con zapallo y tres diferentes niveles (3, 5 y 7%) de ajonjolí, frente a un tratamiento control (0% de ajonjolí), distribuidas bajo un diseño completamente al azar, con cuatro repeticiones por tratamiento y un tamaño de unidad experimental de un litro de yogur, fueron sometidas a los siguientes análisis estadísticos: Análisis de Varianza (ADEVA), separación de medias por Tukey (P < 0,05), análisis de la regresión y correlación y análisis sensorial con la escala hedónica afectiva. Determinándose que las propiedades físico químicas se vieron afectadas estadísticamente presentando un pH de 4.32 y 4.47 para 0 y 7% niveles de ajonjolí respectivamente; el contenido de materia seca de 19.35 y 23.93% (0 y 7% de ajonjolí), Proteína de 2.60 y 3.30 (0 y 5% de ajonjolí), Grasa de 0.54 y 3.18 (0 y 7% de ajonjolí), Capacidad antioxidante de 0.53% y 1.24% corresponde al nivel 0 y 7% de ajonjolí. Los análisis microbiológicos determinaron la ausencia de microorganismos patógenos. En relación a las características organolépticas estas se vieron influenciadas estadísticamente, el yogur elaborado con el 5% de ajonjolí presentó el mayor puntaje de 4/5 que da una calificación de me gusta en cuento a características de color, olor, sabor y textura; por lo tanto se recomienda utilizar el 5% de ajonjolí en la elaboración de yogur.

Influence of Tithonia Diversifolia on Maize (Zea mays L.) Yield, Fertility and Infiltration Status of Two Clay Varied Soils

Towards a more sustainable soil management through recycling of readily available weeds in Akure, Nigeria, different rates of Tithonia diversifolia (tithonia) were compared on a field trial to evaluate its effect on soil properties. The experiment was sited at two locations in South gate of the Federal University of Technology, Akure. Prior to the field establishment, a composite soil sample was collected and analyzed for physico-chemical properties. The sites were cleared and tilled. The experiment was laid out in a Randomized Complete Block Design (RCBD) with three replicates. The treatments consisted of three levels of tithonia application which are 0, 3 and 6 t ha-1. Each experimental unit size was 2 m x 2 m with 1 m alleyway. Maize (Zea mays L. var.TZB-SR) seeds were sown at a spacing of 75 cm by 25 cm and 10 were randomly sampled per plot for growth and yield parameters. Data were collected on maize yield and soil physical and chemical properties after harvest to ascertain sustainability of the mulch material after cropping. Application of tithonia mulch improved growth, and yield indices of maize as well as soil physical and chemical properties. The contents of soil total N, exchangeable cations, , CEC, Organic matter content, total porosity, moisture content and infiltration rate were found to significantly (p>0.05) increase in treatments with tithonia mulch. The best result was from the application rate 6 tha-1 because it improved and left the soil conserved after harvesting maize. Similar trends were observed at the two sites despite variation in inherent soil properties.

Optimum Size and Shape of Experimental Units for Cassava Cropping

In agricultural experimentation, the right size and shape of experimental units increase the precision of the experiment. This study determines the optimum size and shape of the experimental unit for field experimentation with cassava. For this, we carried out a uniformity test in Pacajús, Ceará, under dry conditions, with the cultivar 'Mastruço' planted at a spacing of 1.00 m x 0.60 m. The root yields were collected in 15 rows with 40 plants each, comprising 31 types of experimental units of 23 different pre-established sizes. The optimum size of the experimental unit was estimated by the Hatheway method, and the shape was determined by the relative information method. The Hatheway method indicated several optimum sizes of experimental units, many of which were applicable for evaluation experiments of cassava cultivars. The 15 x 1 rectangular experimental unit (15 rows with one plant and 9.00 m² of useful area) was considered the ideal shape for assessment of cassava production, which was smaller than the size suggested in surveys with of cassava cropping. There was a continuous nonlinear reduction of the coefficient of variation with the increase in plot size.

Variability, plot size and border effect in lettuce trials in protected environment

ABSTRACT The variability within rows of cultivation may reduce the accuracy of experiments conducted in a complete randomized block design if the rows are considered as blocks, however, little is known about this variability in protected environments. Thus, our aim was to study the variability of the fresh mass in lettuce shoot, growing in protected environment, and to verify the border effect and size of the experimental unit in minimizing the productive variability. Data from two uniformity trials carried out in a greenhouse in autumn and spring growing seasons were used. In the statistical analyses, it was considered the existence of parallel cultivation rows the lateral openings of the greenhouse and of columns perpendicular to these openings. Different scenarios were simulated by excluding rows and columns to generate several borders arrangements and also to use different sizes of the experimental unit. For each scenario, homogeneity test of variances between remaining rows and columns was performed, and it was calculated the variance and coefficient of variation. There is variability among rows in trials with lettuce in plastic greenhouses and the border use does not bring benefits in terms of reduction of the coefficient of variation or minimizing the cases of heterogeneous variances among rows. In experiments with lettuce in a plastic greenhouse, the use of an experimental unit size greater than or equal to two plants provides homogeneity of variances among rows and columns and, therefore, allows the use of a completely randomized design.

Variance components for two-way nested design data

This paper discusses the use of projections for the sums of squares in the analyses of variance for two-way nested design data. The model for this data is assumed to only have random effects. Two different sizes of experimental units are required for a given experimental situation, since nesting is assumed to occur both in the treatment structure and in the design structure. So, variance components are coming from the sources of random effects of treatment factors and error terms in different sizes of experimental units. The model for this type of experimental situation is a random effects model with more than one error terms and therefore estimation of variance components are concerned. A projection method is used for the calculation of sums of squares due to random components. Squared distances of projections instead of using the usual reductions in sums of squares that show how to use projections to estimate the variance components associated with the random components in the assumed model. Expectations of quadratic forms are obtained by the Hartley’s synthesis as a means of calculation.

English

The influence of the basic experimental unit size on the plot size estimation determined by the method of maximum curvature of the coefficient of variation model is unknown in sunn hemp. This study aimed to verify the influence of the basic experimental unit (BEU) size in the estimate of the optimum plot size obtained by the method of maximum curvature of the coefficient of variation model for the evaluation of fresh matter of sunn hemp (Crotalaria juncea L.). Fresh matter of sunn hemp at the flowering was evaluated in uniformity trials in two sowing dates. In each sowing date, 4,608 BEU of 0.5 × 0.5 m (0.25 m2) were evaluated and 64 BEU plans were formed with sizes from 0.25 to 64 m2. In each evaluation period for each BEU plan, the first order spatial autocorrelation coefficient, variance, standard deviation, mean, coefficient of variation of the trial and the plot size were determined with the fresh matter data. For each BEU plan, the optimum plot size was determined by the method of maximum curvature of the coefficient of variation model. The estimate of optimum plot size depends on the basic experimental unit size. Determining the plot size to assess the fresh matter in basic experimental units as small as possible is recommended in order to prevent overestimation of the plot size and to contemplate all existing variability. Key words: Crotalaria juncea L., experimental design, basic experimental unit.

Comparison of Satellite Imagery and Ground‐Based Active Optical Sensors as Yield Predictors in Sugar Beet, Spring Wheat, Corn, and Sunflower

Core Ideas Satellite imagery could be used to predict yield the study crops. Satellite imagery could be used to screen fields for in‐season N application. Obtaining satellite imagery early enough in the season to screen fields for in‐season N is a problem. Algorithms using active‐optical (AO) sensors have been developed to direct in‐season N application to crops. Many farmers in the United States have a large number of farm fields to manage. Farmers using AO technology must visit each field and operate the sensor across the entire field in order to conduct in‐season N application. A field might be driven over with an on‐the‐go N fertilizer applicator, but the application might not be required. The objective of this study was to determine whether satellite imagery might be used to predict yield in sugar beet, spring wheat, corn and sunflower similar to the yield prediction possible using AO sensors. If so, the algorithms produced could be used to select fields that would benefit from in‐season N application. Two N‐rate studies in sugar beet, spring wheat, corn and sunflower, were conducted with experimental unit size of 9 by 9 m large enough to fit a satellite pixel of 5 by 5 m size within each unit. The AO sensor and satellite imagery data were related to yield of sugar beet, spring wheat, corn and sunflower in some site‐years. The problem is the ability to acquire the satellite imagery early enough in the season to be useful as a screening tool. These results indicate that even though satellite imagery could be used as a field screening tool, a better option may be to mount an AO sensor on a farm implement for an early season activity, or to explore the use of unmanned aerial vehicles (UAVs).

Effects of experimental warming on biodiversity depend on ecosystem type and local species composition

Climatic warming is a primary driver of change in ecosystems worldwide. Here, we synthesize responses of species richness and evenness from 187 experimental warming studies in a quantitative meta‐analysis. We asked 1) whether effects of warming on diversity were detectable and consistent across terrestrial, freshwater and marine ecosystems, 2) if effects on diversity correlated with intensity, duration, and experimental unit size of temperature change manipulations, and 3) whether these experimental effects on diversity interacted with ecosystem types. Using multilevel mixed linear models and model averaging, we also tested the relative importance of variables that described uncontrolled environmental variation and attributes of experimental units. Overall, experimental warming reduced richness across ecosystems (mean log‐response ratio = –0.091, 95% bootstrapped CI: –0.13, –0.05) representing an 8.9% decline relative to ambient temperature treatments. Richness did not change in response to warming in freshwater systems, but was more strongly negative in terrestrial (–11.8%) and marine (–10.5%) experiments. In contrast, warming impacts on evenness were neutral overall and in aquatic systems, but weakly negative on land (7.6%). Intensity and duration of experimental warming did not explain variation in diversity responses, but negative effects on richness were stronger in smaller experimental units, particularly in marine systems. Model‐averaged parameter estimation confirmed these main effects while accounting for variation in latitude, ambient temperature at the sites of manipulations, venue (field versus lab), community trophic type, and whether experiments were open or closed to colonization. These analyses synthesize extensive experimental evidence showing declines in local richness with increased temperature, particularly in terrestrial and marine communities. However, the more variable effects of warming on evenness were better explained by the random effect of site identity, suggesting that effects on species’ relative abundances were contingent on local species composition.SynthesisA global research priority is to understand the consequences of climate change for biodiversity. A growing number of experimental studies have manipulated climatic drivers, in particular changes in temperature, in local communities. In the first quantitative meta‐analysis of community‐level studies across freshwater, marine and terrestrial experiments, species richness declined consistently with experimental warming. This effect was insensitive to warming intensity, duration, and multiple environmental and procedural covariates. However, evenness responses were weakly negative only in terrestrial systems and more variable across ecosystem types. Linear mixed model analyses revealed that the identity of local sites explained nearly 50% of variance in evenness effect sizes, compared to only 10% for richness. This result provides evidence that local species composition strongly constrains changes in relative species abundances in response to warming.

Synthesis Paper: Assessment of Research on Rangeland Fire as a Management Practice

Rangelands are fire-dependent ecosystems severely altered through direct fire suppression and fuels management. The removal of fire is a dominant cause of ecological sites moving across thresholds with the majority of North American rangelands currently showing moderate or high departure from reference conditions. Recognizing the need to restore fire on rangelands and incorporate prescribed fire into management plans, the Natural Resource Conservation Service initiated the Conservation Effects Assessment Project (CEAP) to evaluate the validity current practices through peer-reviewed scientific literature. We updated the CEAP review and broadened the discussion of prescribed fire as a global management practice. We reviewed and summarized prescribed fire literature available through Web of Science using search terms in the title. The majority of literature (40%) evaluated plant responses to fire with fire behavior and management (29%), wildlife and arthropods (12%), soils (11%), and air quality (4%) evaluated less frequently. Generally, fire effects on plants are neutral to positive and the majority of negative responses lasted less than 2 years. Similarly, soil responses were recovered within 2 yr after burning. However, most studies did not report how long treatments were in place (62%) or the size of experimental units (52%). The experimental literature supporting prescribed burning is in need of greater managerial relevance that can be obtained by directly addressing spatial scale, temporal scale, and interaction with other disturbances, including drought and grazing. Reliance on information from single fires applied on small plots tracked for a relatively short time interval greatly constrains inferences and application to ecosystem management and information should be applied with caution. Therefore, conservation purposes need to incorporate temporal dynamics to the extent that this information is available. The complex interaction of scientific knowledge, social concerns, and variable policies across regions are major limitations to the successful and critical restoration of fire regimes.

Tamanho de unidades experimentais básicas e tamanho ótimo de parcelas para nabo-forrageiro

Resumo: O objetivo deste trabalho foi verificar a influência do tamanho da unidade experimental básica (UEB) sobre a estimativa do tamanho ótimo de parcela para a avaliação da massa de matéria fresca de nabo-forrageiro (Raphanus sativus). Dados de massa de matéria fresca de 3.456 unidades experimentais básicas de 0,5×0,5 m (0,25 m2) foram utilizados, tendo-se formado 36 planos de UEBs com tamanhos entre 0,25 e 16 m2. Para cada plano de UEB, determinou-se o tamanho ótimo de parcela, pelo método da curvatura máxima do modelo do coeficiente de variação. A diferença mínima significativa pelo teste de Tukey foi calculada para 2.016 cenários, formados pelas combinações entre 36 tamanhos ótimos de parcela - um para cada plano de UEB -, i tratamentos (i = 5, 10, 15 e 20) e r repetições (r = 3, 4, 5, 6, 10, 15 e 20), tendo-se considerado tanto os delineamentos inteiramente casualizados como os de blocos ao acaso. O tamanho ótimo de parcela depende do tamanho da unidade experimental básica. Em ensaios de uniformidade com nabo-forrageiro, a avaliação da massa de matéria fresca deve ser feita em unidades experimentais básicas com o menor tamanho possível.

지분계획의 분산성분

본 논문은 요인들의 처리구조와 실험단위들의 설계구조에서 지분이 발생하는 경우의 지분계획모형에서 분산성분을 구하는 방법을 다루고 있다. 지분구조의 고정효과와 확률효과 그리고 실험단위들의 지분구조에 따른 오차성분을 포함하는 지분계획모형을 제안하고 있다. 모형내 확률효과의 분산성분과 다수의 오차항에 따른 분산성분을 추정하는 방법으로 상수적합법을 이용하고 있다. 상수적합법에 의한 제1종 제곱합의 계산은 모형의 단계별 적합에서 주어지는 모형행렬의 사영을 이용하고 구하고 있다. 사영을 이용한 변동요인별 제1종 제곱합의 기댓값 계산에 Hartley의 합성법이 이용된다. 단계별 방법에 의한 모형의 순차적 적합은 모형행렬로의 사영공간을 나타내는 사영행렬의 구조를 파악할 수 있는 이점이 있다. This paper discusses nested design models when nesting occurs in treatment structure and design structure. Some are fixed and others are random; subsequently, the fixed factors having a nested design structure are assumed to be nested in the random factors. The treatment structure can involve random and fixed effects as well as a design structure that can involve several sizes of experimental units. This shows how to use projections for sums of squares by fitting the model in a stepwise procedure. Expectations of sums of squares are obtained via synthesis. Variance components of the nested design model are estimated by the method of moments.

Tamanhos de unidades experimentais básicas e de parcelas em tremoço branco

RESUMO: O objetivo deste trabalho foi verificar a influência do tamanho da unidade experimental básica (UEB) na estimativa do tamanho ótimo de parcela, para a avaliação da massa de matéria verde de tremoço branco ( Lupinus albus L.). Avaliou-se a massa de matéria verde aos 123, 137 e 150 dias após a semeadura. Em cada época, foram avaliadas 432UEB de 1m×1m (1m2) e formaram-se 16 planos de UEB com tamanhos entre 1 e 16m2. Para cada plano de UEB, foi determinado o tamanho ótimo de parcela, pelo método da curvatura máxima do modelo do coeficiente de variação. Em cada época de avaliação, foi calculada a diferença mínima significativa pelo teste de Tukey, em 448 cenários formados pelas combinações de 16 tamanhos ótimos de parcela, i tratamentos (i=5, 10, 15 e 20) e r repetições (r=3, 4, 5, 6, 10, 15 e 20), para o delineamento blocos ao acaso. A estimativa do tamanho ótimo de parcela depende do tamanho da unidade experimental básica. É indicado avaliar a massa de matéria verde em UEB de menor tamanho possível, para serem usadas na estimação do tamanho ótimo de parcela.

Towards an integration of scale and complexity in marine ecology

Manipulative field experiments provide a window into the complexity of nature. Yet there is concern that we lack resolution by conducting experiments on a scale that is too small and short to include the relevant complexity of the study system. We addressed this issue by asking how and why the scale (local and global spatial extent, spatial grain, duration) and complexity (number of species, factors, treatment combinations) of experiments performed on marine hard substrata (rocky intertidal, RI; coral reef, CR; rocky subtidal, RS; mangrove root, MR) has changed by assessing 311 total experiments published since 1961 in Ecology and Ecological Monographs and since 1967 in Journal of Experimental Marine Biology and Ecology. We show that the local spatial extent and all metrics of complexity increased as a positive, log‐linear function of time. In contrast, the size of experimental units (spatial grain) decreased with time. Quantile regression analysis revealed that these trends are largely driven by changes in the upper bounds of experimental scale and complexity; most studies are still relatively simple in design and conducted over small areas. A structural equation model (SEM) incorporated the direct and indirect effects of six metrics indicating that the complexity of field experiments has increased both as a direct effect of time and because experiments have become smaller in spatial grain. The SEM also showed longer experiments tended to be more complex. We show striking habitat differences, as subtidal experiments (CR, RS) involved more species and were carried out on the largest global spatial scales. RI experiments were the longest.Future prospects to incorporate more of the complexity of nature into field experiments include site replication, as only 34.7% of all experiments were conducted at more than one site, open experimental designs monitored by technology, and integrating experimental manipulations with long‐term monitoring to achieve mechanistic insight across scales relevant to human alteration of the biosphere. The increasing resolution of remote sensing also creates opportunities to track experiment‐driven changes in community structure across large scales. We suggest applying these methods to a wider class of problems to enhance our understanding of marine communities and ecosystems.

Linseed (Linum usitatissimum L.) sowing dates, genotypes influence on growth, yield attributes and yield

The experiment was laid out in Split Plot Design with three replications, with eighteen treatment combinations of date of sowing D 1 - 7 th October (MW 40), D 2 - 14 th October (MW 41), D 3 - 20 th October (MW 42), D 4 - 25 th October (MW 43), D 5 - 30 th October (MW 44) and D 6 - 5 th November (MW 45) as main plot treatments, and three cultivars (V 1 - Kiran, V 2 - Garima and V 3 - RLC- 4) as sub plot treatments. The gross and net plot size of experimental unit was 6.4 m × 3.6 m and 5.4 m × 2.4 m, respectively with a row spacing of 30 cm and plant spacing as 10 cm. All recommended agronomical practices were adopted as per schedule. First date (D 1 ) and second date (D 2 ) crop sown in MW 40 and MW 41 recorded significantly higher leaf area index than other dates of sowing. The various growth characters like, plant height, spread of plant were higher in second (D 2 ) date than other dates of sowing. Mean number of branches per plant and dry matter accumulation was found significantly superior in first (D 1 ). D 1 which required less number of days for 50 per cent flowering and more days for maturity. The various yield attributing characters viz., number of capsules plant -1 , weight of capsules plant -1 , number of seeds capsule -1 , seed weight plant -1 and thousand seed weight were found higher in first date of sowing. D 1 recorded significantly higher seed yield, straw yield, biological yield and harvest index than other treatments. The various growth characters viz., number of branches plant -1 , spread of plant, total dry matter accumulation were substantially more in cv. GARIMAexcept plant height, which was recorded more in cv. RLC-4. Number of days required to 50 per cent flowering were also lesser in cv. GARIMA. The number of days required for physiological maturity were more in cv. KIRAN. Remarkably, the various yield attributes like mean number of capsule plant -1 , weight of capsules, mean number of seeds capsule -1 , seed weight plant -1 , weight of straw plant -1 and thousand seed weight were higher in cv. GARIMA over other cultivars. Among the cultivars, Garima recorded higher seed yield, straw yield, and biological yield as well at harvest index.

Fundamentals of Experimental Design: Guidelines for Designing Successful Experiments

We often think of experimental designs as analogous to recipes in a cookbook. We look for something that we like, something that satisfies our needs, and frequently return to those that have become our long‐standing favorites. We can easily become complacent, favoring the tried‐and‐true designs (or recipes) over those that contain unknown or untried ingredients or those that are too complex for our tastes and skills. Instead, I prefer to think of experimental designs as a creative series of decisions that are meant to solve one or more problems. These problems may be real or imagined—we may have direct evidence of a past or current problem or we may simply want insurance against future potential problems. The most significant manifestation of a “problem” or a “failed” design is unsatisfactory P values that prevent us from developing inferences about treatment differences. Four basic tenets or pillars of experimental design— replication, randomization, blocking, and size of experimental units— can be used creatively, intelligently, and consciously to solve both real and perceived problems in comparative experiments. Because research is expensive, both in terms of grant funds and the emotional costs invested in grant competition and administration, biological experiments should be designed under the mantra “failure is not an option.” Guidelines and advice provided in this review are designed to reduce the probability of failure for researchers who are willing to question, evaluate, and possibly modify their decision‐making processes.

Whole-Plot Exchange Algorithms for Constructing D-Optimal Multistratum Designs

Multistratum experiments contain several different sizes of experimental units. Examples include split-plot, strip-plot designs, and randomized block designs. We propose a strategy for constructing a D-optimal multistratum design by improving a randomly generated design through a sequence of whole-plot exchanges. This approach preserves the design structure and simplifies updates to the information and is applicable to any multistratum design where the largest-sized experimental unit is either a whole plot or a block. Two whole-plot exchange algorithms inspired by the point-exchange strategies of Fedorov (1972) and Wynn (1972) are described. The application of the algorithms to several design problems is discussed.

반복측정의 이가반응 자료에 대한 로짓 모형

This paper discusses model building for repeated binary response data with different time-dependent covariates each occasion. Since repeated measurements data are having correlated structure, weighed least squares(WLS) methodology is applied. Repeated measures designs are usually having different sizes of experimental units like split-plot designs. However repeated measures designs differ from split-plot designs in that the levels of one or more factors cannot be randomly assigned to one or more of the sizes of experimental units in the experiment. In this case, the levels of time cannot be assigned at random to the time intervals. Because of this nonrandom assignment, the errors corresponding to the respective experimental units may have a covariance matrix. So, the estimates of effects included in a suggested logit model are obtained by using covariance structures.